Fault-tolerant quantum computation for local leakage faults

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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Is error detection helpful on IBM 5Q chips?

Quantum Information and Computation ◽

10.26421/qic18.11-12-4 ◽

2018 ◽

Vol 18 (11&12) ◽

pp. 949-964 ◽

Cited By ~ 1

Author(s):

Christophe Vuillot

Keyword(s):

Quantum Computation ◽

Error Detection ◽

Fault Tolerant ◽

Quantum Circuits ◽

Average Improvement ◽

Show Evidence ◽

Fault Tolerant Design

This paper reports on experiments realized on several IBM~5Q chips which show evidence for the advantage of using error detection and fault-tolerant design of quantum circuits. We show an average improvement of the task of sampling from states that can be fault-tolerantly prepared in the [4,2,2] code, when using a fault-tolerant technique well suited to the layout of the chip. By showing that fault-tolerant quantum computation is already within our reach, the author hopes to encourage this approach.

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Optimal two-qubit circuits for universal fault-tolerant quantum computation

npj Quantum Information ◽

10.1038/s41534-021-00424-z ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Andrew N. Glaudell ◽

Neil J. Ross ◽

Jacob M. Taylor

Keyword(s):

Lower Bound ◽

Normal Form ◽

Quantum Computation ◽

Normal Forms ◽

Fault Tolerant ◽

Quantum Circuits ◽

Worst Case ◽

Synthesis Algorithm ◽

Phase Gate ◽

Controlled Phase Gate

AbstractWe study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of $$5{{\rm{log}}}_{2}(\frac{1}{\epsilon })+O(1)$$ 5 log 2 ( 1 ϵ ) + O ( 1 ) on the number of CS gates required to ϵ-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.

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Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

Quantum Information Processing ◽

10.1007/s11128-021-03170-5 ◽

2021 ◽

Vol 20 (7) ◽

Author(s):

Ismail Ghodsollahee ◽

Zohreh Davarzani ◽

Mariam Zomorodi ◽

Paweł Pławiak ◽

Monireh Houshmand ◽

...

Keyword(s):

Quantum Computation ◽

Quantum Computer ◽

Quantum Circuit ◽

Quantum Circuits ◽

Connectivity Matrix ◽

Circuit Optimization ◽

Novel Approach ◽

The Matrix ◽

Minimum Number ◽

Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

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Competing ν = 5/2 fractional quantum Hall states in confined geometry

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1614543113 ◽

2016 ◽

Vol 113 (44) ◽

pp. 12386-12390 ◽

Cited By ~ 20

Author(s):

Hailong Fu ◽

Pengjie Wang ◽

Pujia Shan ◽

Lin Xiong ◽

Loren N. Pfeiffer ◽

...

Keyword(s):

Quantum Computation ◽

Filling Factor ◽

Fault Tolerant ◽

Quantum Hall ◽

Point Contact ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Topological Quantum ◽

Quantum Point ◽

Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

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MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES

International Journal of Quantum Information ◽

10.1142/s0219749909005699 ◽

2009 ◽

Vol 07 (06) ◽

pp. 1053-1203 ◽

Cited By ~ 13

Author(s):

ROBERT RAUßENDORF

Keyword(s):

Computational Model ◽

Quantum Computation ◽

Quantum Logic ◽

Network Model ◽

Quantum Computer ◽

Fault Tolerant ◽

Cluster State ◽

Building Blocks ◽

Network Simulator ◽

Classical Level

In this thesis, we describe the one-way quantum computer [Formula: see text], a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the [Formula: see text], describe the underlying computational model and demonstrate that the [Formula: see text] can be operated fault-tolerantly. In Sec. 2, we show that the [Formula: see text] can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the [Formula: see text] as a network simulator is not adequate in every respect. In Sec. 3, we derive the computational model underlying the [Formula: see text], which is very different from the quantum logic network model. The [Formula: see text] has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of [Formula: see text] quantum algorithms. Further, all information that is processed with the [Formula: see text] is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The [Formula: see text] is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource. In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the [Formula: see text]. Further, we outline the concept of checksums in the context of the [Formula: see text], which may become an element in future practical and adequate methods for fault-tolerant [Formula: see text] computation.

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