A trapped ion quantum computer is one proposed approach to a large-scale
quantum computer
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 ...
.
Ions
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
, or charged atomic particles, can be confined and suspended in free space using
electromagnetic fields
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical co ...
.
Qubits
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, ...
are stored in stable electronic states of each ion, and
quantum information
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...
can be transferred through the collective quantized motion of the ions in a shared trap (interacting through the
Coulomb force
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
).
Lasers
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
are applied to induce
coupling
A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. The primary purpose of couplings is to join two pieces of rotating equipment while permitting some degree of misalignment or end mov ...
between the qubit states (for single qubit operations) or coupling between the internal qubit states and the external motional states (for entanglement between qubits).
The fundamental operations of a quantum computer have been demonstrated experimentally with the currently highest accuracy in trapped ion systems. Promising schemes in development to scale the system to arbitrarily large numbers of qubits include transporting ions to spatially distinct locations in an array of
ion traps, building large entangled states via photonically connected networks of remotely entangled ion chains, and combinations of these two ideas. This makes the trapped ion quantum computer system one of the most promising architectures for a scalable, universal quantum computer. As of April 2018, the largest number of particles to be controllably entangled is 20 trapped ions.
History
The first implementation scheme for a controlled-NOT
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 ...
was proposed by
Ignacio Cirac
Juan Ignacio Cirac Sasturain (born 11 October 1965), known professionally as Ignacio Cirac, is a Spanish physicist. He is one of the pioneers of the field of quantum computing and quantum information theory. He is the recipient of the 2006 Pri ...
and
Peter Zoller
Peter may refer to:
People
* List of people named Peter, a list of people and fictional characters with the given name
* Peter (given name)
** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church
* Peter (surname), a su ...
in 1995,
specifically for the trapped ion system. The same year, a key step in the controlled-NOT gate was experimentally realized at
NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
Ion Storage Group, and research in quantum computing began to take off worldwide.

In 2021, researchers from the
University of Innsbruck
The University of Innsbruck (german: Leopold-Franzens-Universität Innsbruck; la, Universitas Leopoldino Franciscea) is a public research university in Innsbruck, the capital of the Austrian federal state of Tyrol, founded on October 15, 1669.
...
presented a quantum computing demonstrator that fits inside two 19-inch
server rack
A 19-inch rack is a standardized frame or enclosure for mounting multiple electronic equipment modules. Each module has a front panel that is wide. The 19 inch dimension includes the edges or "ears" that protrude from each side of the equ ...
s, the world's first quality standards-meeting compact trapped ion quantum computer.
Paul trap
The electrodynamic
quadrupole ion trap
A quadrupole ion trap or paul trap is a type of ion trap that uses dynamic electric fields to trap charged particles. They are also called radio frequency (RF) traps or Paul traps in honor of Wolfgang Paul, who invented the device and shared the N ...
currently used in trapped ion quantum computing research was invented in the 1950s by
Wolfgang Paul
Wolfgang Paul (; 10 August 1913 – 7 December 1993) was a German physicist, who co-developed the non-magnetic quadrupole mass filter which laid the foundation for what is now called an ion trap. He shared one-half of the Nobel Prize in Ph ...
(who received the
Nobel Prize
The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...
for his work in 1989
). Charged particles cannot be trapped in 3D by just electrostatic forces because of
Earnshaw's theorem. Instead, an electric field oscillating at
radio frequency
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 upp ...
(RF) is applied, forming a potential with the shape of a saddle spinning at the RF frequency. If the RF field has the right parameters (oscillation frequency and field strength), the charged particle becomes effectively trapped at the
saddle point
In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function ...
by a restoring force, with the motion described by a set of
Mathieu equations.
This saddle point is the point of minimized energy magnitude,
, for the ions in the potential field. The Paul trap is often described as a harmonic potential well that traps ions in two dimensions (assume
and
without loss of generality) and does not trap ions in the
direction. When multiple ions are at the saddle point and the system is at equilibrium, the ions are only free to move in
. Therefore, the ions will repel each other and create a vertical configuration in
, the simplest case being a linear strand of only a few ions.
Coulomb interactions of increasing complexity will create a more intricate ion configuration if many ions are initialized in the same trap.
Furthermore, the additional vibrations of the added ions greatly complicate the quantum system, which makes initialization and computation more difficult.
Once trapped, the ions should be cooled such that
(see
Lamb Dicke regime
In ion trapping and atomic physics experiments, the Lamb Dicke regime (or Lamb Dicke limit) is a quantum regime in which the coupling (induced by an external light field) between an ion or atom's internal qubit states and its motional states is suf ...
). This can be achieved by a combination of
Doppler cooling
Doppler cooling is a mechanism that can be used to trap and slow the motion of atoms to cool a substance. The term is sometimes used synonymously with laser cooling, though laser cooling includes other techniques.
History
Doppler cooling was si ...
and
resolved sideband cooling Resolved sideband cooling is a laser cooling technique allowing cooling of tightly bound atoms and ions beyond the Doppler cooling limit, potentially to their motional ground state. Aside from the curiosity of having a particle at zero point energy, ...
. At this very low temperature, vibrational energy in the ion trap is quantized into phonons by the energy eigenstates of the ion strand, which are called the center of mass vibrational modes. A single phonon's energy is given by the relation
. These quantum states occur when the trapped ions vibrate together and are completely isolated from the external environment. If the ions are not properly isolated, noise can result from ions interacting with external electromagnetic fields, which creates random movement and destroys the quantized energy states.
Requirements for quantum computation
The full requirements for a functional quantum computer are not entirely known, but there are many generally accepted requirements.
David DiVincenzo
David P. DiVincenzo (born 1959) is an American theoretical physicist. He is the director of the Institute of Theoretical Nanoelectronics at the Peter Grünberg Institute at the Forschungszentrum Jülich and Professor at the Institute for Quantum ...
outlined several of these
criterion for quantum computing.
Qubits
Any two-level quantum system can form a qubit, and there are two predominant ways to form a qubit using the electronic states of an ion:
# Two ground state
hyperfine
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nuc ...
levels (these are called "hyperfine qubits")
# A ground state level and an excited level (these are called the "optical qubits")
Hyperfine qubits are extremely long-lived (decay time of the order of thousands to millions of years) and phase/frequency stable (traditionally used for atomic frequency standards).
Optical qubits are also relatively long-lived (with a decay time of the order of a second), compared to the logic gate operation time (which is of the order of
microseconds
A microsecond is a unit of time in the International System of Units (SI) equal to one millionth (0.000001 or 10−6 or ) of a second. Its symbol is μs, sometimes simplified to us when Unicode is not available.
A microsecond is equal to 1000 n ...
). The use of each type of qubit poses its own distinct challenges in the laboratory.
Initialization
Ionic qubit states can be prepared in a specific qubit state using a process called
optical pumping
Optical pumping is a process in which light is used to raise (or "pump") electrons from a lower energy level in an atom or molecule to a higher one. It is commonly used in laser construction to pump the active laser medium so as to achieve populat ...
. In this process, a laser couples the ion to some excited states which eventually decay to one state which is not coupled to the laser. Once the ion reaches that state, it has no excited levels to couple to in the presence of that laser and, therefore, remains in that state. If the ion decays to one of the other states, the laser will continue to excite the ion until it decays to the state that does not interact with the laser. This initialization process is standard in many physics experiments and can be performed with extremely high
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 ...
(>99.9%).
The system's initial state for quantum computation can therefore be described by the ions in their hyperfine and motional ground states, resulting in an initial center of mass phonon state of
(zero phonons).
Measurement
Measuring the state of the qubit stored in an ion is quite simple. Typically, a laser is applied to the ion that couples only one of the qubit states. When the ion collapses into this state during the measurement process, the laser will excite it, resulting in a photon being released when the ion decays from the excited state. After decay, the ion is continually excited by the laser and repeatedly emits photons. These photons can be collected by a
photomultiplier tube
Photomultiplier tubes (photomultipliers or PMTs for short) are extremely sensitive detectors of light in the ultraviolet, visible, and near-infrared ranges of the electromagnetic spectrum. They are members of the class of vacuum tubes, more specif ...
(PMT) or a
charge-coupled device
A charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a ...
(CCD) camera. If the ion collapses into the other qubit state, then it does not interact with the laser and no photon is emitted. By counting the number of collected photons, the state of the ion may be determined with a very high accuracy (>99.9%).
Arbitrary single qubit rotation
One of the requirements of universal quantum computing is to coherently change the state of a single qubit. For example, this can transform a qubit starting out in 0 into any arbitrary superposition of 0 and 1 defined by the user. In a trapped ion system, this is often done using
magnetic dipole transition The interaction of an electromagnetic wave with an electron bound in an atom or molecule can be described by time-dependent perturbation theory. Magnetic dipole transitions describe the dominant effect of the coupling to the magnetic part of the ele ...
s or stimulated
Raman transitions for hyperfine qubits and electric quadrupole transitions for optical qubits. The term "rotation" alludes to 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 ...
representation of a qubit pure state. Gate fidelity can be greater than 99%.
The
rotation operators and
can be applied to individual ions by manipulating the frequency of an external electromagnetic field from and exposing the ions to the field for specific amounts of time. These controls create 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 ...
of the form
. Here,
and
are the raising and lowering operators of spin (see
Ladder operator
In linear algebra (and its application to quantum mechanics), a raising or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator. In quantum mechanics, the raisin ...
). These rotations are the universal building blocks for single-qubit gates in quantum computing.
To obtain the Hamiltonian for the ion-laser interaction, apply the
Jaynes–Cummings model
The Jaynes–Cummings model (sometimes abbreviated JCM) is a theoretical model in quantum optics. It describes the system of a two-level atom interacting with a quantized mode of an optical cavity (or a bosonic field), with or without the prese ...
. Once the Hamiltonian is found, the formula for the unitary operation performed on the qubit can be derived using the principles of quantum time evolution. Although this model utilizes the
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 ...
, it proves to be effective for the purposes of trapped-ion quantum computing.
Two qubit entangling gates
Besides the
controlled-NOT gate proposed by Cirac and Zoller in 1995, many equivalent, but more robust, schemes have been proposed and implemented experimentally since. Recent theoretical work by JJ. Garcia-Ripoll, Cirac, and Zoller have shown that there are no fundamental limitations to the speed of entangling gates, but gates in this impulsive regime (faster than 1 microsecond) have not yet been demonstrated experimentally. The fidelity of these implementations has been greater than 99%.
Scalable trap designs
Quantum computers must be capable of initializing, storing, and manipulating many qubits at once in order to solve difficult computational problems. However, as previously discussed, a finite number of qubits can be stored in each trap while still maintaining their computational abilities. It is therefore necessary to design interconnected ion traps that are capable of transferring information from one trap to another. Ions can be separated from the same interaction region to individual storage regions and brought back together without losing the quantum information stored in their internal states. Ions can also be made to turn corners at a "T" junction, allowing a two dimensional trap array design. Semiconductor fabrication techniques have also been employed to manufacture the new generation of traps, making the 'ion trap on a chip' a reality. An example is the quantum charge-coupled device (QCCD) designed by D. Kielpinski, C. Monroe, and D.J. Wineland.
QCCDs resemble mazes of electrodes with designated areas for storing and manipulating qubits.
The variable electric potential created by the electrodes can both trap ions in specific regions and move them through the transport channels, which negates the necessity of containing all ions in a single trap. Ions in the QCCD's memory region are isolated from any operations and therefore the information contained in their states is kept for later use. Gates, including those that entangle two ion states, are applied to qubits in the interaction region by the method already described in this article.
Decoherence in scalable traps
When an ion is being transported between regions in an interconnected trap and is subjected to a nonuniform magnetic field, decoherence can occur in the form of the equation below (see
Zeeman effect
The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel prize ...
).
This is effectively changes the relative phase of the quantum state. The up and down arrows correspond to a general superposition qubit state, in this case the ground and excited states of the ion.
Additional relative phases could arise from physical movements of the trap or the presence of unintended electric fields. If the user could determine the parameter α, accounting for this decoherence would be relatively simple, as known quantum information processes exist for correcting a relative phase.
However, since α from the interaction with the magnetic field is path-dependent, the problem is highly complex. Considering the multiple ways that decoherence of a relative phase can be introduced in an ion trap, reimagining the ion state in a new basis that minimizes decoherence could be a way to eliminate the issue.
One way to combat decoherence is to represent the quantum state in a new basis called the
decoherence-free subspaces
A decoherence-free subspace (DFS) is a subspace of a quantum system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the envi ...
, or DFS., with basis states
and
. The DFS is actually the subspace of two ion states, such that if both ions acquire the same relative phase, the total quantum state in the DFS will be unaffected.
Challenges
Trapped ion quantum computers theoretically meet all 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 quantum computing, but implementation of the system can be quite difficult. The main challenges facing trapped ion quantum computing are the initialization of the ion's motional states, and the relatively brief lifetimes of the phonon states.
Decoherence also proves to be challenging to eliminate, and is caused when the qubits interact with the external environment undesirably.
CNOT gate implementation
The
controlled NOT gate
In computer science, the controlled NOT gate (also C-NOT or CNOT), controlled-''X'' gate'','' controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-based ...
is a crucial component for quantum computing, as any quantum gate can be created by a combination of CNOT gates and single-qubit rotations.
It is therefore important that a trapped-ion quantum computer can perform this operation by meeting the following three requirements.
First, the trapped ion quantum computer must be able to perform arbitrary rotations on qubits, which are already discussed in the "arbitrary single-qubit rotation" section.
The next component of a CNOT gate is the controlled phase-flip gate, or the controlled-''X'' gate (see
quantum logic 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 ...
). In a trapped ion quantum computer, the state of the center of mass phonon functions as the control qubit, and the internal atomic spin state of the ion is the working qubit. The phase of the working qubit will therefore be flipped if the phonon qubit is in the state
.
Lastly, a SWAP gate must be implemented, acting on both the ion state and the phonon state.
Two alternate schemes to represent the CNOT gates are presented in
Michael Nielsen
Michael Aaron Nielsen (born January 4, 1974) is a quantum physicist, science writer, and computer programming researcher living in San Francisco.
Work
In 1998, Nielsen received his PhD in physics from the University of New Mexico. In 2004, he wa ...
and
Isaac Chuang
Isaac L. Chuang is an American electrical engineer and physicist. He leads the quanta research group at the Center for Ultracold Atoms at Massachusetts Institute of Technology (MIT). He received his undergraduate degrees in physics (1990) and elec ...
's ''
Quantum Computation and Quantum Information
''Quantum Computation and Quantum Information'' is a textbook about quantum information science written by Michael Nielsen and Isaac Chuang, regarded as a standard text on the subject. It is informally known as "Mike and Ike", after the Mike an ...
'' and Cirac and Zoller's ''Quantum Computation with Cold Trapped Ions''.
References
Additional Resources
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*
Trapped ion computer on arxiv.org*
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{{Quantum computing
Quantum information science