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Fault-Tolerant Quantum Computation for Local Leakage Faults

Panos Aliferis, Barbara M. Terhal

Published Nov 7, 2005• 41 citations
OpenAlex

Abstract

We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage faults by using so-called leakage reduction units such as quantum teleportation. We describe ways to limit the use of leakage reduction while keeping the quantum circuits fault-tolerant. We also show that measurement-based computation is inherently tolerant against leakage faults. 1

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Fault-tolerant quantum computation for local leakage faults

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We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage by using appropriate leakage-reduction units such as quantum teleportation. The leakage noise is described microscopically, by Hamiltonian couplings, and the noise is treated coherently, similar to general non-Markovian noise analyzed in Refs. \cite{Terhal04} and \cite{Aliferis05b}. We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits fault-tolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based computation.

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We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage by using appropriate leakage-reduction units such as quantum teleportation. The leakage noise is described by a Hamiltonian and the noise is treated coherently, similar to general non-Markovian noise analyzed in Refs. quant-ph/0402104 and quant-ph/0504218. We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits fault-tolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based computation.

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We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage faults by using so-called leakage reduction units such as quantum teleportation. We describe ways to limit the use of leakage reduction while keeping the quantum circuits fault-tolerant. We also show that measurement-based computation is inherently tolerant against leakage faults. 1
We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage by using appropriate leakage-reduction units such as quantum teleportation. The leakage noise is described microscopically, by Hamiltonian couplings, and the noise is treated coherently, similar to general non-Markovian noise analyzed in Refs. \cite{Terhal04} and \cite{Aliferis05b}. We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits fault-tolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based computation.
We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage by using appropriate leakage-reduction units such as quantum teleportation. The leakage noise is described by a Hamiltonian and the noise is treated coherently, similar to general non-Markovian noise analyzed in Refs. quant-ph/0402104 and quant-ph/0504218. We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits fault-tolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based computation.
Physical implementations of cryptographic algorithms leak information, which makes them vulnerable to so-called side-channel attacks.Cryptography is now used in an ever-increasing variety of scenarios, and the assumption that the execution of cryptosystems is physically insulated is often not realistic.The field of leakage resilience proposes to mitigate side-channel attacks by designing protocols that are secure even if information leaks during execution.In this work, we study leakage-resilient computation, which concerns the problem of performing secure universal computation in the presence of leakage.Fault-tolerant quantum computation is concerned with the problem of noise in quantum computers.Since it is very hard to insulate quantum systems from noise, fault tolerance proposes schemes for performing computations correctly even if some noise is present.It turns out that there exists a connection between leakage resilience and fault tolerance.In this work, we show that leakage in a classical circuit is a form of noise, when the circuit is interpreted as quantum.We then prove that for an arbitrary leakage model, there exists a corresponding noise model in which a circuit that is fault-tolerant against the noise model is also resilient against the given leakage model.We also show how to use constructions for fault tolerance to implement classical circuits that are secure in specific leakage models.This is done by establishing criteria in which quantum circuits can be converted into classical circuits in such a way that the leakage resilience property is preserved.Using these criteria, we convert an implementation of universal fault-tolerant quantum computation into a classical leakageresilient compiler, i.e., a scheme that compiles an arbitrary circuit into a circuit of the same functionality that is leakage-resilient.vi 4.9 (a): Circuito de codificação para |0 no código de Steane.O circuito que codifica |+ é o mesmo, com a diferença de que alvos e controles são revertidos, e estados |0 são revertidos em |+ e vice-versa.(b):
We describe and analyze leakage errors of singlet-triplet qubits. Even though leakage errors are a natural problem for spin qubits encoded using quantum dot arrays, they have obtained little attention in previous studies. We describe the realization of leakage correction protocols that can be implemented together with the quantum error correction protocol of the surface code. Furthermore we construct explicit leakage reduction units that need, in the ideal setup, as few as three manipulation steps. Our study shows that leakage errors can be corrected without the need of measurements and at the cost of only a few additional ancilla qubits and gate operations compared to standard quantum error correction codes.
A quantum computer is a powerful machine that provides a new approach to information processing based on quantum mechanics. However, basically, qubits are very vulnerable to errors, thus a quantum error correction code (QECC) is needed to build a reliable quantum computer. Moreover, simply using QECCs is not sufficient in order that a quantum computer can tolerate errors. In quantum computation, each operation must be performed on the encoded states. Even when the gates used to perform these operations are noisy, the quantum computation must be tolerable to the errors. This is called fault-tolerant quantum computation and it is an essential condition for implementing a quantum computer. However, considering the fault tolerance, the overhead of the quantum computer increases exponentially. In this paper, we introduce fault-tolerant quantum computation and schemes to reduce the its overhead.
Quantum computation has the potential to solve certain mathematical and physical problems faster than a classical computer. However, one of the key challenges to realizing a quantum computing device is controlling systematic errors and maintaining the coherence of the quantum state. In addition, once a scalable quantum computer is built, we must be able to fault-tolerantly communicate a quantum algorithm to the physical device. In this dissertation, we take several significant steps towards the realization of a quantum computer. We develop a framework for use with any proposed technology to map a quantum algorithm into fault-tolerant machine instructions. Within this framework, we combat errors and decoherence by introducing quantum error correction and fault tolerance into a quantum circuit. We analyze specific fault-tolerant circuitry on two general architectures, nonlocal and nearest-neighbor, to determine failure thresholds of the physical circuit components. These failure thresholds allow physicists to evaluate technology proposals. Our goal is to provide design tools, failure thresholds, and fault-tolerant constructions to combat the faultiness of quantum computation.