High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction

Fukui, Kosuke; Tomita, Akira; Okamoto, Atsushi; Fujii, Keisuke

doi:10.1103/physrevx.8.021054

Cited by 193 publications

(243 citation statements)

References 63 publications

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“…Meanwhile, there have also been studies on scaling up the GKP code by concatenating it with a repetition code [22], the [ [4,2,2]] code [22,23], and the surface code [24][25][26], or by using cluster states and measurement-based quantum computation [25,27,28]. One of the recurring themes in these previous works is that the continuous error information gathered during the GKP code error correction protocol can boost the performance of the next layer of the concatenated error correction.…”

Section: Introductionmentioning

confidence: 99%

“…One of the recurring themes in these previous works is that the continuous error information gathered during the GKP code error correction protocol can boost the performance of the next layer of the concatenated error correction. For example, while the surface code by itself has the code capacity threshold ∼11% [15], the threshold can be increased to ∼14% if the additional error information from GKP-stabilizer measurements is incorporated in the surface code error correction protocol [24][25][26]. These code capacity thresholds are, however, computed by assuming noiseless GKP and surface code stabilizer measurements, or equivalently, by assuming that ideal GKP states (with an infinitely large squeezing) are used for the stabilizer measurements.…”

Section: Introductionmentioning

confidence: 99%

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Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code

Noh

Chamberland²

2020

Phys. Rev. A

148

194

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Bosonic quantum error correction is a viable option for realizing error-corrected quantum information processing in continuous-variable bosonic systems. Various single-mode bosonic quantum error-correcting codes such as cat, binomial, and GKP codes have been implemented experimentally in circuit QED and trapped ion systems. Moreover, there have been many theoretical proposals to scale up such single-mode bosonic codes to realize large-scale fault-tolerant quantum computation. Here, we consider the concatenation of the single-mode GKP code with the surface code, namely, the surface-GKP code. In particular, we thoroughly investigate the performance of the surface-GKP code by assuming realistic GKP states with a finite squeezing and noisy circuit elements due to photon losses. By using a minimum-weight perfect matching decoding algorithm on a 3D space-time graph, we show that fault-tolerant quantum error correction is possible with the surface-GKP code if the squeezing of the GKP states is higher than 11.2dB in the case where the GKP states are the only noisy elements. We also show that the squeezing threshold changes to 18.6dB when both the GKP states and circuit elements are comparably noisy. At this threshold, each circuit component fails with probability 0.69%. Finally, if the GKP states are noiseless, fault-tolerant quantum error correction with the surface-GKP code is possible if each circuit element fails with probability less than 0.81%. We stress that our decoding scheme uses the additional information from GKPstabilizer measurements and we provide a simple method to compute renormalized edge weights of the matching graphs. Furthermore, our noise model is general as it includes full circuit-level noise.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code

Noh

Chamberland²

2020

Phys. Rev. A

148

194

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“…This work opens the possibility of all-optical implementation of various nonlinear interactions which are currently available only at mechanical or microwave frequencies, and motivates advanced integrated optical setups. Conditional quantum Rabi gates by current hybrid quantum optics technology are directly applicable to extend quantum repeaters for secure quantum optical communication [100][101][102][103] and in future, combine it with error correction strategies [104][105][106][107][108][109]. It will stimulate further the development of other implementations of the RI and other deterministic nonlinear interactions beyond rotating-wave approximation at the optical frequencies.…”

Section: Resultsmentioning

confidence: 99%

Hybrid Rabi interactions with traveling states of light

2020

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Keywords: quantum non-Gaussian states of light, quantum optics with photon addition and subtraction, hybrid discrete-continuousvariable quantum information, measurement-induced quantum operations Abstract Hybrid interactions between light and two-level systems and their nonlinear nature are crucial components of advanced quantum information processing and quantum networks. Rabi interaction (RI) exhibits the hybrid nonlinear nature, but its implementation is challenging at optical frequencies where the rotating wave approximation (RWA) is valid. Here, we propose a setup to conditionally induce RI between discrete variable and continuous variable of traveling beams of light. We show that our scheme can generate RI on weak states of light, where signatures of the nonlinear quantum effects are preserved for typical experimental losses. These results prove that a hybrid RI can be realized in all-optical setups, and open a way to experimental investigations of nonlinear quantum optics beyond RWA.

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“…By performing the error correction scheme of [9], measuring the q and p quadratures to perform error correction will always project the state onto a state with a single shift error in q and p. Lastly, we point out that d in definition 5 relates to the largest allowed size of the shift error which occurs during the protocol. This should 5 Using the optimizations considered in [18], using Knill error correction could potentially increase the threshold of p 6 to a larger value.…”

Section: Fault-tolerant Definitionsmentioning

confidence: 99%

“…photon loss), recently it has been shown that GKP codes have better error correction capabilities than such codes under the assumption of perfect encoding and decoding [1][2][3]. In addition, it has been shown how GKP codes can be concatenated with the toric code in order to achieve larger threshold values compared to toric codes with bare physical qubits [4][5][6]. Lastly, given a supply of GKP-encoded Pauli eigenstates, universal fault-tolerant quantum computation can be achieved using only Gaussian operations [7].…”

Section: Introductionmentioning

confidence: 99%

Fault-tolerant preparation of approximate GKP states

Shi

Chamberland²,

Cross³

2019

New J. Phys.

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Gottesman-Kitaev-Preskill (GKP) states appear to be amongst the leading candidates for correcting errors when encoding qubits into oscillators. However the preparation of GKP states remains a significant theoretical and experimental challenge. Until now, no clear definitions for fault-tolerantly preparing GKP states have been provided. Without careful consideration, a small number of faults can lead to large uncorrectable shift errors. After proposing a metric to compare approximate GKP states, we provide rigorous definitions of fault-tolerance and introduce a fault-tolerant phase estimation protocol for preparing such states. The fault-tolerant protocol uses one flag qubit and accepts only a subset of states in order to prevent measurement readout errors from causing large shift errors. We then show how the protocol can be implemented using circuit QED. In doing so, we derive analytic expressions which describe the leading order effects of the nonlinear dispersive shift and Kerr nonlinearity. Using these expressions, we show that to mitigate the nonlinear dispersive shift and Kerr terms would require the protocol to be implemented on time scales four orders of magnitude longer than the time scales relevant to the protocol for physically motivated parameters. Despite these restrictions, we numerically show that a subset of the accepted states of the fault-tolerant phase estimation protocol maintain good error correcting capabilities even in the presence of noise.

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High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction

Cited by 193 publications

References 63 publications

Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code

Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code

Hybrid Rabi interactions with traveling states of light

Fault-tolerant preparation of approximate GKP states

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