Nonuniform code concatenation for universal fault-tolerant quantum computing (original) (raw)

A Low-Overhead Hybrid Approach for Universal Fault-Tolerant Quantum Computation

arXiv: Quantum Physics, 2016

As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, a hybrid approach is proposed which combines the code concatenation technique with the other mentioned approaches. The proposed approach outperforms code concatenation in terms of both number of qubits and error threshold and also significantly reduces the resource overhead of code switching, magic state distillation and pieceable fault-tolerance at the cost of reducing the effective distance of the concatenated code for implementing non-transversal gates.

Low-Overhead Code Concatenation Approaches for Universal Quantum Computation

2017

As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, two approaches for universal fault-tolerant quantum computation, mainly based on code concatenation, are proposed. The proposed approaches outperform code concatenation in terms of both number of qubits and code distance and has also significantly less resource overhead than code switching, magic state distillation and pieceable fault-tolerance at the cost of reducing the effective distance of the concatenated code for implementing non-transversal gates.

Universal Fault-Tolerant Quantum Computation with Only Transversal Gates and Error Correction

Physical Review Letters, 2013

A general scheme to perform universal quantum computation within decoherence-free subspaces (DFSs) of a system's Hilbert space is presented. This scheme leads to the first fault-tolerant realization of universal quantum computation on DFSs with the properties that (i) only one-and two-qubit interactions are required, and (ii) the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under "collective decoherence" (qubit-permutation-invariant system-bath coupling). Our results have immediate relevance to a number of solid-state quantum computer implementations, in particular those in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled GaAs quantum dot arrays and the Si: 31 P nuclear spin arrays.

Fault-Tolerant Error Correction with Efficient Quantum Codes

Physical Review Letters, 1996

We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The quantum networks obtained are fault tolerant, that is, they can function successfully even if errors occur during the error correction. Our construction is derived using a recently introduced group-theoretic framework for unifying all known quantum codes.

Fault-tolerant quantum error correction code conversion

2011

In this paper we demonstrate how data encoded in a five-qubit quantum error correction code can be converted, fault-tolerantly, into a seven-qubit Steane code. This is achieved by progressing through a series of codes, each of which fault-tolerantly corrects at least one error. Throughout the conversion the encoded qubit remains protected. We found, through computational search, that the method used to convert between codes given in this paper is optimal.

A comparative code study for quantum fault tolerance

Quantum Information and Computation, 2009

We study a comprehensive list of quantum codes as candidates for codes used at the physical level in a fault-tolerant code architecture. Using the Aliferis-Gottesman-Preskill (AGP) ex-Rec method we calculate the pseudo-threshold for these codes against depolarizing noise at various levels of overhead. We estimate the logical noise rate as a function of overhead at a physical error rate of p_0=1times10−4p_0=1 \times 10^{-4}p_0=1times10−4. The Bacon-Shor codes and the Golay code are the best performers in our study.

A Scheme of Concatenated Quantum Code to Protect against both Computational Error and an Erasure

Corr, 2010

We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used encoding and decoding via scheme of GHZ states for protection against the occurrence of one quantum erasure. Grassl et al.[4] considered a situation in which the position of the erroneous qubits is known. According to classical coding theory, they called this model the quantum erasure channel (QEC). Alterations or changes caused by the environment can be characterized as being of two types: (i) those that satisfy to certain conditions that allow their correction, i.e., that agree with the conditions established by Knill and Laflamme[2]. They are represented by Pauli matrices and are called "computational errors"[5]. Such matrices constitute the computational space, and (ii) those that lead the state encoded out of the computational space. These alterations characterize the QEC. Erasures are both detectable and locatable, which suggests that they should be easier to rectify than computational errors. In fact, quantum communication channels can tolerate a higher rate of erasure (p erasure < 0.5) than depolarization (p comp < 1/3)[6]. Dawson et al.[7] considered an error model which contains both erasure and computational errors, finding that fault-tolerant quantum computation is possible with p erasure < 3 × 10 −3 and p comp < 10 −4 .

Leveraging automorphisms of quantum codes for fault-tolerant quantum computation

2013 IEEE International Symposium on Information Theory, 2013

Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal set of quantum gates that act on the code space of an underlying quantum code. To implement such a universal gate set faulttolerantly is an expensive task in terms of physical operations, and any possible shortcut to save operations is potentially beneficial and might lead to a reduction in overhead for faulttolerant computations. We show how the automorphism group of a quantum code can be used to implement some operators on the encoded quantum states in a fault-tolerant way by merely permuting the physical qubits. We derive conditions that a code has to satisfy in order to have a large group of operations that can be implemented transversally when combining transversal CNOT with automorphisms. We give several examples for quantum codes with large groups, including codes with parameters [[8, 3, 3]], [[15, 7, 3]], [[22, 8, 4]], and [[31, 11, 5]].

Teleportation-based Fault-tolerant Quantum Computation in Multi-qubit Large Block Codes

2015

A major goal for fault-tolerant quantum computation (FTQC) is to reduce the overhead needed for error correction. One approach is to use block codes that encode multiple qubits, which can achieve significantly higher rates for the same code distance than single-qubit code blocks or topological codes. We present a scheme for universal quantum computation using multi-qubit Calderbank-Shor-Steane (CSS) block codes, where codes admitting different transversal gates are used to achieve universality, and logical teleportation is used to move qubits between code blocks. All circuits for both computation and error correction are transversal. We also argue that single shot fault-tolerant error correction can be done in Steane syndrome extraction. Then, we present estimates of information lifetime for a few possible codes, which suggests that highly nontrivial quantum computations can be achieved at reasonable error rates, using codes that require significantly less than 100 physical qubits per logical qubit.

Experimental Implementation of a Concatenated Quantum Error-Correcting Code

Physical Review Letters, 2005

Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct against phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error correcting codes offers a practical tool to handle realistic noise contributed by both independent and correlated errors.