Quantum volume is a metric that measures the capabilities and error rates of a
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 ...
. It expresses the maximum size of square
quantum circuit
In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly othe ...
s that can be implemented successfully by the computer. The form of the circuits is independent from the quantum computer architecture, but compiler can transform and optimize it to take advantage of the computer's features. Thus, quantum volumes for different architectures can be compared.
The current world record for highest quantum volume as of February 2023 is 32,768 (2
15), accomplished by
Quantinuum's H1 Ion trap quantum computer.
Introduction
Quantum computers are difficult to compare. Quantum volume is a single number designed to show all around performance. It is a measurement and not a calculation, and takes into account several features of a quantum computer, starting with its number 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—other measures used are gate and measurement errors, crosstalk and connectivity.
IBM defined its Quantum Volume metric
because a classical computer's transistor count and a quantum computer's quantum bit count aren't the same. Qubits decohere with a resulting loss of performance so a few fault tolerant bits are more valuable as a performance measure than a larger number of noisy, error-prone qubits.
Generally, the larger the quantum volume, the more complex the problems a quantum computer can solve.
Alternative benchmarks, such as
Cross-entropy benchmarking Cross-entropy benchmarking (also referred to as XEB) is a quantum computer, quantum benchmarking protocol which can be used to demonstrate quantum supremacy. In XEB, a random quantum circuit is executed on a quantum computer multiple times in order ...
and
IonQ
IonQ is a quantum computing hardware and software company based in College Park, Maryland. They are developing a general-purpose trapped ion quantum computer and software to generate, optimize, and execute quantum circuits.
History
IonQ was co-f ...
's Algorithmic Qubits, have also been proposed.
Definition
Original Definition
The quantum volume of a quantum computer was originally defined in 2018 by Nikolaj Moll ''et al.''
[
] However, since around 2021 that definition has been supplanted by IBM's 2019
redefinition
The second season of the television series ''Angel'', the spin-off of ''Buffy the Vampire Slayer'', premiered on September 26, 2000 on The WB and concluded its 22-episode season on May 22, 2001. It maintained its previous timeslot, airing Tuesdays ...
.
The original definition depends on the number of qubits ''N'' as well as the number of steps that can be executed, the circuit depth ''d''
:
The circuit depth depends on the effective error rate
as
:
The effective error rate
is defined as the average error rate of a two-qubit gate. If the physical two-qubit gates do not have all-to-all connectivity, additional
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 ...
gates may be needed to implement an arbitrary two-qubit gate and
, where
is the error rate of the physical two-qubit gates. If more complex hardware gates are available, such as the three-qubit
Toffoli gate
In logic circuits, the Toffoli gate (also CCNOT gate), invented by Tommaso Toffoli, is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. It is also known as the "controlle ...
, it is possible that
.
The allowable circuit depth decreases when more qubits with the same effective error rate are added. So with these definitions, as soon as