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arXiv:quant-ph/0206025 · Physical Review Letters

Universal Fault-Tolerant Quantum Computation in the Presence of Spontaneous Emission and Collective Dephasing

Kaveh Khodjasteh, Daniel A. Lidar

Published Oct 23, 2002• 27 citations
arXivHTMLPDF

Abstract

A universal and fault-tolerant scheme for quantum computation is proposed which utilizes a class of error correcting codes that is based on the detection of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme is compatible with a number of promising solid-state and quantum-optical proposals for quantum computer implementations, such as quantum dots in cavities, electrons on helium, and trapped ions.

DOI
10.1103/physrevlett.89.197904

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A universal and fault-tolerant scheme for quantum computation is proposed which utilizes a class of error correcting codes that is based on the detection of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme is compatible with a number of promising solid-state and quantum-optical proposals for quantum computer implementations, such as quantum dots in cavities, electrons on helium, and trapped ions.
A method for quantum computation in the presence of spontaneous emission is proposed. The method combines strong and fast (dynamical decoupling) pulses and a quantum error correcting code that encodes n logical qubits into only n+1n+1n+1 physical qubits. Universal, fault-tolerant, quantum computation is shown to be possible in this scheme using Hamiltonians relevant to a range of promising proposals for the physical implementation of quantum computers.
Quantum computing is an exciting field that promises great improvements to our ability to solve certain intractable classes of problem. Implementing a quantum computer will require a physical system in which quantum effects are strongly evident. Many different physical systems have been proposed for this task, including ion traps, quantum dots, neutral atoms and photons. This thesis focuses on optical implementations of a quantum computer, and specifically on single-photon designs, as opposed to those utilising coherent states. Photonic systems have shown a great deal of promise for quantum computing tasks since it was shown by Knill, Laflamme and Milburn (KLM) that scalable efficient quantum computing could be performed using only linear optical elements and measurement. This was made viable through the use of error-correcting codes. The work in this thesis covers the use of error-correcting codes in single-photon linear optics quantum computing (LOQC). The central feature of these schemes is the parity code introduced by KLM and used to overcome the gate errors that are inherent in this type of LOQC. First is a discussion of an improved scheme that incorporates the fusion gates used in Browne and Rudolph's cluster state proposal in order to simplify the encoding and gate procedures. This results in high-probability gates with a resource usage comparable to the cluster state schemes. The remainder of the thesis examines the application of further error correcting codes to handle other errors that may arise in any practical implementation of an optical quantum computer. The most significant type of error in any optical system is photon loss, and hence an extension of the parity code is presented that allows loss errors to be detected and corrected. Procedures for performing universal quantum computation whilst employing this encoding are also described. These enable the establishment of loss thresholds for parity-state based LOQC, revealing this code is capable of handling up to 10\% loss in all elements during general computation, or 17\% if it is used solely as an active memory. Although loss is the most common type of optical error, other types of error will also become an issue when attempting to produce large quantum computing systems. An analysis of the error thresholds and resource usage which can be expected when applying a general error correcting code such as the Steane code to this type of LOQC system is also presented. The error thresholds and resource requirements established are greater than those found for cat state optical quantum computing, but fall below those calculated for cluster states. However, the resource requirements of the scheme are significantly smaller than the cluster state requirements for an equivalent circuit. Finally, a new experiment is proposed, achievable with today's technology, for testing the loss-tolerant encoding described earlier. Expansions of the experiment that would demonstrate tolerance of actual experimental error are also discussed.
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.
In this thesis, we consider steps towards building a useful quantum computer in the presence of realistic errors. We start by presenting a novel scheme for fault-tolerant quantum computation with Rydberg atoms. The scheme uses topological error correction codes to provide fault-tolerance and utilises electromagnetically induced transparency to perform entangling gates between qubits. We examine the benefits of this scheme compared to alternative approaches, and we investigate the errors that are likely to occur and how these can be managed. We then consider how to perform quantum computation with a surface code based quantum computer that has permanently faulty components. We study both faulty links between qubits, which prevent qubits from interacting, and faulty qubits themselves; such faults could affect a wide variety of physical implementations, including schemes that use superconducting qubits and those that use trapped ions. The approach we propose for dealing with these faulty components requires minimal modification to the quantum operations required by the surface code and should therefore be implementable by almost all current and future proposals for surface code based quantum devices. Finally, we consider how to perform fault-tolerant quantum computation with components that fail probabilistically. This section is largely motivated by quantum computation with linear optics and therefore focuses on quantum computation with cluster states. We show that these probabilistic failures can be tolerated providing the failure rate is suitably low, and we present methods for increasing error thresholds in the presence of such errors.
We propose a teleportation-based scheme to implement a universal set of quantum gates with a four-component cat code, assisted by appropriate entangled resource states and photon-number-resolving detection. The four-component cat code features the ability to recover from single-photon loss. Here we propose a concrete procedure to correct the single-photon loss, including detecting the single-photon-loss event and recovering the initial states. By concatenating with standard qubit error-correcting codes, we estimate the loss threshold for fault-tolerant quantum computation and obtain a significant improvement over the two-component cat code.