DOCSLIB.ORG

A Scalable Decoder Micro-Architecture for Fault-Tolerant Quantum Computing

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Scalable Decoder Micro-Architecture for Fault-Tolerant Quantum Computing A Scalable Decoder Micro-architecture for Fault-Tolerant Quantum Computing Poulami Das,1 Christopher A. Pattison,2 Srilatha Manne,3 Douglas Carmean,3 Krysta Svore,3 Moinuddin Qureshi,1 and Nicolas Delfosse∗3 1Georgia Institute of Technology, Atlanta, GA, USA 2California Institute of Technology, Pasadena, CA, USA 3Microsoft Quantum Systems and Microsoft Research, Redmond, WA, USA Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error correction is required to execute a useful quantum algorithm. The decoder is a key component of the error correction scheme whose role is to identify errors faster than they accumulate in the quantum computer and that must be implemented with minimum hardware resources in order to scale to the regime of practical applications. In this work, we consider surface code error correction, which is the most popular family of error correcting codes for quantum computing, and we design a decoder micro-architecture for the Union-Find decoding algorithm. We propose a three-stage fully pipelined hardware implementation of the decoder that significantly speeds up the decoder. Then, we optimize the amount of decoding hardware required to perform error correction simultaneously over all the logical qubits of the quantum computer. By sharing resources between logical qubits, we obtain a 67% reduction of the number of hardware units and the memory capacity is reduced by 70%. Moreover, we reduce the bandwidth required for the decoding process by a factor at least 30x using low-overhead compression algorithms. Finally, we provide numerical evidence that our optimized micro-architecture can be executed fast enough to correct errors in a quantum computer. Quantum computing promises significant speed-up rection cycles that removes the noise injected by logical over conventional computers for specific applications such gates. Both quantum error correction and logical quan- as integer factorization [1], physics and chemistry simu- tum gates must be implemented through fault-tolerant lations [2–4] and database search [5]. gadgets [11–13] to avoid the injection of pathological er- The primary obstacle to the implementation of quan- ror configurations that would be uncorrectable by the tum algorithms solving industrial size problems is the subsequent correction cycle. high noise rate in any quantum device that makes the In this work, we consider a fault-tolerant quantum output of a quantum computation indistinguishable from computer based on surface codes [14, 15] which is the a random output. A fault-tolerant quantum computer, most promising family of error-correcting codes for very in which quantum bits, or qubits, are regularly refreshed noisy quantum hardware. Surface codes can correct up to by quantum error correction [6], is necessary to perform 1% of noise on all the basic components of the quantum a useful computation on noisy quantum hardware. computer and they can be implemented on a square grid Most classical error correction schemes can be adapted of qubits using exclusively local quantum gates acting on to the quantum setting thanks to the CSS construc- nearest neighbor qubits. For comparison, most quantum tion [7, 8] and the stabilizer formalism [9], providing a error correction codes such as quantum Hamming code quantum version of standard families of classical error- (Steane code) requires an error rate below 10−5 [16]. correcting codes [10] such as repetition codes, Hamming In this paper, we focus on the design of an error de- codes, Reed-Muller codes, BCH codes, LDPC codes and coder, or simply decoder, which is the primary building polar codes. block in charge of error correction. The decoder takes as The main difference with the classical setting is the an input the syndrome, which is the data extracted from arXiv:2001.06598v1 [quant-ph] 18 Jan 2020 very high noise rate that affects current quantum hard- quantum parity check measurements and it returns an ware, often of the order of 1% per quantum gate, which estimation of the error. Given this estimation, the effect makes quantum error correction much more challenging of the error can be easily reversed. In a fault-tolerant to implement. This is because it relies on the measure- quantum computer, the decoder must satisfy the three ment of quantum parity checks that are likely to intro- following design constraints. duce additional noise to the qubits. Moreover, one must 1. Accuracy Constraint: The decoder must cor- be able to implement a universal set of quantum gates on rectly identify the error with high probability. encoded qubits, or logical qubits. In a fault-tolerant quan- tum computer (FTQC), the computation is performed by 2. Latency Constraint: The decoder must be fast alternating logical quantum gates and quantum error cor- enough to correct errors within one error correction cycle. 3. Scalability Constraint: The decoder design ∗[email protected] must feasible to implement in the regime of practi- 2 cal applications that may require millions of phys- with the unit type and across the logical qubits ical qubits. and hence propose an efficient time-division multi- plexing that allows logical qubits to share decoding A number of surface code decoding algorithms have been resources within a decoder block without compro- proposed in the past 20 years [14, 17–68] and many satisfy mising the error correction capabilities. the Accuracy Constraint which is often the main motiva- tion. However, it remains unclear whether the decoding 4. We propose different compression algorithms can be made fast enough to satisfy the Latency Con- adapted to a cryogenic setting in order to reduce straint without degrading the decoder performance [69]. the bandwidth consumed to send the syndrome Moreover, the decoding problem is generally studied for data to the decoder. a single logical qubit, ignoring the Scalability Constraint, whereas practical applications require hundreds or thou- 5. Combining all the previous results, we describe an sand of logical qubits encoded into millions of physical Error Decoding Architecture (EDA) represented in qubits [3]. A substantial amount of decoding hardware Fig. 1 that scales the decoder design for a large is required to decoding simultaneously all the qubits of FTQC while reducing hardware costs. The number the quantum computer. Most of the work in quantum er- of hardware units is reduced by 67% and we obtain ror correction decoders focuses on algorithmic aspects of a 30× bandwidth reduction while preserving the the problem. Here, we consider this problem through the decoder accuracy. Moreover, we demonstrate by lens of computer architecture and we propose a decoder numerical simulations that our architecture leads to micro-architecture that satisfies simultaneously our three a decoder that is fast enough to satisfy the Latency design contraints. Constraint, despite the high noise rate of quantum hardware. Individual Error Decoders Error Decoding Architecture (EDA) Item 1 and 2 provide a hardware acceleration of the Decoder Decoder … Decoder N-Qubit … N-Qubit Decoder Block Decoder Block decoder and 3 and 4 lead to a satisfying solution to the Scalability Constraint. Our EDA is optimized carefully Syndrome Decompression in order to guarantee that the error correction capability High Bandwidth Interface of the initial UF decoder is preserved, which guarantees Syndrome Compression that the Accuracy Constraint is satisfied. The numerical Qubit Qubit … Qubit Qubit … Qubit Qubit … Qubit simulation of our optimized micro-architecture (item 5) accounts for the limitation imposed by shared hardware resources which demonstrates that our decoder satisfy Figure 1: A naive decoding architecture with a decoder asso- simultaneously the three design constraints. ciated with each logical qubit and our Error Decoding Archi- This article exploits a number of ideas from computer tecture based on optimized decoder blocks shared across mul- tiple logical qubits. A low-overhead compression algorithm is architecture such as pipelining and resource optimiza- used to reduce the bandwidth cost. Our optimized decoder tion. We believe this approach is necessary in order to block is described in Fig. 12. scale quantum machines. Even though we provide a de- tailed micro-architecture for the Union-Find decoder, the We propose a decoder micro-architecture based on the general principles of our design apply to any decoding al- Union-Find decoding algorithm [30, 43]. We choose the gorithm. A key ingredient is the simplicity of the decoder Union-Find decoder for its accuracy and its simplicity. It and the decomposition in independent steps, which leads is proven to achieve good decoding performance. More- to a natural pipeline and a speed-up by instruction-level over, it comes with a almost-linear time complexity and it parallelism. is also very fast in practice because it requires no floating- point arithmetic and no matrix operations. Finally, the simplicity of the decoder allows us to design a special- I. BACKGROUND AND MOTIVATION ized hardware implementation that leads to a significant speed-up. Our main contributions are the following. A. Qubits and decoherence 1. We propose a hardware implementation of the We refer to Preskill’s lecture notes [70] and Nielsen Union-Find decoder based on three hardware units and Chuang’s book [71] for a great overview of field corresponding to each step of the algorithm. of quantum computation and quantum information the- 2. We design a three-stage pipepline based on our ory. A qubit is the basic unit of information in a quan- three hardware units that brings an important tum computer. A qubit is described by complex vector speed-up to the Union-Find decoder by paralleliz- j i = αj0i + βj1i, which represents the superposition ing the implementation of the decoding stages. of two basis state j0i and j1i, with α; β 2 C such that jαj2 + jβj2 = 1. Without error correction, a quantum 3.
Load more

Recommended publications
  • Simulating Quantum Field Theory with a Quantum Computer
    Simulating quantum field theory with a quantum computer John Preskill Lattice 2018 28 July 2018 This talk has two parts (1) Near-term prospects for quantum computing. (2) Opportunities in quantum simulation of quantum field theory. Exascale digital computers will advance our knowledge of QCD, but some challenges will remain, especially concerning real-time evolution and properties of nuclear matter and quark-gluon plasma at nonzero temperature and chemical potential. Digital computers may never be able to address these (and other) problems; quantum computers will solve them eventually, though I’m not sure when. The physics payoff may still be far away, but today’s research can hasten the arrival of a new era in which quantum simulation fuels progress in fundamental physics. Frontiers of Physics short distance long distance complexity Higgs boson Large scale structure “More is different” Neutrino masses Cosmic microwave Many-body entanglement background Supersymmetry Phases of quantum Dark matter matter Quantum gravity Dark energy Quantum computing String theory Gravitational waves Quantum spacetime particle collision molecular chemistry entangled electrons A quantum computer can simulate efficiently any physical process that occurs in Nature. (Maybe. We don’t actually know for sure.) superconductor black hole early universe Two fundamental ideas (1) Quantum complexity Why we think quantum computing is powerful. (2) Quantum error correction Why we think quantum computing is scalable. A complete description of a typical quantum state of just 300 qubits requires more bits than the number of atoms in the visible universe. Why we think quantum computing is powerful We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers.
    [Show full text]
  • Universal Control and Error Correction in Multi-Qubit Spin Registers in Diamond T
    LETTERS PUBLISHED ONLINE: 2 FEBRUARY 2014 | DOI: 10.1038/NNANO.2014.2 Universal control and error correction in multi-qubit spin registers in diamond T. H. Taminiau 1,J.Cramer1,T.vanderSar1†,V.V.Dobrovitski2 and R. Hanson1* Quantum registers of nuclear spins coupled to electron spins of including one with an additional strongly coupled 13C spin (see individual solid-state defects are a promising platform for Supplementary Information). To demonstrate the generality of quantum information processing1–13. Pioneering experiments our approach to create multi-qubit registers, we realized the initia- selected defects with favourably located nuclear spins with par- lization, control and readout of three weakly coupled 13C spins for ticularly strong hyperfine couplings4–10. To progress towards each NV centre studied (see Supplementary Information). In the large-scale applications, larger and deterministically available following, we consider one of these NV centres in detail and use nuclear registers are highly desirable. Here, we realize univer- two of its weakly coupled 13C spins to form a three-qubit register sal control over multi-qubit spin registers by harnessing abun- for quantum error correction (Fig. 1a). dant weakly coupled nuclear spins. We use the electron spin of Our control method exploits the dependence of the nuclear spin a nitrogen–vacancy centre in diamond to selectively initialize, quantization axis on the electron spin state as a result of the aniso- control and read out carbon-13 spins in the surrounding spin tropic hyperfine interaction (see Methods for hyperfine par- bath and construct high-fidelity single- and two-qubit gates. ameters), so no radiofrequency driving of the nuclear spins is We exploit these new capabilities to implement a three-qubit required7,23–28.
    [Show full text]
  • Unconditional Quantum Teleportation
    R ESEARCH A RTICLES our experiment achieves Fexp 5 0.58 6 0.02 for the field emerging from Bob’s station, thus Unconditional Quantum demonstrating the nonclassical character of this experimental implementation. Teleportation To describe the infinite-dimensional states of optical fields, it is convenient to introduce a A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, pair (x, p) of continuous variables of the electric H. J. Kimble,* E. S. Polzik field, called the quadrature-phase amplitudes (QAs), that are analogous to the canonically Quantum teleportation of optical coherent states was demonstrated experi- conjugate variables of position and momentum mentally using squeezed-state entanglement. The quantum nature of the of a massive particle (15). In terms of this achieved teleportation was verified by the experimentally determined fidelity analogy, the entangled beams shared by Alice Fexp 5 0.58 6 0.02, which describes the match between input and output states. and Bob have nonlocal correlations similar to A fidelity greater than 0.5 is not possible for coherent states without the use those first described by Einstein et al.(16). The of entanglement. This is the first realization of unconditional quantum tele- requisite EPR state is efficiently generated via portation where every state entering the device is actually teleported. the nonlinear optical process of parametric down-conversion previously demonstrated in Quantum teleportation is the disembodied subsystems of infinite-dimensional systems (17). The resulting state corresponds to a transport of an unknown quantum state from where the above advantages can be put to use. squeezed two-mode optical field.
    [Show full text]
  • Quantum Error Modelling and Correction in Long Distance Teleportation Using Singlet States by Joe Aung
    Quantum Error Modelling and Correction in Long Distance Teleportation using Singlet States by Joe Aung Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2002 @ Massachusetts Institute of Technology 2002. All rights reserved. Author ................... " Department of Electrical Engineering and Computer Science May 21, 2002 72-1 14 Certified by.................. .V. ..... ..'P . .. ........ Jeffrey H. Shapiro Ju us . tn Professor of Electrical Engineering Director, Research Laboratory for Electronics Thesis Supervisor Accepted by................I................... ................... Arthur C. Smith Chairman, Department Committee on Graduate Students BARKER MASSACHUSE1TS INSTITUTE OF TECHNOLOGY JUL 3 1 2002 LIBRARIES 2 Quantum Error Modelling and Correction in Long Distance Teleportation using Singlet States by Joe Aung Submitted to the Department of Electrical Engineering and Computer Science on May 21, 2002, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract Under a multidisciplinary university research initiative (MURI) program, researchers at the Massachusetts Institute of Technology (MIT) and Northwestern University (NU) are devel- oping a long-distance, high-fidelity quantum teleportation system. This system uses a novel ultrabright source of entangled photon pairs and trapped-atom quantum memories. This thesis will investigate the potential teleportation errors involved in the MIT/NU system. A single-photon, Bell-diagonal error model is developed that allows us to restrict possible errors to just four distinct events. The effects of these errors on teleportation, as well as their probabilities of occurrence, are determined.
    [Show full text]
  • Phd Proposal 2020: Quantum Error Correction with Superconducting Circuits
    PhD Proposal 2020: Quantum error correction with superconducting circuits Keywords: quantum computing, quantum error correction, Josephson junctions, circuit quantum electrodynamics, high-impedance circuits • Laboratory name: Laboratoire de Physique de l'Ecole Normale Supérieure de Paris • PhD advisors : Philippe Campagne-Ibarcq ([email protected]) and Zaki Leghtas ([email protected]). • Web pages: http://cas.ensmp.fr/~leghtas/ https://philippecampagneib.wixsite.com/research • PhD location: ENS Paris, 24 rue Lhomond Paris 75005. • Funding: ERC starting grant. Quantum systems can occupy peculiar states, such as superpositions or entangled states. These states are intrinsically fragile and eventually get wiped out by inevitable interactions with the environment. Protecting quantum states against decoherence is a formidable and fundamental problem in physics, and it is pivotal for the future of quantum computing. Quantum error correction provides a potential solution, but its current envisioned implementations require daunting resources: a single bit of information is protected by encoding it across tens of thousands of physical qubits. Our team in Paris proposes to protect quantum information in an entirely new type of qubit with two key specicities. First, it will be encoded in a single superconducting circuit resonator whose innite dimensional Hilbert space can replace large registers of physical qubits. Second, this qubit will be rf-powered, continuously exchanging photons with a reservoir. This approach challenges the intuition that a qubit must be isolated from its environment. Instead, the reservoir acts as a feedback loop which continuously and autonomously corrects against errors. This correction takes place at the level of the quantum hardware, and reduces the need for error syndrome measurements which are resource intensive.
    [Show full text]
  • Arxiv:0905.2794V4 [Quant-Ph] 21 Jun 2013 Error Correction 7 B
    Quantum Error Correction for Beginners Simon J. Devitt,1, ∗ William J. Munro,2 and Kae Nemoto1 1National Institute of Informatics 2-1-2 Hitotsubashi Chiyoda-ku Tokyo 101-8340. Japan 2NTT Basic Research Laboratories NTT Corporation 3-1 Morinosato-Wakamiya, Atsugi Kanagawa 243-0198. Japan (Dated: June 24, 2013) Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. This development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future.
    [Show full text]
  • Machine Learning Quantum Error Correction Codes: Learning the Toric Code
    ,, % % hhXPP ¨, hXH(HPXh % ,¨ Instituto de F´ısicaTe´orica (((¨lQ e@QQ IFT Universidade Estadual Paulista el e@@l DISSERTAC¸ AO~ DE MESTRADO IFT{D.009/18 Machine Learning Quantum Error Correction Codes: Learning the Toric Code Carlos Gustavo Rodriguez Fernandez Orientador Leandro Aolita Dezembro de 2018 Rodriguez Fernandez, Carlos Gustavo R696m Machine learning quantum error correction codes: learning the toric code / Carlos Gustavo Rodriguez Fernandez. – São Paulo, 2018 43 f. : il. Dissertação (mestrado) - Universidade Estadual Paulista (Unesp), Instituto de Física Teórica (IFT), São Paulo Orientador: Leandro Aolita 1. Aprendizado do computador. 2. Códigos de controle de erros(Teoria da informação) 3. Informação quântica. I. Título. Sistema de geração automática de fichas catalográficas da Unesp. Biblioteca do Instituto de Física Teórica (IFT), São Paulo. Dados fornecidos pelo autor(a). Acknowledgements I'd like to thank Giacomo Torlai for painstakingly explaining to me David Poulin's meth- ods of simulating the toric code. I'd also like to thank Giacomo, Juan Carrasquilla and Lauren Haywards for sharing some very useful code I used for the simulation and learning of the toric code. I'd like to thank Gwyneth Allwright for her useful comments on a draft of this essay. I'd also like to thank Leandro Aolita for his patience in reading some of the final drafts of this work. Of course, I'd like to thank the admin staff in Perimeter Institute { in partiuclar, without Debbie not of this would have been possible. I'm also deeply indebted to Roger Melko, who supervised this work in Perimeter Institute (where a version of this work was presented as my PSI Essay).
    [Show full text]
  • Arxiv:2009.06242V1 [Quant-Ph] 14 Sep 2020 Special Type of Highly Entangled State
    Quantum teleportation of physical qubits into logical code-spaces Yi-Han Luo,1, 2, ∗ Ming-Cheng Chen,1, 2, ∗ Manuel Erhard,3, 4 Han-Sen Zhong,1, 2 Dian Wu,1, 2 Hao-Yang Tang,1, 2 Qi Zhao,1, 2 Xi-Lin Wang,1, 2 Keisuke Fujii,5 Li Li,1, 2 Nai-Le Liu,1, 2 Kae Nemoto,6, 7 William J. Munro,6, 7 Chao-Yang Lu,1, 2 Anton Zeilinger,3, 4 and Jian-Wei Pan1, 2 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China 2CAS Centre for Excellence in Quantum Information and Quantum Physics, Hefei, 230026, China 3Austrian Academy of Sciences, Institute for Quantum Optics and Quantum Information (IQOQI), Boltzmanngasse 3, A-1090 Vienna, Austria 4Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, A-1090 Vienna, Austria 5Graduate School of Engineering Science Division of Advanced Electronics and Optical Science Quantum Computing Group, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531 6NTT Basic Research Laboratories & NTT Research Center for Theoretical Quantum Physics, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa, 243-0198, Japan 7National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan Quantum error correction is an essential tool for reliably performing tasks for processing quantum informa- tion on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that non-transverse operations, which are essential for universal quantum computation, lead to the spread of errors.
    [Show full text]
  • Quantum Information Processing and Quantum Optics with Circuit Quantum Electrodynamics
    FOCUS | REVIEW ARTICLE FOCUS | REVIEWhttps://doi.org/10.1038/s41567-020-0806-z ARTICLE Quantum information processing and quantum optics with circuit quantum electrodynamics Alexandre Blais 1,2,3 ✉ , Steven M. Girvin 4,5 and William D. Oliver6,7,8 Since the first observation of coherent quantum behaviour in a superconducting qubit, now more than 20 years ago, there have been substantial developments in the field of superconducting quantum circuits. One such advance is the introduction of the concepts of cavity quantum electrodynamics (QED) to superconducting circuits, to yield what is now known as circuit QED. This approach realizes in a single architecture the essential requirements for quantum computation, and has already been used to run simple quantum algorithms and to operate tens of superconducting qubits simultaneously. For these reasons, circuit QED is one of the leading architectures for quantum computation. In parallel to these advances towards quantum information process- ing, circuit QED offers new opportunities for the exploration of the rich physics of quantum optics in novel parameter regimes in which strongly nonlinear effects are readily visible at the level of individual microwave photons. We review circuit QED in the context of quantum information processing and quantum optics, and discuss some of the challenges on the road towards scalable quantum computation. avity quantum electrodynamics (QED) studies the interac- introduce the basic concepts of circuit QED and how the new tion of light and matter at its most fundamental level: the parameter regimes that can be obtained in circuit QED, compared Ccoherent interaction of single atoms with single photons. with cavity QED, lead to new possibilities for quantum optics.
    [Show full text]
  • Introduction to Quantum Error Correction
    Schrödinger Cats, Maxwell’s Demon and Quantum Error Correction Experiment Theory Michel Devoret SMG Luigi Frunzio Liang Jiang Rob Schoelkopf Leonid Glazman M. Mirrahimi ** Andrei Petrenko Nissim Ofek Shruti Puri Reinier Heeres Yaxing Zhang Philip Reinhold Victor Albert** Yehan Liu Kjungjoo Noh** Zaki Leghtas Richard Brierley Brian Vlastakis Claudia De Grandi +….. Zaki Leghtas Juha Salmilehto Matti Silveri Uri Vool Huaixui Zheng Marios Michael +….. QuantumInstitute.yale.edu 1 Quantum Information Science Control theory, Coding theory, Computational Complexity theory, Networks, Systems, Information theory Ultra-high-speed digital, analog, Programming languages, Compilers microwave electronics, FPGA Electrical Computer Engineering Science QIS Physics Applied Quantum Physics Chemistry Quantum mechanics, Quantum optics, Circuit QED, Materials Science http://quantuminstitute.yale.edu/ 2 Is quantum information carried by waves or by particles? YES! 3 Is quantum information analog or digital? YES! 4 Quantum information is digital: Energy levels of a quantum system are discrete. We use only the lowest two. Measurement of the state of a qubit yields ENERGY (only) 1 classical bit of information. 4 3 2 excited state 1 =e = ↑ 1 0 } ground state 0 =g = ↓ 5 Quantum information is analog: A quantum system with two distinct states can exist in an Infinite number of physical states (‘superpositions’) intermediate between ↓ and ↑ . Bug: We are uncertain which state the bit is in. Measurement results are truly random. Feature: Qubit is in both states at once, so we can do parallel processing. Potential exponential speed up. 6 Quantum Computing is a New Paradigm • Quantum computing: a completely new way to store and process information. • Superposition: each quantum bit can be BOTH a zero and a one.
    [Show full text]
  • Quantum Error Correction Todd A
    Quantum Error Correction Todd A. Brun Summary Quantum error correction is a set of methods to protect quantum information—that is, quantum states—from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space, without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Most work on quantum error correction has focused on systems of quantum bits, or qubits, which are two-level quantum systems. These can be physically realized by the states of a spin-1/2 particle, the polarization of a single photon, two distinguished levels of a trapped atom or ion, the current states of a microscopic superconducting loop, or many other physical systems. The most widely-used codes are the stabilizer codes, which are closely related to classical linear codes. The code space is the joint +1 eigenspace of a set of commuting Pauli operators on n qubits, called stabilizer generators; the error syndrome is determined by measuring these operators, which allows errors to be diagnosed and corrected.
    [Show full text]
  • Arxiv:Quant-Ph/9705032V3 26 Aug 1997
    CALT-68-2113 QUIC-97-031 quant-ph/9705032 Quantum Computing: Pro and Con John Preskill1 California Institute of Technology, Pasadena, CA 91125, USA Abstract I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum al- gorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault-tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high-precision experimental physics. A broad interdisci- plinary effort will be needed if quantum computers are to fulfill their destiny as the world’s fastest computing devices. This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, 17 December 1996. 1 Introduction The purpose of this panel discussion is to explore the future prospects for quantum computation. It seems to me that there are three main questions about quantum computers that we should try to address here: Do we want to build one? What will a quantum computer be good for? There is no doubt • that constructing a working quantum computer will be a great technical challenge; we will be persuaded to try to meet that challenge only if the potential payoff is correspondingly great.
    [Show full text]