Flag verification techniques are useful in quantum error correction for detecting critical faults. Here we present an application of flag verification techniques to improving post-selected performance of near-term algorithms. We extend the definition of what constitutes a flag by creating error-detection gadgets based on known transformations of unitary operators. In the case of Clifford or near-Clifford circuits, these unitary operators can be chosen to be controlled Pauli gates, leading to gadgets which require only a small number of additional Clifford gates. We show that such flags can improve circuit fidelities by up to a factor of 2 after post selection, and demonstrate their effectiveness over error models featuring single-qubit depolarizing noise, crosstalk, and two-qubit coherent overrotation.
Constant-Time Surgery on 2D Hypergraph Product Codes with Near-Constant Space Overhead
IBM Quantum, IBM T. J. Watson Research Center（IBM量子，IBM托马斯·J·沃森研究中心）；Department of Physics, Yale University（耶鲁大学物理系）；Yale Quantum Institute, Yale University（耶鲁大学量子研究所）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）
The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient schemes for simulating non-Clifford gates in a fault-tolerant way. However, since magic state distillation circuits are not fault-tolerant, all Clifford operations must be encoded in a large distance code in order to have comparable failure rates with the magic states being distilled. In this work, we introduce a new concept which we call redundant ancilla encodin…
It is hard to achieve a theoretical quantum advantage on NISQ devices. Besides the attempts to reduce error using error mitigation and dynamical decoupling, small quantum error correction and fault-tolerant schemes that reduce the high overhead of traditional schemes have also been proposed. According to the recent advancements in fault tolerance, it is possible to minimize the number of ancillary qubits using flags. While implementing those schemes is still impossible, it is worthwhile to bridge the gap between the NISQ era and the FTQC era. Here, we introduce a benchmarking method to test fa…
In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting from $v$ faults in the circuit have weight greater than $v$. The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of co…
Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded Clifford gates with negligible error. In this paper we present a scheme to fault-tolerantly and directly prepare magic states using flag qubits. One of these schemes uses a single extra ancilla, even with noisy Clifford gates. We compare the physical qubit and gate cost of this scheme to the magic state distillation protocol of Meier, Eastin, and Knill, whic…
Fault-tolerant (FT) computation by using quantum error correction (QEC) is essential for realizing large-scale quantum algorithms. Devices are expected to have enough qubits to demonstrate aspects of fault tolerance in the near future. However, these near-term quantum processors will only contain a small amount of noisy qubits and allow limited qubit connectivity. Fault-tolerant schemes that not only have low qubit overhead but also comply with geometrical interaction constraints are therefore necessary. In this work, we combine flag fault tolerance with quantum circuit mapping, to enable an e…
University of Science and Technology of China（中国科学技术大学）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院量子信息中心）；Hefei National Laboratory（合肥国家实验室）；CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学院量子信息与量子物理学前沿卓越创新中心）
Protecting bosonic codes from ancilla-induced errors with continuous-variable flags
Alice & Bob（爱丽丝与鲍勃）；Laboratoire de Physique de l’École Normale Supérieure, Inria, ENS, Mines ParisTech, Université PSL, Sorbonne Université（巴黎高等师范学院物理实验室、法国国家信息与自动化研究所、巴黎高等师范学院、巴黎矿业学院、巴黎文理研究大学、索邦大学）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）
Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, these gadgets reduce the accuracy threshold and can increase overhead and experimental complexity, and these costs have not been thoroughly understood. Our work explores a variety of techniques for leakage-resilient, fault-tolerant error correction in the context of topological codes. Our contributions are thr…
Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors arising from a few faults can be detected by a few ancillas and distinguished using subsequent syndrome measurements. The technique can be further improved using the fact that for some families of codes, errors of any weight are logically equivalent if they have the same syndrome and weight parity, as previously shown in [Phys. Rev. A 104, 042410 (2021)]. In…
Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing
School of Physics, Peking University（北京大学物理学院）；Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学前沿交叉学科研究院计算机学院）
UC Berkeley（加州大学伯克利分校）；Simons Institute for the Theory of Computing（西蒙斯理论计算研究所）；Department of EECS, UC Berkeley（加州大学伯克利分校电气工程和计算机科学系）；Departments of EECS & Mathematics, UC Berkeley（加州大学伯克利分校电气工程和计算机科学系及数学系）
