Quantum circuits for measuring Levin-Wen operators

Bonesteel, N. E.; DiVincenzo, David P.

doi:10.1103/physrevb.86.165113

Cited by 31 publications

(40 citation statements)

References 37 publications

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“…We furthermore quantify the effect of non-local two-qubit correlated errors, which would be expected in arrays of qubits coupled by a polynomially decaying interaction, and when using many-qubit coupling devices. We surprisingly find that the surface code is very robust to this class of errors, despite a provable lack of a threshold error rate when such errors are present.Many different approaches to achieving reliable quantum computation are under investigation [1][2][3][4][5]. The current most practical known approach, the Kitaev surface code [6,7], calls for a 2-D array of qubits with nearest neighbor interactions and a universal set of quantum gates with error rates below an approximate threshold of 1% [8][9][10].…”

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confidence: 99%

Quantifying the effects of local many-qubit errors and nonlocal two-qubit errors on the surface code

Fowler

Martinis

2014

Phys. Rev. A

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Topological quantum error correction codes are known to be able to tolerate arbitrary local errors given sufficient qubits. This includes correlated errors involving many local qubits. In this work, we quantify this level of tolerance, numerically studying the effects of many-qubit errors on the performance of the surface code. We find that if increasingly large area errors are at least moderately exponentially suppressed, arbitrarily reliable quantum computation can still be achieved with practical overhead. We furthermore quantify the effect of non-local two-qubit correlated errors, which would be expected in arrays of qubits coupled by a polynomially decaying interaction, and when using many-qubit coupling devices. We surprisingly find that the surface code is very robust to this class of errors, despite a provable lack of a threshold error rate when such errors are present.Many different approaches to achieving reliable quantum computation are under investigation [1][2][3][4][5]. The current most practical known approach, the Kitaev surface code [6,7], calls for a 2-D array of qubits with nearest neighbor interactions and a universal set of quantum gates with error rates below an approximate threshold of 1% [8][9][10]. Superconducting qubits with error rates at the surface code threshold now exist [11].There is extensive prior work showing the existence of a threshold error rate when arbitrary quantum error correction codes are subjected to a wide variety of noise models, including algebraically decaying two-body correlated noise [12], Gaussian non-Markovian noise [13], and arbitrarily many-body correlated noise [14]. In this work we focus on the simulated performance of the surface code below threshold.To date, when the surface code has been simulated, quantum gates have only had the potential to introduce errors on the qubits they manipulated directly. In reality, manipulating any given qubit may disturb the state of a large number of surrounding qubits. Not all types of disturbance are particularly dangerous. Small random or systematic rotations of surrounding qubits lead only to independent random errors. Only correlated manyqubit errors deserve specific attention. This distinction is discussed in detail in Section I. In this work we present a detailed study of precisely how well the surface code can handle this class of correlated errors.Another important class of errors that has not received attention to date is those that would arise in an array of qubits interacting directly with one another via a polynomially decaying interaction such as the Coulomb or magnetic dipole interaction, or via a device coupling to many qubits. Pairs of qubits initially antiparallel can both flip without changing the energy of the total system. Two-qubit errors can therefore appear on widely separated qubits. We also present a detailed study of this class of correlated errors.The discussion is organized as follows. In Section I, the meaning of independent and correlated errors is dis-cussed in detail. In Section II, the sur...

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confidence: 99%

Quantifying the effects of local many-qubit errors and nonlocal two-qubit errors on the surface code

Fowler

Martinis

2014

Phys. Rev. A

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“…The measurement results are then used to detect and correct possible errors. Designing explicit quantum circuits for syndrome measurements and finding fault tolerant error correction schemes for specific variants of Turaev-Viro codes are subjects of ongoing research [9,16,24].…”

Section: Hyperbolic Turaev-viro Codementioning

confidence: 99%

Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes

Lavasani

Zhu

Barkeshli

2019

Quantum

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A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded with constant space overhead (i.e. finite encoding rate) in the limit of arbitrarily large code distance d through the use of topological codes associated to triangulations of hyperbolic surfaces. We introduce explicit protocols to demonstrate how Dehn twists of the hyperbolic surface can be implemented on the code through constant depth unitary circuits, without increasing the space overhead. The circuit for a given Dehn twist consists of a permutation of physical qubits, followed by a constant depth local unitary circuit, where locality here is defined with respect to a hyperbolic metric that defines the code. Applying our results to the hyperbolic Fibonacci Turaev-Viro code implies the possibility of applying universal logical gate sets on encoded qubits through constant depth unitary circuits and with constant space overhead. Our circuits are inherently protected from errors as they map local operators to local operators while changing the size of their support by at most a constant factor; in the presence of noisy syndrome measurements, our results suggest the possibility of universal fault tolerant quantum computation with constant space overhead and time overhead of O(d/ log d). For quantum circuits that allow parallel gate operations, this yields the optimal scaling of spacetime overhead known to date.

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“…22 Here we focus on a particular Levin-Wen model, namely the Fibonacci Levin-Wen model. 4,5 Its name takes its origin in the nature of the excitations above the ground states; indeed they are Fibonacci anyons with topological charge τ and fusion rules…”

Section: A Fibonacci Levin-wen Modelmentioning

confidence: 99%

“…2, following the plaquette reduction method of Ref. 5. The data and ancillary qubits are labeled according to the notation of Fig.…”

Section: A Fibonacci Levin-wen Modelmentioning

confidence: 99%

Methodology for bus layout for topological quantum error correcting codes

Wosnitzka

Pedrocchi

DiVincenzo

2016

EPJ Quantum Technol.

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Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them as basic building elements of a quantum code. We then propose a simple framework to determine the optimal experimental layout to realize quantum codes. We show that this engineering optimization problem can be reduced to the solution of standard binary linear programs. While solving such programs is a NP-hard problem, we propose a way to find scalable optimal architectures that require solving the linear program for a restricted number of qubits and couplers. We apply our methods to two celebrated quantum codes, namely the surface code and the Fibonacci code.

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Quantum circuits for measuring Levin-Wen operators

Cited by 31 publications

References 37 publications

Quantifying the effects of local many-qubit errors and nonlocal two-qubit errors on the surface code

Quantifying the effects of local many-qubit errors and nonlocal two-qubit errors on the surface code

Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes

Methodology for bus layout for topological quantum error correcting codes

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