Quantum teleportation enables quantum information transmission, but requires distribution of entangled resource states. Unfortunately, decoherence, caused by environmental interference during quantum state storage, can degrade quantum states, leading to entanglement loss in the resource state and reduction of the fidelity of the teleported information. In this work, we investigate the use of error correction and error syndrome information in scheduling teleportation at a quantum network node in the presence of multiple teleportation requests and a finite rate of remote entanglement distribution. Specifically, we focus on the scenario where stored qubits undergo decoherence over time due to imperfect memories. To protect the qubits from the resulting errors, we employ quantum encodings, and the stored qubits undergo repeated error correction, generating error syndromes in each round. These error syndromes can provide additional benefits, as they can be used to calculate qubit-specific error likelihoods, which can then be utilized to make better scheduling decisions. By integrating error correction techniques into the scheduling process, our goal is to minimize errors and decoherence effects, thereby enhancing the fidelity and efficiency of teleportation in a quantum network setting.
We investigate a quantum repeater scheme for quantum key distribution based on the work by Muralidharan et al., Phys. Rev. Lett. 112, 250501 (2014). Our scheme extends that work by making use of error syndrome measurement outcomes available at the repeater stations. We show how to calculate the secret key rates for the case of optimizing the syndrome information, while the known key rate is based on a scenario of coarse-graining the syndrome information. We show that these key rates can surpass the Pirandola-Laurenza-Ottaviani-Banchi bound on secret key rates of direct transmission over lossy …
AlphaSyndrome: Tackling the Syndrome Measurement Circuit Scheduling Problem for QEC Codes
University of Pennsylvania（宾夕法尼亚大学）；University of California, Berkeley（加州大学伯克利分校）；Amazon Quantum Technologies（亚马逊量子技术）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）
Quantum teleportation channels can overcome the effects of photonic loss, a major challenge in the implementation of a quantum network over fiber. Teleportation channels are created by distributing an entangled state between two nodes which is a probabilistic process requiring classical communication. This causes critical delays that can cause information loss as quantum data suffers from decoherence when stored in memory. In this work, we quantify the effect of decoherence on fidelity at a node in a quantum network due to the storage of qubits in noisy memory platforms. We model the memory pl…
A major goal for fault-tolerant quantum computation (FTQC) is to reduce the overhead needed for error correction. One approach is to use block codes that encode multiple qubits, which can achieve significantly higher rates for the same code distance than single-qubit code blocks or topological codes. We present a scheme for universal quantum computation using multi-qubit Calderbank-Shor-Steane (CSS) block codes, where codes admitting different transversal gates are used to achieve universality, and logical teleportation is used to move qubits between code blocks. All circuits for both computat…
We discuss a simple variant of the one-way quantum computing model [R. Raussendorf and H.-J. Briegel, PRL 86, 5188, 2001], called the Pauli measurement model, where measurements are restricted to be along the eigenbases of the Pauli X and Y operators, while auxiliary qubits can be prepared both in the $\ket{+_{π\over 4}}:={1/\sqrt{2}}(\ket{0}+e^{i{π\over 4}}\ket{1})$ state, and the usual $\ket{+}:={1/ \sqrt{2}}(\ket{0}+\ket{1})$ state. We prove the universality of this quantum computation model, and establish a standardization procedure which permits all entanglement and state preparation to b…
Clifford circuits play an important role in quantum computation. Gottesman and Chuang proposed a gate teleportation protocol so that a quantum circuit can be implemented by the teleportation circuit with specific ancillary qubits. In particular, an $n$-qubit Clifford circuit $U$ can be implemented by preparing an ancillary stabilizer state $(I\otimes U)|Φ^+\rangle^{\otimes n}$ for teleportation and doing a Pauli correction conditioned on the measurement. In this paper, we provide an alternative procedure to implement a Clifford circuit through Pauli measurements, by preparing $O(1)$ ancillas t…
Optimal Compilation of Syndrome Extraction Circuits for General Quantum LDPC Codes
Tsinghua University（清华大学）；Pengcheng Laboratory（鹏城实验室）；Key Laboratory of System Software (Chinese Academy of Sciences)（中国科学院系统软件重点实验室）；The Hong Kong University of Science and Technology（香港科技大学）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）
Flag qubits have recently been proposed in syndrome extraction circuits to detect high-weight errors arising from fewer faults. The use of flag qubits allows the construction of fault-tolerant protocols with the fewest number of ancillas known to-date. In this work, we prove some critical properties of CSS codes constructed from classical cyclic codes that enable the construction of a flag fault-tolerant error correction scheme. We then develop fault-tolerant protocols as well as a family of circuits for flag fault-tolerant error correction and operator measurement, requiring only four ancilla…
Dense packing of the surface code: code deformation procedures and hook-error-avoiding gate scheduling
Graduate School of Science and Technology, Keio University（庆应义塾大学理工学研究科）；Graduate School of Media Design, Keio University（庆应义塾大学媒体设计研究科）；Department of Physics & Astronomy, University College London（伦敦大学学院物理与天文系）；Faculty of Science and Technology, Keio University（庆应义塾大学理工学部）
Imperial College London（帝国理工学院）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；The Graduate University for Advanced Studies（综合研究大学院大学）；National Institute of Informatics（信息学国立研究所）
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery operator independent definition of error-correcting codes. We relate t…
Error Threshold of SYK Codes from Strong-to-Weak Parity Symmetry Breaking
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Logical qubits with erasure conversion using metastable neutral atoms
Princeton University（普林斯顿大学）；Peking University（北京大学）；University of California, Berkeley（加州大学伯克利分校）；The Hong Kong University of Science and Technology（香港科技大学）；Yale University（耶鲁大学）
As current Noisy Intermediate Scale Quantum (NISQ) devices suffer from decoherence errors, any delay in the instruction execution of quantum control microarchitecture can lead to the loss of quantum information and incorrect computation results. Hence, it is crucial for the control microarchitecture to issue quantum operations to the Quantum Processing Unit (QPU) in time. As in classical microarchitecture, parallelism in quantum programs needs to be exploited for speedup. However, three challenges emerge in the quantum scenario: 1) the quantum feedback control can introduce significant pipelin…
