Physical and logical qubits

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In quantum computing, a qubit is a unit of information analogous to a bit (binary digit) in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ways more powerful than classical bits for some tasks. Qubits are used in quantum circuits and quantum algorithms composed of quantum logic gates to solve computational problems, where they are used for input/output and intermediate computations.

Contents

A physical qubit is a physical device that behaves as a two-state quantum system, used as a component of a computer system. [1] [2] A logical qubit is a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit [3] subject to unitary transformations, has a long enough coherence time to be usable by quantum logic gates (c.f. propagation delay for classical logic gates). [1] [4] [5]

Since the development of the first quantum computer in 1998, most technologies used to implement qubits face issues of stability, decoherence, [6] [7] fault tolerance [8] [9] and scalability. [6] [9] [10] Because of this, many physical qubits are needed for the purposes of error-correction to produce an entity which behaves logically as a single qubit would in a quantum circuit or algorithm; this is the subject of quantum error correction. [3] [11] Thus, contemporary logical qubits typically consist of many physical qubits to provide stability, error-correction and fault tolerance needed to perform useful computations. [1] [7] [11]

In 2023, Google researchers showed how quantum error correction can improve logical qubit performance by increasing the physical qubit count. [12] These results found that a larger logical qubit (49 physical qubits) had a lower error rate, about 2.9 percent per round of error correction, compared to a rate of about 3.0 percent for the smaller logical qubit (17 physical qubits). [13]

In 2024, IBM researchers created a quantum error correction code 10 times more efficient than previous research, protecting 12 logical qubits for roughly a million cycles of error checks using 288 qubits. [14] [15] The work demonstrates error correction on near-term devices while reducing overhead – the number of physical qubits required to keep errors low. [16]

In 2024, Microsoft and Quantinuum announced experimental results that showed logical qubits could be created with significantly fewer physical qubits. [17] The team used quantum error correction techniques developed by Microsoft and Quantinuum’s trapped ion hardware to use 30 physical qubits to form four logical qubits. Scientists used a qubit virtualization system and active syndrome extraction—also called repeated error correction to accomplish this. [18] This work defines how to achieve logical qubits within quantum computation. [19]

Overview

1-bit and 2-bit quantum gate operations have been shown to be universal. [20] [21] [22] [23] A quantum algorithm can be instantiated as a quantum circuit. [24] [25]

A logical qubit specifies how a single qubit should behave in a quantum algorithm, subject to quantum logic operations which can be built out of quantum logic gates. However, issues in current technologies preclude single two-state quantum systems, which can be used as physical qubits, from reliably encoding and retaining this information for long enough to be useful. Therefore, current attempts to produce scalable quantum computers require quantum error correction, and multiple (currently many) physical qubits must be used to create a single, error-tolerant logical qubit. Depending on the error-correction scheme used, and the error rates of each physical qubit, a single logical qubit could be formed of up to 1,000 physical qubits. [26]

Topological quantum computing

The approach of topological qubits, which takes advantage of topological effects in quantum mechanics, has been proposed as needing many fewer or even a single physical qubit per logical qubit. [10] Topological qubits rely on a class of particles called anyons which have spin that is neither half-integral (fermions) nor integral (bosons), and therefore obey neither the Fermi–Dirac statistics nor the Bose–Einstein statistics of particle behavior. [27] Anyons exhibit braid symmetry in their world lines, which has desirable properties for the stability of qubits. Notably, anyons must exist in systems constrained to two spatial dimensions or fewer, according to the spin–statistics theorem, which states that in 3 or more spatial dimensions, only fermions and bosons are possible. [27]

See also

Related Research Articles

<span class="mw-page-title-main">Quantum computing</span> Technology that uses quantum mechanics

A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. In particular, a large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.

This is a timeline of quantum computing.

In logic circuits, the Toffoli gate, also known as the CCNOT gate (“controlled-controlled-not”), invented by Tommaso Toffoli, is a CNOT gate with two control qubits and one target qubit. That is, the target qubit will be inverted if the first and second qubits are both 1. It is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. Formally, we describe the Toffoli gate with the following truth table and matrix:

In physics, an anyon is a type of quasiparticle so far observed only in two-dimensional systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical properties intermediate between fermions and bosons. In general, the operation of exchanging two identical particles, although it may cause a global phase shift, cannot affect observables. Anyons are generally classified as abelian or non-abelian. Abelian anyons, detected by two experiments in 2020, play a major role in the fractional quantum Hall effect.

Quantum error correction (QEC) is a set of techniques used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum state preparation, and faulty measurements. Effective quantum error correction would allow quantum computers with low qubit fidelity to execute algorithms of higher complexity or greater circuit depth.

A topological quantum computer is a theoretical quantum computer proposed by Russian-American physicist Alexei Kitaev in 1997. It employs quasiparticles in two-dimensional systems, called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime. These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable. Small, cumulative perturbations can cause quantum states to decohere and introduce errors in the computation, but such small perturbations do not change the braids' topological properties. This is like the effort required to cut a string and reattach the ends to form a different braid, as opposed to a ball bumping into a wall.

<span class="mw-page-title-main">One-way quantum computer</span> Method of quantum computing

The one-way or measurement-based quantum computer (MBQC) is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements.

In quantum computing, the threshold theorem states that a quantum computer with a physical error rate below a certain threshold can, through application of quantum error correction schemes, suppress the logical error rate to arbitrarily low levels. This shows that quantum computers can be made fault-tolerant, as an analogue to von Neumann's threshold theorem for classical computation. This result was proven by the groups of Dorit Aharanov and Michael Ben-Or; Emanuel Knill, Raymond Laflamme, and Wojciech Zurek; and Alexei Kitaev independently. These results built on a paper of Peter Shor, which proved a weaker version of the threshold theorem.

The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice. It is the simplest and most well studied of the quantum double models. It is also the simplest example of topological order—Z2 topological order (first studied in the context of Z2 spin liquid in 1991). The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit. It was introduced by Alexei Kitaev.

In quantum many-body physics, topological degeneracy is a phenomenon in which the ground state of a gapped many-body Hamiltonian becomes degenerate in the limit of large system size such that the degeneracy cannot be lifted by any local perturbations.

Linear optical quantum computing or linear optics quantum computation (LOQC), also photonic quantum computing (PQC), is a paradigm of quantum computation, allowing (under certain conditions, described below) universal quantum computation. LOQC uses photons as information carriers, mainly uses linear optical elements, or optical instruments (including reciprocal mirrors and waveplates) to process quantum information, and uses photon detectors and quantum memories to detect and store quantum information.

In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem. The term was coined by John Preskill in 2012, but the concept dates to Yuri Manin's 1980 and Richard Feynman's 1981 proposals of quantum computing.

Continuous-variable (CV) quantum information is the area of quantum information science that makes use of physical observables, like the strength of an electromagnetic field, whose numerical values belong to continuous intervals. One primary application is quantum computing. In a sense, continuous-variable quantum computation is "analog", while quantum computation using qubits is "digital." In more technical terms, the former makes use of Hilbert spaces that are infinite-dimensional, while the Hilbert spaces for systems comprising collections of qubits are finite-dimensional. One motivation for studying continuous-variable quantum computation is to understand what resources are necessary to make quantum computers more powerful than classical ones.

Quantum volume is a metric that measures the capabilities and error rates of a quantum computer. It expresses the maximum size of square quantum circuits 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 Eastin–Knill theorem is a no-go theorem that states: "No quantum error correcting code can have a continuous symmetry which acts transversely on physical qubits". In other words, no quantum error correcting code can transversely implement a universal gate set, where a transversal logical gate is one that can be implemented on a logical qubit by the independent action of separate physical gates on corresponding physical qubits.

The current state of quantum computing is referred to as the noisy intermediate-scale quantum (NISQ) era, characterized by quantum processors containing up to 1,000 qubits which are not advanced enough yet for fault-tolerance or large enough to achieve quantum advantage. These processors, which are sensitive to their environment (noisy) and prone to quantum decoherence, are not yet capable of continuous quantum error correction. This intermediate-scale is defined by the quantum volume, which is based on the moderate number of qubits and gate fidelity. The term NISQ was coined by John Preskill in 2018.

The five-qubit error correcting code is the smallest quantum error correcting code that can protect a logical qubit from any arbitrary single qubit error. In this code, 5 physical qubits are used to encode the logical qubit. With and being Pauli matrices and the Identity matrix, this code's generators are . Its logical operators are and . Once the logical qubit is encoded, errors on the physical qubits can be detected via stabilizer measurements. A lookup table that maps the results of the stabilizer measurements to the types and locations of the errors gives the control system of the quantum computer enough information to correct errors.

This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.

<span class="mw-page-title-main">Zhenghan Wang</span> Chinese-American mathematician

Zhenghan Wang is a Chinese-American mathematician. He is a principal researcher at Microsoft Station Q, as well as a professor of mathematics at the University of California, Santa Barbara.

References

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