The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of quantum systems; an error corrected during the previous cycle may reoccur later due to physical processes specific for each physical implementation of the qubits. In this paper we study quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm we propose allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code when the two logical qubits $\mid 0_L>$ and $\mid 1_L>$ are entangled states of $2^{n}$ basis states in $\mathcal{H}_{2^n}$.
Correlated Atom Loss as a Resource for Quantum Error Correction
University of Strasbourg（斯特拉斯堡大学）；CNRS（法国国家科学研究中心）；CESQ and ISIS (UMR 7006)（CESQ与ISIS联合研究实验室（UMR 7006））；aQCess；QPERFECT SAS（QPERFECT公司）；University of Luxembourg（卢森堡大学）；Institut Universitaire de France (IUF)（法国高等研究院）
Preserving Heisenberg-Limited Metrological Information during Storage via Correlated-Noise Correction
Shanghai Jiao Tong University（上海交通大学）；Anhui University（安徽大学）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）
The error model of a quantum computer is essential for optimizing quantum algorithms to minimize the impact of errors using quantum error correction or error mitigation. Noise with temporal correlations, e.g. low-frequency noise and context-dependent noise, is common in quantum computation devices and sometimes even significant. However, conventional tomography methods have not been developed for obtaining an error model describing temporal correlations. In this paper, we propose self-consistent tomography protocols to obtain a model of temporally correlated errors, and we demonstrate that our…
We introduce a technique for the suppression of state-dependent and correlated measurement errors, which are commonly observed on modern superconducting quantum devices. Our method leverages previous results, establishing that correlated errors tend to be physically localised on quantum devices to perform characterisations over the coupling map of the device, and to join overlapping measurement calibrations as a series of sparse matrices. We term this `Coupling Map Calibration'. We quantitatively demonstrate the advantages of our proposed error mitigation system design across a range of curren…
Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer co…
This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ unitary operator. In previous literature, a recursive quantum error correction scheme can be used to protect $k$ qubits using $(k+1)$-qubit ancilla. We implement this scheme on 3-qubit and 5-qubit channels using the IBM quantum computers, where we uncover an error in the previous paper related to the decomposition of the encoding/decoding operator into elementary quantum gates. Here, we …
Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error rates. We propose a protocol for monitoring error rates in real time without interrupting the quantum error correction. Any adaptation of the quantum error correction code or its implementation circuit is not required. The protocol can be directly applied to the most advanced quantum error correction techniques, e.g. surface code. A Gaussian processes algorithm …
We study efficient quantum error correction schemes for the fully correlated channel on an $n$-qubit system with error operators that assume the form $σ_x^{\otimes n}$, $σ_y^{\otimes n}$, $σ_z^{\otimes n}$. Previous schemes are improved to facilitate implementation. In particular, when $n$ is odd and equals $2k+1$, we describe a quantum error correction scheme using one arbitrary qubit $σ$ to protect the data state $ρ$ in a $2k$-qubit system. The encoding operation $σ\otimes ρ\mapsto Φ(σ\otimes ρ)$ only requires $3k$ CNOT gates (each with one control bit and one target bit). After the encoded …
We experimentally demonstrate that we can detect correlated errors in a twin-field quantum key distribution (TFQKD) system by using a technique that is related to self-consistent tomography. We implement a TFQKD system based on a fiber-Sagnac loop, in which Alice and Bob encode information in the phase of weak coherent states that propagate in opposite directions around the loop. These states interfere as they exit the loop and are detected by a third party, Charlie, who reports the results of their measurements to Alice and Bob. We find that it is possible for Alice and Bob to detect correlat…
To improve the performance of multi-qubit algorithms on quantum devices it is critical to have methods for characterizing non-local quantum errors such as crosstalk. To address this issue, we propose and test an extension to the analysis of simultaneous randomized benchmarking data -- correlated randomized benchmarking. We fit the decay of correlated polarizations to a composition of fixed-weight depolarizing maps to characterize the locality and weight of crosstalk errors. From these errors we introduce a crosstalk metric which indicates the distance to the closest map with only local errors.…
Topological error correction provides an effective method to correct errors in quantum computation. It allows quantum computation to be implemented with higher error threshold and high tolerating loss rates. We present a topological a error correction scheme with continuous variables based on an eight-partite Gaussian cluster state. We show that topological quantum correlation between two modes can be protected against a single quadrature phase displacement error occurring on any mode and some of two errors occurring on two modes. More interestingly, some cases of errors occurring on three mod…
To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large scale quantum computation with the GKP qubit [Phys. Rev. X. {\bf 8}, 021054 (2018)], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit level quantum error …
