Physical and logical qubits

Short description: Types of quantum information

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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.

A physical qubit is a physical device that behaves as a two-state quantum system, used as a component of a computer system.[1] A logical qubit is a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit[2] 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][3][4]

(As of September 2018), most technologies used to implement qubits face issues of stability, decoherence,[5][6] fault tolerance[7][8] and scalability.[5][8][9] 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.[2][10] Thus, contemporary logical qubits typically consist of many physical qubits to provide stability, error-correction and fault tolerance needed to perform useful computations.[1][6][10]

## Contents

* 1 Overview
* 2 Topological quantum computing
* 3 See also
* 4 References

## Overview

1-bit and 2-bit quantum gate operations have been shown to be universal.[11][12][13][14] A quantum algorithm can be instantiated as a quantum circuit.[15][16]

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.[17]

## 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.[9] 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.[18] 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.[18]

## See also

* Quantum error correction and the quantum threshold theorem
* Quantum computing § Obstacles
* Superconductive quantum computing
* Josephson junction
* Trapped-ion quantum computing
* Semiconductor-based quantum computing
* Quantum dot
* Topological quantum computing

## References

1. ↑ 1.0 1.1 1.2 Shaw, Bilal; Wilde, Mark M.; Oreshkov, Ognyan; Kremsky, Isaac; Lidar, Daniel A. (2008-07-18). "Encoding One Logical Qubit Into Six Physical Qubits". Journal of Physics A: Mathematical and General 34 (35): 7067–7079. doi:10.1088/0305-4470/34/35/331. ISSN 0305-4470. Bibcode: 2001JPhA...34.7067V.
2. ↑ 2.0 2.1 Heeres, Reinier W.; Reinhold, Philip; Ofek, Nissim; Frunzio, Luigi; Jiang, Liang; Devoret, Michel H.; Schoelkopf, Robert J. (2016-08-08). "Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator". Nature Communications 8 (1): 94. doi:10.1038/s41467-017-00045-1. ISSN 2041-1723. PMID 28733580.
3. ↑ "Logical Qubits (LogiQ)" (in en-us). https://www.iarpa.gov/index.php/research-programs/logiq/logical-qubits.
4. ↑ "Logical Qubits (LogiQ)" (in en-us). https://www.iarpa.gov/index.php/research-programs/logiq/logical-qubits.
5. ↑ 5.0 5.1 Ristè, D.; Poletto, S.; Huang, M.-Z.; Bruno, A.; Vesterinen, V.; Saira, O.-P.; DiCarlo, L. (2014-10-20). "Detecting bit-flip errors in a logical qubit using stabilizer measurements". Nature Communications 6 (1): 6983. doi:10.1038/ncomms7983. ISSN 2041-1723. PMID 25923318.
6. ↑ 6.0 6.1 Kapit, Eliot (2016-04-12). "A Very Small Logical Qubit". Physical Review Letters 116 (15): 150501. doi:10.1103/PhysRevLett.116.150501. ISSN 0031-9007. PMID 27127945.
7. ↑ Nigg, Daniel; Mueller, Markus; Martinez, Esteban A.; Schindler, Philipp; Hennrich, Markus; Monz, Thomas; Martin-Delgado, Miguel A.; Blatt, Rainer (2014-07-18). "Experimental Quantum Computations on a Topologically Encoded Qubit". Science 345 (6194): 302–305. doi:10.1126/science.1253742. ISSN 0036-8075. PMID 24925911. Bibcode: 2014Sci...345..302N.
8. ↑ 8.0 8.1 "Achieving scalability in quantum computing" (in en-US). Microsoft Cloud Blogs (Microsoft). 2018-05-16. https://cloudblogs.microsoft.com/quantum/2018/05/16/achieving-scalability-in-quantum-computing/.
9. ↑ 9.0 9.1 Mishmash, Ryan; Alicea, Jason (2017-08-16). "Topological qubits: Arriving in 2018?". https://quantumfrontiers.com/2017/08/16/topological-qubits-arriving-in-2018/.
10. ↑ 10.0 10.1 Jones, Cody; Fogarty, Michael A.; Morello, Andrea; Gyure, Mark F.; Dzurak, Andrew S.; Ladd, Thaddeus D. (2018-06-01). "A logical qubit in a linear array of semiconductor quantum dots". Physical Review X 8 (2): 021058. doi:10.1103/PhysRevX.8.021058. ISSN 2160-3308. Bibcode: 2018PhRvX...8b1058J.
11. ↑ DiVincenzo, David P. (1995-02-01). "Two-bit gates are universal for quantum computation". Physical Review A 51 (2): 1015–1022. doi:10.1103/PhysRevA.51.1015. PMID 9911679. Bibcode: 1995PhRvA..51.1015D.
12. ↑ Deutsch, David; Barenco, Adriano; Ekert, Artur (1995-06-08). "Universality in Quantum Computation". Proceedings of the Royal Society of London A: Mathematical and Physical Sciences 449 (1937): 669–677. doi:10.1098/rspa.1995.0065. ISSN 1471-2946. Bibcode: 1995RSPSA.449..669D.
13. ↑ Barenco, Adriano (1995-06-08). "A Universal Two-Bit Gate for Quantum Computation". Proceedings of the Royal Society of London A: Mathematical and Physical Sciences 449 (1937): 679–683. doi:10.1098/rspa.1995.0066. ISSN 1471-2946. Bibcode: 1995RSPSA.449..679B.
14. ↑ Lloyd, Seth (1995-07-10). "Almost Any Quantum Logic Gate is Universal". Physical Review Letters 75 (2): 346–349. doi:10.1103/PhysRevLett.75.346. PMID 10059671. Bibcode: 1995PhRvL..75..346L.
15. ↑ Yazdani, Maryam; Zamani, Morteza Saheb; Sedighi, Mehdi (2013-06-09). "A Quantum Physical Design Flow Using ILP and Graph Drawing". Quantum Information Processing Journal 12 (10): 3239. doi:10.1007/s11128-013-0597-6. Bibcode: 2013QuIP...12.3239Y.
16. ↑ Whitney, Mark; Isailovic, Nemanja; Patel, Yatish; Kubiatowicz, John (2007-04-02). "Automated Generation of Layout and Control for Quantum Circuits". ACM Computing Frontiers. https://archive.org/details/arxiv-0704.0268.
17. ↑ Fowler, Austin G.; Mariantoni, Matteo; Martinis, John M.; Cleland, Andrew N. (2012). "Surface codes: Towards practical large-scale quantum computation". Physical Review A 86 (3): 032324. doi:10.1103/PhysRevA.86.032324. ISSN 1050-2947. Bibcode: 2012PhRvA..86c2324F.
18. ↑ 18.0 18.1 Wilczek, Frank (2018-02-27). "How 'Anyon' Particles Emerge From Quantum Knots | Quanta Magazine". Quanta Magazine. https://www.quantamagazine.org/how-anyon-particles-emerge-from-quantum-knots-20170228/.

* v
* t
* e

Quantum information science

General|

* Quantum computing
* Qubit
* physical vs. logical
* DiVincenzo's criteria
* Quantum information
* Quantum programming
* Quantum processors
* Cloud-based quantum computing
* Timeline of quantum computing

Theorems|

* Bell's theorem
* Gleason's theorem
* Gottesman–Knill theorem
* Holevo's theorem
* Margolus–Levitin theorem
* No-broadcast theorem
* No-cloning theorem
* No-communication theorem
* No-deleting theorem
* No-hiding theorem
* No-teleportation theorem
* PBR theorem
* Quantum threshold theorem

Quantum
communication|

* Quantum capacity
* Classical capacity
* Entanglement-assisted classical capacity
* Quantum channel
* Quantum network
* Quantum cryptography
* Quantum key distribution
* BB84
* SARG04
* Three-stage quantum cryptography protocol
* Quantum teleportation
* Superdense coding
* LOCC
* Entanglement distillation

Quantum algorithms|

* Universal quantum simulator
* Deutsch–Jozsa algorithm
* Grover's algorithm
* Quantum Fourier transform
* Shor's algorithm
* Simon's problem
* Quantum phase estimation algorithm
* Quantum counting algorithm
* Quantum annealing
* Quantum algorithm for linear systems of equations
* Amplitude amplification

Quantum
complexity theory|

* Quantum Turing machine
* EQP
* BQP
* QMA
* PostBQP
* QIP

Quantum
computing models|

* Quantum circuit
* Quantum logic gate
* One-way quantum computer
* cluster state
* Adiabatic quantum computation
* Topological quantum computer

Quantum
error correction|

* Stabilizer codes
* Entanglement-Assisted Quantum Error Correction
* Shor code
* Steane code
* CSS code
* Quantum convolutional codes
* Toric code

Physical
implementations|

| Quantum optics|

* Cavity QED
* Circuit QED
* Linear optical quantum computing
* KLM protocol
* Boson sampling

|

Ultracold atoms|

* Trapped ion quantum computer
* Optical lattice

Spin-based|

* Nuclear magnetic resonance QC
* Kane QC
* Loss–DiVincenzo QC
* Nitrogen-vacancy center

Superconducting
quantum computing|

* Charge qubit
* Flux qubit
* Phase qubit
* Transmon

Software|

* libquantum
* OpenQASM
* Q#
* Qiskit
* IBM Q Experience

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