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Cambridge University Press eBooks

Introduction to quantum fault tolerance

Panos Aliferis

Published Sep 5, 2013• 5 citations
Publisher

Abstract

One of the applications of quantum error correction is protecting quantum computers from noise. Certainly, there is nothing particularly quantum mechanical in the idea of protecting information by encoding it. Even ordinary digital computers use various fault tolerance methods at the software level to correct errors during the storage or the transmission of information; e.g., the integrity of the bits stored in hard disks is verified by using parity checks (checksums). In addition, for critical computing systems such as those inside airplanes or nuclear reactors, software fault tolerance methods are also applied during the processing of information; e.g., airplane control computers compare the results from multiple parallel processors to detect faults. In general, however, the hardware of modern computers is remarkably robust to noise, so that for most applications the processing of information can be executed with high reliability without using software error correction. In contrast to the ease and robustness with which classical information can be processed, the processing of quantum information appears at present to be much more challenging. Although constructing reliable quantum computing hardware is certainly a daunting task, we have nevertheless strong hopes that large-scale quantum computers, able to implement useful long computations, can in fact be realized. This optimism is founded on methods of quantum fault tolerance , which show that scalable quantum computation is, in principle, possible against a variety of noise processes.

DOI
10.1017/cbo9781139034807.007

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Cambridge University Press eBooks•Sep 5, 2013•0 citations
One of the applications of quantum error correction is protecting quantum computers from noise. Certainly, there is nothing particularly quantum mechanical in the idea of protecting information by encoding it. Even ordinary digital computers use various fault tolerance methods at the software level to correct errors during the storage or the transmission of information; e.g., the integrity of the bits stored in hard disks is verified by using parity checks (checksums). In addition, for critical computing systems such as those inside airplanes or nuclear reactors, software fault tolerance methods are also applied during the processing of information; e.g., airplane control computers compare the results from multiple parallel processors to detect faults. In general, however, the hardware of modern computers is remarkably robust to noise, so that for most applications the processing of information can be executed with high reliability without using software error correction. In contrast to the ease and robustness with which classical information can be processed, the processing of quantum information appears at present to be much more challenging. Although constructing reliable quantum computing hardware is certainly a daunting task, we have nevertheless strong hopes that large-scale quantum computers, able to implement useful long computations, can in fact be realized. This optimism is founded on methods of quantum fault tolerance , which show that scalable quantum computation is, in principle, possible against a variety of noise processes.
Quantumcomputation is the modern version of Schrödinger’s cat experiment. It is backed up in principle by the theory and thinking about it can make people equally uncomfortable and excited. Besides, its practical realization seems so extremely challenging that some people even doubt it is possible. On the other hand, we are nowadays much closer to realizing quantum computation and in addition, it has much more implications than Schrödinger’s original cat experiment. One of the major difficulties in realizing quantum computation is the inevitable presence of noise in realistic quantum devices which makes the direct realization of quantum computers impossible. In order to protect quantum information and quantum processes against noise, quantum error correction and fault-tolerance have been devised. Although the gap between experiments and the requirements of fault-tolerance is still daunting, the field of quantum error correction and fault-tolerance extends and influences architectural decisions from the hardware to the ideal quantum programs that we want to run. That is why it has the potential to make or break the practicality of quantum computation and a lot of research effort goes into this field. In this thesis we investigate and improve several aspects of fault-tolerant schemes and quantum error correction. We implement an experiment which validates on a small device the usefulness of fault-tolerance for quantum computation. We investigate the advantages of harnessing quantum continuous degrees of freedom present in the lab to protect discrete quantum information in a scalable way. We establish a framework to analyze the fault-tolerant properties of code deformation techniques which are versatile techniques to process quantum information protected by an error correcting code. We also present some novel code deformation techniques with the potential to increase reliability. Finally we define a new class of quantum error correcting codes, quantum pin codes, with built in capabilities for fault-tolerant quantum gates. We give some practical constructions and show some protocols with interesting parameters. The roads towards universal and fault-tolerant quantum computation are still steep but research efforts are pushing in the right directions.
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring and actively correcting the hardware faults. We discuss parallels and differences with similar methods for ordinary digital computation, we discuss some of the noise models used in designing and analyzing noisy quantum circuits, and we sketch the logic of some of the central results in this area of research.
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve fragile quantum states without copying them, measuring them directly, or destroying the information they encode. Driven by rapid progress in both theory and experiment, this challenge has grown into one of the most active areas of quantum information science. This tutorial gives a guided introduction to modern QEC, developing the core concepts of codes, syndromes, stabilizers, decoding, and fault tolerance before connecting them to major code families and current research directions. We cover both established constructions and newer developments, including topological and subsystem codes, bosonic and qudit codes, dynamical codes, and quantum low-density parity-check (qLDPC) codes. The emphasis is on building operational understanding: explaining not only what the main objects are, but how they are used in code design, error diagnosis, decoding, and fault-tolerant computation. The tutorial is intended for newcomers seeking a first path through QEC, as well as researchers looking for a coherent reference for the concepts, code families, and tools that arise in current work.
One reason why building large-scale quantum computers will be particularly challenging is that quantum computers are far more susceptible to making errors than conventional digital computers. I will explain the principles of quantum error correction and fault-tolerant quantum computation, which can enable a properly designed quantum computer with imperfect components to achieve good reliability. Some recent developments in the theory of quantum fault tolerance will be reviewed, including quantum error-correcting codes for systems described by continuous quantum variables, robust storage of quantum information based on topological principles, and applications of quantum error-correcting codes to quantum cryptography.
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.
The principles of fault tolerance In this chapter we will consider some of the practical difficulties in building a large-scale quantum computing device. This discussion relies heavily upon the prior chapters that introduced faulttolerant quantum computation. Assuming that fault tolerance is possible allows us to focus on the physical realization of these ideas with a few specific examples. Before going into detail, we review the governing ideas behind any fault-tolerant architecture. These are the necessary components that we analyze in this chapter: good quantum memory, high-fidelity quantum operations, long-range quantum gates, and highly parallel operation, such that error correction in different sections of the device can be accomplished at the same time. While a wide variety of potential implementations may be possible, the goal of a fault-tolerant architecture is not only to be scalable, i.e., to be able to run an arbitrarily large computation with at most polynomial overhead [S95, S96e], but also to be as efficient as possible. Efficiency in this context means using the fewest physical resources (quantum bits, time, control operations) necessary to accomplish the desired computation [S03b]. From this perspective, the recipe for fault tolerance is well established. First, we need to identify what quantum operations are available for the various quantum bits at our disposal. Developing error models for these operations forms the bulk of this chapter. Important questions about operations include noise, implementation time, and bandwidth (how many such operations may be performed in parallel).