The performance of a given quantum error correction (QEC) code depends upon the noise model that is assumed. Independent Pauli noise, applied after each quantum operation, is a simplistic noise model that is easy to simulate and understand in the context of stabilizer codes. Although such a noise model is artificial, it is equivalent to independent, random, unbiased qubit rotations. What about spatially or temporally correlated qubit rotations? Such a noise model is applicable to global operations (e.g., NMR or ESR), common control sources (e.g., lasers), or slow drift (e.g., charge or magnetic noise) in various qubit technologies. In the worst case, such errors can combine constructively and result in a post-correction failure rate that increases with the number of error correction cycles. However, we show that this worst case does not generally arise unless taking active corrective actions while performing QEC. That is, by employing virtual Pauli frame updates ("passive" error correction) rather than physical corrections ("active" error correction), coherent errors do not compound appreciably. Starting in a random Pauli frame is also advantageous. In fact, through perturbation theory arguments and supporting numerical simulations, we show that the logical qubit performance beyond distance 3 for correlated single-qubit Hamiltonian noise models (i.e., global errant qubit rotations), when employing these "lazy" strategies, essentially matches the performance of Pauli noise model with the same process fidelity (fidelity after one application). In a more general circuit model of noise, correlations may add constructively within syndrome extraction rounds but Pauli frame randomization from passive error correction mitigates this effect across multiple rounds.
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting quantum computation, we perform full quantum process tomography of single qubits in a real quantum processor in which echo experiments are implemented. Besides error sources already included in standard models, the obtained results show the dominant role of coherent errors, which we practically correct by inserting random single-qubit unitaries in the quant…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively unknown. Here, we prove that encoding a system in a stabilizer code and measuring error syndromes decoheres errors, that is, causes coherent errors to converge toward probabilistic Pauli errors, even when no recovery operations are applied. Two practical consequences are that the error rate in a logical circuit is well quantified by the average gate fidelit…
Crosstalk and several sources of operational interference are invisible when qubit or a gate is calibrated or benchmarked in isolation. These are unlocked during the execution of full quantum circuit applying entangling gates to several qubits simultaneously. Unwanted Z-Z coupling on superconducting cross-resonance CNOT gates, is a commonly occurring unitary crosstalk noise that severely limits the state fidelity. This work presents (1) method of tracing unitary errors, which exploits their sensitivity to the arrangement of CNOT gates in the circuit and (2) correction scheme that modifies orig…
Quantum error correcting codes can be cast in a way which is strikingly similar to a quantum heat engine undergoing an Otto cycle. In this paper we strengthen this connection further by carrying out a complete assessment of the thermodynamic properties of 4-strokes operator-based error correcting codes. This includes an expression for the entropy production in the cycle which, as we show, contains clear contributions stemming from the different sources of irreversibility. To illustrate our results, we study a classical 3-qubit error correcting code, well suited for incoherent states, and the 9…
In this paper, we analyze the evolution of quantum coherence in a two-qubit system going through the amplitude damping channel. After they have gone through this channel many times, we analyze the systems with respect to the coherence of their output states. When only one subsystem goes through the channel, frozen coherence occurs if and only if this subsystem is incoherent and an auxiliary condition is satisfied for the other subsystem. When two subsystems go through this quantum channel, quantum coherence can be frozen if and only if the two subsystems are both incoherent. We also investigat…
Universal quantum computers require a large network of qubits robust against errors. Recent theoretical and experimental studies on donor nuclear spins in silicon, engineered on semiconductor platforms compatible with industrial fabrication, show their coherent behavior and potential for scalability. Here we present a hardware-efficient quantum protocol that corrects phase flips of a nuclear spin using explicit experimentally feasible operations. We introduce the MAUS encoding (Moment AngUlar System encoding) which uses the large Hilbert space provided by the nuclear spin of the donor to encod…
Bosonic quantum error-correcting codes with finite stellar rank
Chalmers University of Technology（查尔姆斯理工大学）；The University of Sydney（悉尼大学）；École Normale Supérieure, PSL University（巴黎高等师范学院，PSL大学）；Università degli Studi di Milano（米兰大学）
New York University Shanghai, NYU-ECNU Institute of Physics at NYU Shanghai（纽约大学上海分校，纽约大学上海NYU-ECNU物理研究所）；PSL Dauphine University（巴黎文理研究大学达芬奇学院）；Department of Physics, New York University（纽约大学物理系）；Mathematical Institute, University of Oxford（牛津大学数学研究所）；State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University（华东师范大学精密光谱科学与技术国家重点实验室，物理与材料科学学院）
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when the error correction steps are performed noiselessly. Our examples include the entire family of repetition codes, the 5-qubit, Steane, Shor, and surface codes. When errors are measured in terms of the diamond norm, we find that the error correction is typically much more effective for unitary errors than for dephasing. We observe this behavior for a wide range…
The notion of nonreciprocity, in essence when going forwards is different from going backwards, emerges in all branches of physics from cosmology to electromagnetism. Intriguingly, the breakdown of reciprocity is typically associated with extraordinary phenomena, which may be readily capitalized on in the design of (for example) nontrivial electromagnetic devices when Lorentz reciprocity is broken. However, in order to enable the exploitation of nonreciprocal-like effects in the next generation of quantum technologies, basic quantum optical theories are required. Here we present a versatile mo…
We study variants of Shor's code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shor's code basis states, we calculate the logical channel applied to the encoded information when subjected to coherent and correlated single qubit idling errors, followed by stabilizer measurement. Changing the signs of the stabilizer generators allows us to change how the coherent errors interfere, leading to a quantum error correcting code which performs as well as a classical repetition code of …
Non-conventional receivers for phase-coherent states based on non-Gaussian measurements such as photon counting surpass the sensitivity limits of shot-noise-limited coherent receivers, the quantum noise limit (QNL). These non-Gaussian receivers can have a significant impact in future coherent communication technologies. However, random phase changes in realistic communication channels, such as optical fibers, present serious challenges for extracting the information encoded in coherent states. While there are methods for correcting random phase noise with conventional heterodyne detection, pha…
BARC codes: general polynomial framework for coherent-state superposition codes
Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR)（先进智能与计算研究所，科学、技术与研究局）；Singapore University of Technology and Design（新加坡科技设计大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院南洋量子枢纽）
The well studied quantum optical Schrödinger cat state is a superposition of two distinguishable states, with quantum coherence between these macroscopically distinguishable states being of foundational and, in the context of quantum-information processing, practical use. We refer to these quantum-optical cat states as quantum dichotomous states, reflecting that the state is a superposition of two options, and we introduce the term quantum multichotomous state to refer to a superposition of multiple macroscopically distinguishable options. For a single degree of freedom, such as position, we c…
Circuit-based characterization of finite-temperature quantum phases and self-correcting quantum memory
Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；Department of Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校物理系）；Kadanoff Center for Theoretical Physics & Enrico Fermi Institute, The University of Chicago（芝加哥大学卡达诺夫理论物理中心与恩里科·费米研究所）；Department of Physics, Stanford University（斯坦福大学物理系）
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the si…
