Giulio Chiribella, Michele Dall'Arno, Giacomo Mauro D'Ariano, Chiara Macchiavello, Paolo Perinotti
We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by exhibiting examples where the quantum packing bound is violated.
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We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant improvements to the fidelity bounds and optimal entanglement decay profiles.
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 …
Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand, do not require active error correction, but perform poorly in terms of minimum distance. In this paper, examples of degenerate quantum codes are constructed that have better minimum distance than decoherence free subspaces and allow some errors of small weight that do not require active error correction. In particular, two new families of [[n,1,>= sqrt(n)]]…
We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by $σ_x^{\otimes n}$, $σ_y^{\otimes n}$ and $σ_z^{\otimes n}$, where $n>2$ is the number of qubits encoding the codeword. It is proved that (i) $n$ qubits codeword encodes $(n-1)$ data qubits when $n$ is odd and (ii) $n$ qubits codeword implements a noiseless subsystem encoding $(n-2)$ data qubits when $n$ is even. Quantum circuits implementing these schemes are constructed.
We show that errors are not generated correlatedly provided that quantum bits do not directly interact with (or couple to) each other. Generally, this no-qubits-interaction condition is assumed except for the case where two-qubit gate operation is being performed. In particular, the no-qubits-interaction condition is satisfied in the collective decoherence models. Thus, errors are not correlated in the collective decoherence. Consequently, we can say that current quantum error correcting codes which correct single-qubit-errors will work in most cases including the collective decoherence.
Most of the research done on quantum error correction studies an error model in which each qubit is affected by noise, independently of the other qubits. In this paper we study a different noise model -- one in which the noise may be correlated with the qubits it acts upon. We show both positive and negative results. On the one hand, we show controlled-X errors cannot be perfectly corrected, yet can be approximately corrected with sub-constant approximation error. On the other hand, we show that no non-trivial quantum error correcting code can approximately correct controlled phase error with …
We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for degenerate systems. The same formalism can be used to find non-adiabatic corrections to the non-Abelian Wilczek-Zee geometric phase. These corrections are relevant to assess the validity of the practical implementation of the concept of fractional exchange statistics. We illustrate the formalism by exactly solving a time-dependent problem and comparing its solu…
We discuss experiments to produce and detect atom correlations in a degenerate or nearly degenerate gas of neutral atoms. First we treat the atomic analog of the celebrated Hanbury Brown Twiss experiment, in which atom correlations result simply from interference effects without any atom interactions.We have performed this experiment for both bosons and fermions. Next we show how atom interactions produce correlated atoms using the atomic analog of spontaneous four-wavemixing. Finally, we briefly mention experiments on a one dimensional gas on an atom chip in which correlation effects due to b…
Correlated Atom Loss as a Resource for Quantum Error Correction
研究通过利用原子损失的相关性，改进中性原子量子处理器的表面码纠错，显著降低逻辑错误概率并提升抗损失阈值。
A new simple entanglement measurement method is proposed for the bright EPR beams generated from a non-degenerate optical parametric amplifier operating at deamplification. Due to the output signal and idler modes are frequency degenerate and in phase, the needed phase shift of interference for the measurement of the correlated phase quadratures and anti-correlated amplitude quadratures can be accomplished by a quarter-wave plate and a half wave plate without separating the signal and idler beam. Therefore, phase locking and local oscillators are avoided.
Noise is the main obstacle for the realization of fault tolerant quantum information processing and secure communication over long distances. In this work, we propose a communication protocol relying on simple linear optics that optimally protects quantum states from non-Markovian or corre- lated noise. We implement the protocol experimentally and demonstrate the near ideal protection of coherent and entangled states in an extremely noisy channel. Since all real-life channels are exhibit- ing pronounced non-Markovian behavior, the proposed protocol will have immediate implications in improving…
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that are capable of implementing a universal set of gates with error rates below approximately 1%, requirements compatible with experimental reality. Consequently, a number of authors are attempting to squeeze additional performance out of the surface code. We describe an optimal complexity error suppression algorithm, parallelizable to O(1) given constant compu…
We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between physical qubits. We show that for short times the quantum error correction interprets such entanglement as errors and suppresses it. However for longer time, although quantum error correction is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.
We consider quantum error correction of quantum-noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kind of noise correlations have a strong negative impact on quantum error correction.
A five-level four-pulse phase-sensitive extended stimulated Raman adiabatic passage scheme is proposed to realize complete control of the population transfer branching ratio between two degenerate target states. The control is achieved via a three-node null eigenstate that can be correlated with an arbitrary superposition of the target states. Our results suggest that complete suppression of the yield of one of two degenerate product states, and therefore absolute selectivity in photochemistry, is achievable and predictable, even without studying the properties of the unwanted product state be…
We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.
Preserving Heisenberg-Limited Metrological Information during Storage via Correlated-Noise Correction
该研究提出关联噪声校正协议，可在量子探针存储阶段保护其量子费舍尔信息，为传感驱动的量子信息处理提供实用构建模块。
Concatenating quantum error-correcting codes with decoherence-free subspaces and vice versa
本文研究量子纠错码与无退相干子空间码的两种级联顺序，证明强关联错误下DFS作内码更优、独立错误下QECC作内码更优，并通过具体码例验证了容错性能。
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 …
Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expect degeneracy would simplify the decoding since two different errors might not and need not be distinguished …
Learning correlated noise in a 39-qubit quantum processor
本文提出一种提取量子器件检错子提取线路中噪声信息的方法，在39比特超导器件上构建图模型精确学习相关噪声，并证明准确的关联噪声模型对预测量子纠错亚阈值行为至关重要。
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 …
Characterizing the Burst Error Correction Ability of Quantum Cyclic Codes
本文研究了量子循环码的突发错误纠正能力，通过算法确定了其纠正极限，并提出了一种高效的解码器以提升突发错误纠正性能。
Fault-tolerant quantum computation techniques rely on weakly correlated noise. Here I show that it is enough to assume weak spatial correlations: time correlations can take any form. In particular, single-shot error correction techniques exhibit a noise threshold for quantum memories under spatially local stochastic noise.
A room-temperature cavity-magnonic source of correlated microwave pairs
本研究在室温下利用混合磁子-光子平台实现了相干微波对源，通过非退相干激发和非线性动力学产生真实随机性和多通道相关性，为经典和量子应用提供新途径。
Surface-Code Quantum Error Correction for Molecular Tweezer Arrays: Encoding, Layout, and Correlated Noise
本文针对分子光镊阵列的表面码量子纠错，构建了编码映射，对比不同旋转量子位维度的编码，揭示关联损耗空间嵌入的重要性及单扇区基准的局限性。
Double-pair Coulomb and Breit photon correction to the correlated relativistic energy
本文计算了双对修正对相关相对论能量的影响，采用贝塔-萨尔佩特方程并开发了数值方法，结果与非相对论量子电动力学的修正一致。
Mid-circuit correction of correlated phase errors using an array of spectator qubits
本文提出利用铯旁观者量子比特阵列，通过序列内读出、实时处理与前馈操作，在线路执行中途相干校正铷数据量子比特的关联相位错误，为扩展中性原子量子处理器提供了关键工具。
Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians
本文通过用高斯函数线性组合近似$1/r$因子，解决了fECGs中$1/r_{ix}1/r_{jy}$型算子矩阵元未知的难题，实现了Drachmann正则化相对论修正，为多原子体系势能面的高精度相对论修正和电子哈密顿量平方矩阵表示的构建提供了新途径。
Spatiotemporal Pauli processes: Quantum combs for modeling correlated noise in quantum error correction
本文提出时空泡利过程（SPPs）用于建模量子纠错中的相关噪声，通过多时间泡利扭动和过程张量映射，实现非马尔可夫动力学的高效表示，并通过表面码模拟验证其在临界行为中的应用。
The interplay between crystallinity and superfluidity is of great fundamental and technological interest in condensed matter settings. In particular, electronic quantum liquid crystallinity arises in the non-Fermi liquid, pseudogap regime neighboring a cuprate's unconventional superconducting phase. While the techniques of ultracold atomic physics and quantum optics have enabled explorations of the strongly correlated, many-body physics inherent in, e.g., the Hubbard model, lacking has been the ability to create a quantum degenerate Fermi gas with interparticle interactions---such as the stron…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can…
We create a one-dimensional strongly correlated quantum gas of $^{133}$Cs atoms with attractive interactions by direct laser cooling in 300~ms. After compressing and cooling the optically trapped atoms to the vibrational ground state along two tightly confined directions, the emergence of a non-Gaussian time-of-flight distribution along the third, weakly confined direction reveals that the system enters a quantum degenerate regime. We observe a strong reduction of two- and three-body spatial correlations and infer that the atoms are directly cooled into a highly correlated excited metastable s…
Non-degenerate SPDC photon-pair source for UV-A illumination
本研究提出一种基于二阶非线性晶体、通过自发参量下转换产生UV-A与红外非简并光子对的源，可解耦传感与探测波长以复用可见光相机技术，为紫外量子传感开辟新场景，有望推动生物医学、无损检测领域发展。
We present an exact solution of an experimentally realizable and strongly interacting one-dimensional spin system which is a limiting case of a quantum Ising model with long range interaction in a transverse and longitudinal field. Pronounced quantum fluctuations lead to a strongly correlated liquid ground state. For open boundary conditions the ground state manifold consists of four degenerate sectors whose quantum numbers are determined by the orientation of the edge spins. Explicit expressions for the entanglement properties, the excitation gap as well as the exact wave functions for a coup…
We analyze the emergence of correlated optical phenomena in the transmission of light through a waveguide that confines classical or ultracold quantum degenerate atomic ensembles. The conditions of the correlated collective response are identified in terms of atom density, thermal broadening, and photon losses by using stochastic Monte-Carlo simulations and transfer matrix methods of transport theory. We also calculate the "cooperative Lamb shift" for the waveguide transmission resonance, and discuss line shifts that are specific to effectively one-dimensional waveguide systems.
We provide an integration of the universal, perturbative explicitly correlated [2]$_\text{R12}$-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. Our proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction; these can be measured after having reached convergence in VQE. The RDMs are then combined with a set of molecular integrals. This computation comes a…
Error correction is of utmost necessity for large-scale quantum computing. Quantum error correcting codes can be degenerate, if more than one type of error can map the input state to the same error state. In this paper, we propose a 6-qubit degenerate CSS code. We show that our proposed code can correct a single bit flip error, but arbitrarily many phase flip errors occurring on the codeword. Furthermore, it follows from a bound on CSS codes that the proposed code is the minimal binary CSS code which can encode a single qubit of information. We also perform a comparative study of the gate coun…
Polarization correlation in a linear basis, but not entanglement, is observed between the biexciton and single-exciton photons emitted by a single InAs quantum dot in a two-photon cascade. The results are well described quantitatively by a probabilistic model that includes two decay paths for a biexciton through a non-degenerate pair of one-exciton states, with the polarization of the emitted photons depending on the decay path. The results show that spin non-degeneracy due to quantum-dot asymmetry is a significant obstacle to the realization of an entangled-photon generation device.
Strong quantum correlations in matter are responsible for some of the most extraordinary properties of material, from magnetism to high-temperature superconductivity, but their integration in quantum devices requires a strong, coherent coupling with photons, which still represents a formidable technical challenge in solid state systems. In cavity quantum electrodynamics, quantum gases such as Bose-Einstein condensates or lattice gases have been strongly coupled with light. However, neither Fermionic quantum matter, comparable to electrons in solids, nor atomic systems with controlled interacti…
Mitigating cosmic ray-like correlated events with a modular quantum processor
本文提出利用模块化量子架构和定制纠错码缓解量子处理器中芯片级相关错误的方法。
We analyze the long time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, we find formal expressions for the probability of a faulty path and the residual decoherence encoded in the reduced density matrix. Systems with non-zero gate times (``long gates'') are included in our analysis by using an upper bound on the noise. In order to introduce the local error probability for a qubit, we assume that propagation of si…
Stark Energy Shifts due to Quantum Gravity in RGUP Algebra
本文将相对论性广义不确定原理（RGUP）引入氢原子斯塔克效应研究，推导能谱修正，得到含β正比项的能量位移，验证其极限可退化为经典结果，构建了相对论量子系统最小长度效应的通用分析框架。
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