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Superconducting quantum computing is a branch of solid state quantum computing which implements
superconducting Superconductivity is a set of physical properties observed in certain materials where Electrical resistance and conductance, electrical resistance vanishes and magnetic field, magnetic flux fields are expelled from the material. Any material e ...
electronic circuit An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. It is a type of electrical ...
s using superconducting qubits as artificial atoms, or
quantum dot Quantum dots (QDs) are semiconductor particles a few nanometres in size, having light, optical and electronics, electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanote ...
s. For superconducting qubits, the two logic states are the
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
and the
excited state In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers to a ...
, denoted , g\rangle \text , e\ranglerespectively. Research in superconducting quantum computing is conducted by companies such as
Google Google LLC () is an American multinational technology company focusing on search engine technology, online advertising, cloud computing, computer software, quantum computing, e-commerce, artificial intelligence, and consumer electronics. ...
, IBM,
IMEC Interuniversity Microelectronics Centre (IMEC) is an international research & development organization, active in the fields of nanoelectronics and digital technologies, with headquarters in Belgium. Luc Van den hove has served as President an ...
,
BBN Technologies Raytheon BBN (originally Bolt Beranek and Newman Inc.) is an American research and development company, based next to Fresh Pond in Cambridge, Massachusetts, United States. In 1966, the Franklin Institute awarded the firm the Frank P. Brown ...
, Rigetti, and
Intel Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the developers of the x86 seri ...
. Many recently developed QPU's (
quantum processing unit Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
s, or quantum chips) utilize superconducting architecture. , up to 9 fully controllable
qubit In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...
s are demonstrated in the 1D
array An array is a systematic arrangement of similar objects, usually in rows and columns. Things called an array include: {{TOC right Music * In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...
, and up to 16 in 2D architecture. In October 2019, the Martinis group, partnered with
Google Google LLC () is an American multinational technology company focusing on search engine technology, online advertising, cloud computing, computer software, quantum computing, e-commerce, artificial intelligence, and consumer electronics. ...
, published an article demonstrating novel
quantum supremacy In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum device can solve a problem that no classical computer can solve in any feasible amount of time (irrespective of the usefulness of ...
, using a chip composed of 53 superconducting qubits. More than 2,000 superconducting qubits are in a commercial product by
D-Wave Systems D-Wave Systems Inc. is a Canadian quantum computing company, based in Burnaby, British Columbia, Canada. D-Wave was the world's first company to sell computers to exploit quantum effects in their operation. D-Wave's early customers include Loc ...
. However, these qubits implement
quantum annealing Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations. Quantum annealing is used mainl ...
as opposed to a
universal Universal is the adjective for universe. Universal may also refer to: Companies * NBCUniversal, a media and entertainment company ** Universal Animation Studios, an American Animation studio, and a subsidiary of NBCUniversal ** Universal TV, a ...
model of quantum computation.


Background

Classical
computation Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An es ...
models rely on physical implementations consistent with the laws of
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
. Classical descriptions are accurate only for specific systems consisting of a relatively large number of atoms. Amore general description of nature is given by
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
.
Quantum computation Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
studies quantum phenomena applications beyond the scope of classical approximation for the purpose of informing artificial intelligence processing and communication. Various models of quantum computation exist, but the most popular models incorporate concepts of
qubit In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...
s and
quantum gate In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, lik ...
s (or gate-based superconducting quantum computing). Superconductors are implemented due to the fact that at low temperatures they have almost infinite conductivity and almost zero resistance. Each qubit is built using semiconductor circuits with an LC circuit, a capacitor and an inductor. Capacitor and inductors are specifically used as they do not produce heat during super-conduction which can blemish quantum information. For superconducting quantum circuits we construct artificial atoms to resemble qubits. Theoretical and physical implementations of quantum circuits are widely different. Implementing a quantum circuit had its own set of challenges and must abide by DiVincenzo's criterium, conditions proposed by theoretical physicist David P DiVincenzo, which is list of criterium for the physical implementation of superconducting quantum computing, where the initial five criteria ensure that the quantum computer is in line with the postulates of quantum mechanics and the remaining two pertaining to the relaying of this information over a network. We map the ground and excited states of these atoms to the 0 and 1 state as these are discrete and distinct energy values and therefore it is in line with the postulates of quantum mechanics. In such a construction however an electron can jump to multiple other energy states and not be confined to our excited state therefore it is imperative that the system be limited to be affected only by particles of light with energy difference required to jump from the ground state to the excited state. However, this leaves one major issue, we require uneven spacing between our energy levels to prevent photons with the same energy causing transitions between neighboring pairs of states. This is where implementing the Josephson Junction becomes imperative. The use of this junction allows us to create the uneven space required in the energy levels of our superconducting circuit.


Qubits

A qubit is a generalization of a
bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
(a system with two possible states) capable of occupying a
quantum superposition Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum ...
of both states. A quantum gate, on the other hand, is a generalization of a
logic gate A logic gate is an idealized or physical device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, ...
describing the
transformation Transformation may refer to: Science and mathematics In biology and medicine * Metamorphosis, the biological process of changing physical form after birth or hatching * Malignant transformation, the process of cells becoming cancerous * Trans ...
of one or more qubits once a gate is applied given their initial state. Physical implementation of qubits and gates is challenging for the same reason that quantum phenomena are difficult to observe in everyday life given the minute scale on which they occur. One approach to achieving quantum computers is by implementing
superconductors Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
whereby quantum effects are macroscopically observable, though at the price of extremely low operation
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
s.


Superconductors

Unlike typical conductors, superconductors posses a
critical temperature Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in ...
at which resistivity plummet to nearly zero and conductivity is drastically increased. In superconductors, the basic charge carriers are pairs of
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s (known as
Cooper pairs In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
), rather than single
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
s as found in typical conductors. Cooper pairs are loosely bound and have an energy state lower than that of
Fermi Energy The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi ga ...
. Electrons forming Cooper pairs possess equal and opposite momentum and spin so that the total
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
of the Cooper pair is an
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
spin. Hence, Cooper pairs are
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
s. Two such superconductors which have been used in superconducting qubit models are
niobium Niobium is a chemical element with chemical symbol Nb (formerly columbium, Cb) and atomic number 41. It is a light grey, crystalline, and ductile transition metal. Pure niobium has a Mohs hardness rating similar to pure titanium, and it has sim ...
and
tantalum Tantalum is a chemical element with the symbol Ta and atomic number 73. Previously known as ''tantalium'', it is named after Tantalus, a villain in Greek mythology. Tantalum is a very hard, ductile, lustrous, blue-gray transition metal that is ...
, both d-band superconductors.


Bose-Einstein condensates

Once cooled to nearly
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
, a collection of bosons collapse into their lowest energy quantum state (the
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
) to form a state of matter known as
Bose–Einstein condensate In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67&n ...
. Unlike fermions, bosons may occupy the same quantum energy level (or
quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
) and do not obey the
Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated ...
. Classically, Bose-Einstein Condensate can be conceptualized as multiple particles occupying the same position in space and having equal
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
. Because interactive forces between bosons are minimized, Bose-Einstein Condensates effectively act as a superconductor. Thus, superconductors are implemented in quantum computing because they possess both near infinite
conductivity Conductivity may refer to: *Electrical conductivity, a measure of a material's ability to conduct an electric current **Conductivity (electrolytic), the electrical conductivity of an electrolyte in solution **Ionic conductivity (solid state), elec ...
and near zero resistance. The advantages of a superconductor over a typical conductor, then, are twofold in that superconductors can, in theory, transmit signals nearly instantaneously and run infinitely with no energy loss. The prospect of actualizing superconducting quantum computers becomes all the more promising considering
NASA The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeeding t ...
's recent development of the Cold Atom Lab in outer space where Bose-Einstein Condensates are more readily achieved and sustained (without rapid dissipation) for longer periods of time without the constraints of
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
.


Electrical circuits

At each point of a superconducting electronic circuit (a network of
electrical element Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be analyzed as multiple electrica ...
s), the condensate
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
describing
charge Charge or charged may refer to: Arts, entertainment, and media Films * '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqu ...
flow is well-defined by some
complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
probability amplitude In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The modulus squared of this quantity represents a probability density. Probability amplitudes provide a relationship between the quan ...
. In typical conductor electrical circuits, this same description is true for individual
charge carrier In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is used ...
s except that the various wave functions are averaged in macroscopic analysis, making it impossible to observe quantum effects. The condensate
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
becomes useful in allowing design and measurement of macroscopic quantum effects. Similar to the discrete atomic
energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The te ...
s in the
Bohr model In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar Syste ...
, only discrete numbers of magnetic flux quanta can penetrate a superconducting loop. In both cases, quantization results from complex
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...
continuity. Differing from microscopic implementations of quantum computers (such as
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s or
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s), parameters of superconducting circuits are designed by setting (classical) values to the electrical elements composing them such as by adjusting
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
or
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
. To obtain a quantum mechanical description of an electrical circuit, a few steps are required. Firstly, all electrical elements must be described by the condensate wave function amplitude and phase rather than by closely related macroscopic
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
and
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
descriptions used for classical circuits. For instance, the square of the wave function amplitude at any arbitrary point in space corresponds to the probability of finding a charge carrier there. Therefore the squared amplitude corresponds to a classical charge distribution. The second requirement to obtain a quantum mechanical description of an electrical circuit is that generalized
Kirchhoff's circuit laws Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhof ...
are applied at every node of the circuit network to obtain the system's
equations of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...
. Finally, these equations of motion must be reformulated to
Lagrangian mechanics In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Lou ...
such that a quantum Hamiltonian is derived describing the total energy of the system.


Technology


Manufacturing

Superconducting quantum computing devices are typically designed in the
radio-frequency spectrum Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upper ...
, cooled in
dilution refrigerator A 3He/4He dilution refrigerator is a cryogenics, cryogenic device that provides continuous cooling to temperatures as low as 2 Kelvin, mK, with no moving parts in the low-temperature region. The cooling power is provided by the heat o ...
s below 15mK (milli-Kelvin) and addressed with conventional electronic instruments, e.g.
frequency synthesizer A frequency synthesizer is an electronic circuit that generates a range of frequencies from a single reference frequency. Frequency synthesizers are used in many modern devices such as radio receivers, televisions, mobile telephones, radioteleph ...
s and
spectrum analyzer A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most co ...
s. Typical dimensions fall on the range of micrometers, with sub-micrometer resolution, allowing for the convenient design of a
Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...
system with well-established
integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny ...
technology. Manufacturing superconducting qubits follows a process involving
lithography Lithography () is a planographic method of printing originally based on the immiscibility of oil and water. The printing is from a stone (lithographic limestone) or a metal plate with a smooth surface. It was invented in 1796 by the German a ...
, depositing of metal,
etching Etching is traditionally the process of using strong acid or mordant to cut into the unprotected parts of a metal surface to create a design in intaglio (incised) in the metal. In modern manufacturing, other chemicals may be used on other types ...
, and controlled
oxidation Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a d ...
as described in. Manufacturers continue to improve the lifetime of superconducting qubits and have made significant improvements since the early 2000's as illustrated in the chart to the right.


Josephson junctions

One distinguishable attribute of superconducting quantum circuits is the use of
Josephson junction In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mec ...
s. Josephson junctions are an
electrical element Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be analyzed as multiple electrica ...
which does not existent in normal conductors. Recall that a
junction Junction may refer to: Arts and entertainment * ''Junction'' (film), a 2012 American film * Jjunction, a 2002 Indian film * Junction (album), a 1976 album by Andrew Cyrille * Junction (EP), by Basement Jaxx, 2002 * Junction (manga), or ''Hot ...
is a weak connection between two leads of wire (in this case a superconductive wire) on either side of a thin layer of insulator material only a few
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s thick, usually implemented using shadow evaporation technique. The resulting Josephson junction device exhibits the
Josephson Effect In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mech ...
whereby the junction produces a supercurrent. An image of a single Josephson junction is shown to the right. The condensate wave function on the two sides of the junction are weakly correlated, meaning that they are allowed to have different superconducting phases. This distinction of
nonlinearity In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
contrasts continuous superconducting wire for which the wave function across the junction must be
continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...
. Current flow through the junction occurs by
quantum tunneling In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...
, seeming to instantaneously "tunnel" from one side of the junction to the other. This tunneling phenomenon is unique to quantum systems. Thus, quantum tunneling is used to create nonlinear inductance, essential for qubit design as it allows a design of anharmonic oscillators for which energy levels are discretized (or quantized) with nonuniform spacing between energy levels, denoted \Delta E. In contrast, the
quantum harmonic oscillator 量子調和振動子 は、 古典調和振動子 の 量子力学 類似物です。任意の滑らかな ポテンシャル は通常、安定した 平衡点 の近くで 調和ポテンシャル として近似できるため、最 ...
''cannot'' be used as a qubit as there is no way to address only two of its states.


Qubit archetypes

The three primary superconducting qubit archetypes are the
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
,
charge Charge or charged may refer to: Arts, entertainment, and media Films * '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqu ...
and
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...
qubit In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, ...
. Many hybridizations of these archetypes exist including the Fluxonium,
transmon In quantum computing, and more specifically in superconducting quantum computing, a transmon is a type of superconducting charge qubit that was designed to have reduced sensitivity to charge noise. The transmon was developed by Robert J. Schoelko ...
, Xmon, and Quantronium. For any qubit implementation the logical
quantum states In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement in quantum mechanics, measurement on a system. Knowledge of the quantum state together with the rul ...
\ are mapped to different states of the physical system (typically to discrete
energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The te ...
s or their
quantum superposition Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum ...
s). Each of the three archetypes possess a distinct range of Josephson energy to charging energy ratio. Josephson energy refers to the energy stored in Josephson junctions when current passes through, and charging energy is the energy required for one Cooper pair to charge the junction's total capacitance. Josephson energy can be written U_j = - \frac cos \delta, where I_0 is the critical current parameter of the Josephson junction, \Phi_0 = \frac is (superconducting) flux quantum, and \delta is the
phase difference In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it v ...
across the junction. Notice that the term cos \delta indicates nonlinearity of the Josephson junction. Charge energy is written E_C = \frac, where C is the junction's capacitance and e is electron charge. Of the three archetypes, phase qubits allow the most of Cooper pairs to tunnel through the junction, followed by flux qubits, and charge qubits allow the fewest.


Phase qubit

The phase qubit possesses a Josephson to charge energy ratio on the order of magnitude 10^6. For phase qubits, energy levels correspond to different quantum charge oscillation
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...
s across a Josephson junction, where charge and
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
are analogous to momentum and position respectively as analogous to a
quantum harmonic oscillator 量子調和振動子 は、 古典調和振動子 の 量子力学 類似物です。任意の滑らかな ポテンシャル は通常、安定した 平衡点 の近くで 調和ポテンシャル として近似できるため、最 ...
. Note that in this context phase is the complex argument of the superconducting wave function (also known as the superconducting
order parameter In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
), not the phase between the different states of the qubit.


Flux qubit

The flux qubit (also known as a persistent-current qubit) possesses a Josephson to charging energy ratio on the order of magnitude 10. For flux qubits, the energy levels correspond to different
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
numbers of magnetic flux quanta trapped in a superconducting ring.


Fluxonium

Fluxonium qubits are a specific type of flux qubit operable at relatively low
frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
(approximately 600 MHz). This results in longer qubit lifetime. The fluxonium circuit's Hamiltonian can be written as follows: H = 4 E_C n^2 + \frac E_L \phi^2 - E_J cos(\phi - \phi_), consistent with the notation in. Note that E_L = (\hbar/2e)^2 / L .


Charge qubit

The charge qubit, also known as the Cooper pair box, possesses a Josephson to charging energy ratio on the order of magnitude < 1. For charge qubits, different energy levels correspond to an integer number of
Cooper pair In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
s on a superconducting island (a small superconducting area with a controllable number of charge carriers). Indeed, the first experimentally realized qubit was the Cooper pair box, achieved in 1999.


Transmon

Transmon In quantum computing, and more specifically in superconducting quantum computing, a transmon is a type of superconducting charge qubit that was designed to have reduced sensitivity to charge noise. The transmon was developed by Robert J. Schoelko ...
s are a special type of qubit with a shunted capacitor specifically designed to mitigate
noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
. The transmon qubit model was based on the Cooper pair box (illustrated in the table above in row one column one). It was also the first qubit to demonstrate
quantum supremacy In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum device can solve a problem that no classical computer can solve in any feasible amount of time (irrespective of the usefulness of ...
. The increased ratio of Josephson to charge energy mitigates noise. Two transmons can be coupled using a
coupling capacitor Capacitive coupling is the transfer of energy within an electrical network or between distant networks by means of displacement current between circuit(s) nodes, induced by the electric field. This coupling can have an intentional or accidental ...
. For this 2-qubit system the Hamiltonian is written \hat = \frac (\sigma_^ \sigma_^ + \sigma_^ \sigma_^), where J is
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
and \sigma is surface charge density.


Xmon

The Xmon is very similar in design to a transom in that it originated based on the planar transmon model. An Xmon is essentially a tunable transmon. The major distinguishing difference between transmon and Xmon qubits is the Xmon qubits is grounded with one of its capacitor pads.


Gatemon

Another variation of the transmon qubit is the Gatemon. Like the Xmon, the Gatemon is a tunable variation of the transmon. The Gatemon is tunable via gate voltage.


Unimon

In 2022 researchers from IQM Quantum Computers,
Aalto University Aalto University ( fi, Aalto-yliopisto; sv, Aalto-universitetet) is a public research university located in Espoo, Finland. It was established in 2010 as a merger of three major Finnish universities: the Helsinki University of Technology, the He ...
, and VTT Technical Research Centre of Finland discovered a novel superconducting qubit known as the Unimon. A relatively simple qubit, the Unimon consists of a single Josephson junction shunted by a linear inductor (possessing an inductance not depending on current) inside a (superconducting)
resonator A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...
. Unimons have increased anharmocity and display faster operation time resulting in lower susceptibility to noise errors. In addition to increased anharmocity, other advantages Unimon qubit include decreased susceptibility to flux noise and complete insensitivity to dc charge noise. In the table above, the three superconducting qubit archetypes are reviewed. In the first row, the qubit's electrical circuit diagram is presented. The second row depicts a quantum Hamiltonian derived from the circuit. Generally, the Hamiltonian is the sum of the system's
kinetic Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory of gases, Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to i ...
and
potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple re ...
energy components (analogous to a particle in a
potential well A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captur ...
). For the Hamiltonians denoted, \phi is the superconducting
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
phase difference across the junction, C_J is the
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
associated with the
Josephson junction In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mec ...
, and q is the charge on the
junction Junction may refer to: Arts and entertainment * ''Junction'' (film), a 2012 American film * Jjunction, a 2002 Indian film * Junction (album), a 1976 album by Andrew Cyrille * Junction (EP), by Basement Jaxx, 2002 * Junction (manga), or ''Hot ...
capacitance. For each potential depicted, only solid wave functions are used for computation. The qubit potential is indicated by a thick red line, and schematic
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
solutions are depicted by thin lines, lifted to their appropriate
energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The te ...
for clarity. Note that particle mass corresponds to an
inverse function In mathematics, the inverse function of a function (also called the inverse of ) is a function that undoes the operation of . The inverse of exists if and only if is bijective, and if it exists, is denoted by f^ . For a function f\colon X\t ...
of the circuit
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
and that the shape of the potential is governed by regular
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
s and Josephson junctions. Schematic wave solutions in the third row of the table show the complex amplitude of the phase variable. Specifically, if a qubit's phase is measured while the qubit occupies a particular state, there is a non-zero probability of measuring a specific value ''only'' where the depicted wave function oscillates. All three rows are essentially different presentations of the same physical system.


Single qubits

The
GHz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one he ...
energy gap between energy levels of a superconducting qubit is designed to be compatible with available electronic equipment, due to the
terahertz gap Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the ITU-designated band of freq ...
(lack of equipment in the higher
frequency band A frequency band is an interval in the frequency domain, delimited by a lower frequency and an upper frequency. The term may refer to a radio band or an interval of some other spectrum. The frequency range of a system is the range over which i ...
). The superconductor energy gap implies a top limit of operation below ~1THz beyond which Cooper pairs break, so energy level separation cannot be too high. On the other hand, energy level separation cannot be too small due to cooling considerations: a temperature of 1K implies energy fluctuations of 20 GHz. Temperatures of tens of mili-Kelvin are achieved in
dilution refrigerator A 3He/4He dilution refrigerator is a cryogenics, cryogenic device that provides continuous cooling to temperatures as low as 2 Kelvin, mK, with no moving parts in the low-temperature region. The cooling power is provided by the heat o ...
s and allow qubit operation at a ~5 GHz energy level separation. Qubit energy level separation is frequently adjusted by controlling a dedicated bias current line, providing a "knob" to fine tune the qubit parameters.


Single qubit gates

A single qubit gate is achieved by rotation in the
Bloch sphere In quantum quantum mechanics, mechanics and Quantum computing, computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level system, two-level quantum mechanical system (qubit), named after the physicist Felix ...
. Rotations between different energy levels of a single qubit are induced by
microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
pulses sent to an
antenna Antenna ( antennas or antennae) may refer to: Science and engineering * Antenna (radio), also known as an aerial, a transducer designed to transmit or receive electromagnetic (e.g., TV or radio) waves * Antennae Galaxies, the name of two collid ...
or
transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
coupled to the qubit with a
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
resonant with the energy separation between levels. Individual qubits may be addressed by a dedicated
transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
or by a shared one if the other qubits are off
resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
. The
axis of rotation Rotation around a fixed axis is a special case of rotational motion. The fixed-axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rota ...
is set by
quadrature amplitude modulation Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signal ...
of microwave pulse, while pulse length determines the
angle of rotation In mathematics, the angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle. A clockwise rotation is considered a negative rotation, so that, for instance ...
. More formally (following the notation of ) for a driving signal \mathcal(t)=\mathcal^x(t)\cos(\omega_d t)+\mathcal^y(t)\sin(\omega_d t) of frequency \omega_d, a driven qubit Hamiltonian in a
rotating wave approximation The rotating-wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian that oscillate rapidly are neglected. This is a valid approximation when the applied electromagnetic radi ...
is H^R/\hbar=(\omega-\omega_d), 1\rangle\langle 1, +\frac\sigma_x+\frac\sigma_y, where \omega is the qubit resonance and \sigma_x,\sigma_y are
Pauli matrices In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (), they are occasionally denoted by tau () when used in ...
. To implement a rotation about the X axis, one can set \mathcal^y(t)=0 and apply a microwave pulse at frequency \omega_d=\omega for time t_g. The resulting transformation is U_x=\exp\left\=\exp\left\. This is exactly the rotation operator R_X(\theta) by angle \theta=\int_0^\mathcal^x(t) dt about the X axis in the Bloch sphere. A rotation about the Y axis can be implemented in a similar way. Showing the two rotation operators is sufficient for satisfying universality as every single qubit unitary operator U may be presented as U=R_X(\theta_1)R_Y(\theta_2)R_X(\theta_3) (up to a global
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
which is physically inconsequential) by a procedure known as the X-Y decomposition. Setting \int_0^\mathcal^x(t) dt=\pi results in the transformation U_x=\exp\left\=e^=-i\sigma_x up to the global phase -i and is known as the NOT gate.


Coupling qubits

The ability to couple qubits is essential for implementing 2-qubit
gates Gates is the plural of gate, a point of entry to a space which is enclosed by walls. It may also refer to: People * Gates (surname), various people with the last name * Gates Brown (1939-2013), American Major League Baseball player * Gates McFadde ...
. Coupling two qubits can be achieved by connecting both to an intermediate electrical coupling circuit. The circuit may be either a fixed element (such as a
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
) or be controllable (like the DC-SQUID). In the first case, decoupling qubits during the time the gate is switched off is achieved by tuning qubits out of resonance one from another, making the energy gaps between their computational states different. This approach is inherently limited to nearest-neighbor coupling since as physical electrical circuit must be laid out between connected qubits. Notably,
D-Wave Systems D-Wave Systems Inc. is a Canadian quantum computing company, based in Burnaby, British Columbia, Canada. D-Wave was the world's first company to sell computers to exploit quantum effects in their operation. D-Wave's early customers include Loc ...
' nearest-neighbor coupling achieves a highly connected
unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
of 8 qubits in Chimera graph configuration.
Quantum algorithm In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequ ...
s typically require coupling between arbitrary qubits. Consequently, multiple
swap Swap or SWAP may refer to: Finance * Swap (finance), a derivative in which two parties agree to exchange one stream of cash flows against another * Barter Science and technology * Swap (computer programming), exchanging two variables in t ...
operations are necessary, limiting the length of quantum computation possible before processor
decoherence Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wa ...
.


Quantum bus

Another method of coupling two or more qubits is by way of a
quantum bus A quantum bus is a device which can be used to store or transfer information between independent qubits in a quantum computer, or combine two qubits into a superposition. It is the quantum analog of a classical bus. There are several physical s ...
, by pairing qubits to this intermediate. A quantum bus is often implemented as a
microwave cavity A microwave cavity or ''radio frequency (RF) cavity'' is a special type of resonator, consisting of a closed (or largely closed) metal structure that confines electromagnetic fields in the microwave region of the spectrum. The structure is eithe ...
modeled by a
quantum harmonic oscillator 量子調和振動子 は、 古典調和振動子 の 量子力学 類似物です。任意の滑らかな ポテンシャル は通常、安定した 平衡点 の近くで 調和ポテンシャル として近似できるため、最 ...
. Coupled qubits may be brought in and out of resonance with the bus and with each other, eliminating the nearest-neighbor limitation. Formalism describing coupling is
cavity quantum electrodynamics Cavity quantum electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles, under conditions where the quantum nature of photons is significant. It could in principle be u ...
. In cavity quantum electrodynamics, qubits are analogous to atoms interacting with an optical photon cavity with a difference of GHz (rather than the THz regime of electromagnetic radiation). Resonant excitation exchange among these artificial atoms is potentially useful for direct implementation of multi-qubit gates. Following the dark state
manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
, the Khazali-Mølmer scheme performs complex multi-qubit operations in a single step, providing a substantial shortcut to the conventional circuit model.


Cross resonant gate

One popular gating mechanism uses two qubits and a bus, each tuned to different energy level separations. Applying microwave excitation to the first qubit, with a frequency resonant with the second qubit, causes a \sigma_x rotation of the second qubit. Rotation direction depends on the state of the first qubit, allowing a controlled phase gate construction. Following the notation of, the drive Hamiltonian describing the excited system through the first qubit driving line is formally written H_D/\hbar=A(t)\cos(\tilde_2t)\left(\sigma_x \otimes I-\frac\sigma_z\otimes\sigma_x+m_I\otimes\sigma_x\right), where A(t) is the shape of the microwave pulse in time, \tilde_2 is resonance frequency of the second qubit, \ are the
Pauli matrices In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (), they are occasionally denoted by tau () when used in ...
, J is the coupling coefficient between the two qubits via the resonator, \Delta_\equiv \omega_1-\omega_2 is qubit detuning, m_ is stray (unwanted) coupling between qubits, and \hbar is Planck's constant divided by 2\pi. The time
integral In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...
over A(t) determines the angle of rotation. Unwanted rotations from the first and third terms of the Hamiltonian can be compensated for with single qubit operations. The remaining component, combined with single qubit rotations, forms a basis for the
su(4) In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the specia ...
Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...
.


Qubit readout

Architecture-specific readout, or
measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
, mechanisms exist. Readout of a phase qubit is explained in the qubit archetypes table above. A flux qubit state is often read using an adjustable DC-
SQUID True squid are molluscs with an elongated soft body, large eyes, eight arms, and two tentacles in the superorder Decapodiformes, though many other molluscs within the broader Neocoleoidea are also called squid despite not strictly fitting t ...
magnetometer A magnetometer is a device that measures magnetic field or magnetic dipole moment. Different types of magnetometers measure the direction, strength, or relative change of a magnetic field at a particular location. A compass is one such device, o ...
. States may also be measured using an
electrometer An electrometer is an electrical instrument for measuring electric charge or electrical potential difference. There are many different types, ranging from historical handmade mechanical instruments to high-precision electronic devices. Modern ...
. A more general readout scheme includes a coupling to a microwave
resonator A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...
, where resonance frequency of the resonator is dispersively shifted by the qubit state.


DiVincenzo's criteria

DiVincenzo's criteria The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 2000 by the theoretical physicist David P. DiVincenzo, as being those necessary to construct such a computer—a computer first proposed b ...
is a list describing the requirements for a physical system to be capable of implementing a logical qubit.
DiVincenzo's criteria The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 2000 by the theoretical physicist David P. DiVincenzo, as being those necessary to construct such a computer—a computer first proposed b ...
is satisfied by superconducting quantum computing implementation. Much of the current development effort in superconducting quantum computing aim to achieve interconnect, control, and readout in the 3rd dimension with additional
lithography Lithography () is a planographic method of printing originally based on the immiscibility of oil and water. The printing is from a stone (lithographic limestone) or a metal plate with a smooth surface. It was invented in 1796 by the German a ...
layers.The list of
DiVincenzo's criteria The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 2000 by the theoretical physicist David P. DiVincenzo, as being those necessary to construct such a computer—a computer first proposed b ...
for a physical system to implement a logical qubit is satisfied by the implementation of superconducting qubits. Although DiVincenzo’s criteria as originally proposed consists of five criterium required for physically implementing a quantum computer, the more complete list consists of seven criterium as it takes into account communication over a computer network capable of transmitting quantum information between computers, known as the “quantum internet”. Therefore, the first five criterium ensure successful quantum computing, while the final two criterium allow for quantum communication. # A scalable physical system with well characterized qubits. "Well characterized implies that that Hamiltonian function must be well-defined i.e the energy eigenstates of the qubit should be able to be quantified.. A scalable system is self-explanatory, it indicates that this ability to regulate a qubit should be augmentable for multiple more qubits. Herein lies the major issue Quantum Computers face, as more qubits are implemented it leads to a exponential increase in cost and other physical implementations which pale in comparison to the enhanced speed it may offer. As superconducting qubits are fabricated on a chip, the many-qubit system is readily scalable. Qubits are allocated on the 2D surface of the chip. The demand for well characterized qubits is fulfilled with (a) qubit non-linearity (accessing only two of the available energy levels) and (b) accessing a single qubit at a time (rather than the entire many-qubit system) by way of per-qubit dedicated control lines and/or frequency separation, or tuning out, of different qubits. # Ability to initialize the state of qubits to a simple fiducial state. A fiducial state is one that is easily and consistently replicable and is useful in quantum computing as it may be used to guarantee the initial state of qubits. One simple way to initialize a superconducting qubit is to wait long enough for the qubits to relax to the ground state. Controlling qubit potential with tuning knobs allows faster initialization mechanisms. # Long relevant decoherence times. Decoherence of superconducting qubits is affected by multiple factors. Most decoherence is attributed to the quality of the Josephson junction and imperfections in the chip substrate. Due to their mesoscopic scale, superconducting qubits are relatively short lived. Nevertheless, thousands of gate operations have been demonstrated in these many-qubit systems. # A “universal” set of quantum gates. Superconducting qubits allow arbitrary rotations in the Bloch sphere with pulsed microwave signals, implementing single qubit gates. \sigma_z \sigma_z and \sigma_x \sigma_x couplings are shown for most implementations and for complementing the universal gate set. This criterium may also be satisfied by coupling two transmons with a coupling capacitor. # Qubit-specific measurement ability. In general, single superconducting qubits are utilized for control or for measurement. # Interconvertibility of stationary and flying qubits. While stationary qubits are used to store information or perform calculations, flying qubits transmit information macroscopically. Qubits should be capable of converting from being a stationary qubit to being a flying qubit and vice versa. # Reliable transmission of flying qubits between specified locations. The final two criterium have been experimentally proven by research performed by
ETH (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , a ...
with two superconducting qubits connected by a
coaxial cable Coaxial cable, or coax (pronounced ) is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric ( insulating material); many coaxial cables also have a p ...
.


Challenges

One of the primary challenges of superconducting quantum computing is the extremely low temperatures at which superconductors like Bose-Einstein Condensates exist. Other basic challenges in superconducting qubit design are shaping the potential well and choosing particle mass such that energy separation between two specific energy levels is unique, differing from all other interlevel energy separation in the system, since these two levels are used as logical states of the qubit. Superconducting quantum computing must also mitigate
quantum noise Quantum noise is noise arising from the indeterminate state of matter in accordance with fundamental principles of quantum mechanics, specifically the uncertainty principle and via zero-point energy fluctuations. Quantum noise is due to the appa ...
(disruptions of the system caused by its interaction with an environment) as well as leakage (information being lost to the surrounding environment). One way to reduce leakage is with
parity measurement Parity measurement (also referred to as Operator measurement) is a procedure in Quantum information science used for error detection in quantum qubits. A parity measurement checks the equality of two qubits to return either a true or false answer, w ...
s. Many current challenges faced by superconducting quantum computing lie in the field of microwave engineering. As superconducting quantum computing approaches larger scale devices, researchers face difficulties in qubit coherence, scalable
calibration In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of know ...
software, efficient determination of
fidelity Fidelity is the quality of faithfulness or loyalty. Its original meaning regarded duty in a broader sense than the related concept of ''fealty''. Both derive from the Latin word ''fidēlis'', meaning "faithful or loyal". In the City of London f ...
of quantum states across an entire chip, and qubit and gate fidelity. Moreover, superconducting quantum computing devices must be reliably reproducable at increasingly large scales such that they are compatible with these improvements. The Journey of Superconducting Quantum Computing: Although not the newest development, the focus began to shift onto Superconducting qubits in the latter half of the 1990's when quantum tunneling across Josephson Junctions became apparent which allowed for the realization that Quantum Computing could be achieved through these superconducting qubits. At the end of the century in 1999, a paper was published by Yasunobu Nakamura, which exhibited the initial design of a superconducting qubit which is now known as the "charge qubit". This is the primary basis point on which later designs amended upon. These initial qubits had their limitations in respect to maintaining long coherence times and destructive measurements. The further amendment to this initial breakthrough lead to the invention of the phase and flux qubit and subsequently resulting in the Transmon qubit which is now widely and primarily used in Superconducting Quantum Computing.The Transmon qubit has enhanced original designs and has further cushioned charge noise from the qubit. The journey has been long, arduous and full of breakthroughs but has seen significant advancements in the recent history and has massive potential for revolutionizing computing. The Future of Superconducting Quantum Computing: The sectors leading industry giants like Google, IBM and Baidu are using Superconducting Quantum Computing and the transmon qubits to make huge leaps and bounds in the area of Quantum Computing In August 2022, Baidu released its plans to build a fully integrated top to bottom Quantum Computer which incorporated superconducting qubits. This computer will be all encompassing with hardware, software and applications fully integrated. This is a first in the world of quantum computing and will lead to ground-breaking advancements. IBM released the following roadmap publicly that they have set for their Quantum Computers which also incorporated superconducting qubits and the transmon qubit. 2021: In 2021, IBM came out with their 127-qubit processor 2022: On November 9, IBM announced its 433 qubit processor called "Osprey" 2023: IBM plan on releasing their Condor quantum processor with 1,121 qubits 2024: IBM plan on releasing their Flamingo quantum processor with 1,386+ qubits 2025: IBM plan on releasing their Kookaburra quantum processor with 4,158+ qubits 2026 and beyond:IBM plan on releasing a quantum processor that scaled beyond 10,00 qubits to a 100,000 qubits Google in 2016, implemented 16 qubits to convey a demonstration of the Fermi-Hubbard Model. In other recent experiment, Google used 17 qubits to optimize the Sherrington-Kirkpatrick model. Google produced the Sycamore quantum computer which performed a task in 200 seconds that would have taken 10,000 years on a classical computer.


References


External links


IBM Quantum
offers access to over 20 quantum computer systems. *Th
IBM Quantum Experience
offers free access to writing quantum algorithms and executing them on 5 qubit quantum computers.
IBM's roadmap for quantum computing
shows 65 qubit systems available in 2020 and 127 qubits to be available sometime in 2021. {{quantum computing Quantum information science Quantum electronics Superconductivity