Transversal CNOTs are ubiquitous for entangling logical qubits of identical CSS codes pairwise. For distinct codes, the options are much more limited, and are typically known only for structurally related code families. We introduce an automated framework for synthesising inter-code logical CNOT circuits between arbitrary CSS codes using chain maps. Given a prescribed bipartite logical CNOT network between these codes, our method constructs the affine space of chain maps realising the desired logical action, and then searches this space for shallow and sparse physical circuit candidates. We benchmark this method on a range of heterogeneous CSS code pairs, recovering known transversal constructions, and finding new low-depth solutions, including distance-preserving and partially distance-preserving examples, which we demonstrate can be promoted to the full code distance using additional flag measurements. We discuss applications to code switching, magic-state injection, Pauli product measurements, and operations on concatenated codes, where bespoke chain maps offer favourable spacetime tradeoffs for logical interfaces tailored to heterogeneous architectures. Finally, we show how our framework straightforwardly extends to targeted logical CZ gates.
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 imp…
Quantum computers have the potential to be a profoundly transformative technology, particularly in the context of quantum chemistry. However, running a chemistry application that is demonstrably useful currently requires a prohibitive number of logical operations. For example, the canonical estimate of the number of operations required to simulate the molecule FeMoco, the key component in biological nitrogen fixation, requires around $10^{15}$ logical gates. A quantum computer that is capable of applying logical operations at 1 Mhz rates would require more than 30 years to complete such a calc…
University of Strasbourg（斯特拉斯堡大学）；CNRS, CESQ and ISIS (UMR 7006)（法国国家科学研究中心、CESQ和ISIS联合研究实验室）；aQCess；QPerfect；Institut Universitaire de France (IUF)（法兰西学院）
Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates
OptQC Corp.（OptQC公司）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；Department of Applied Physics, Graduate School of Engineering, The University of Tokyo（东京大学工学研究科应用物理系）
Constant-depth magic state cultivation with Clifford measurements by gauging
IBM Quantum, IBM T. J. Watson Research Center（IBM量子，IBM托马斯·J·沃森研究中心）；IBM Denmark（IBM丹麦）；University of Sydney（悉尼大学）；IBM Almaden Research Center（IBM阿尔马登研究中心）
In-situ benchmarking of fault-tolerant quantum circuits. I. Clifford circuits
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机联合中心，美国国家标准与技术研究院/马里兰大学）；Simons Institute for the Theory of Computing, University of California at Berkeley（西蒙斯计算理论研究所，加州大学伯克利分校）；Institute for Theoretical Physics, ETH Zürich（理论物理研究所，苏黎世联邦理工学院）；Department of Physics, Harvard University（物理学系，哈佛大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）
Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode $k>1$ qubits in $n$ physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the fault-tolerant (FT) logical operations for the encoded qubits are difficult to find and implement, which usually takes not only a very large resource overhead but also long $\textit{in-situ}$ computation time. In this paper, we focus on Calderbank-Shor-Steane $[\![ n,k,d ]\!]$ (CSS) codes and their logical FT Clifford circuits. We show that the depth of an arbitr…
The design of a four-dimensional toric code is explored with the goal of finding a lattice capable of implementing a logical $\mathsf{CCCZ}$ gate transversally. The established lattice is the octaplex tessellation, which is a regular tessellation of four-dimensional Euclidean space whose underlying 4-cell is the octaplex, or hyper-diamond. This differs from the conventional 4D toric code lattice, based on the hypercubic tessellation, which is symmetric with respect to logical $X$ and $Z$ and only allows for the implementation of a transversal Clifford gate. This work further develops the estab…
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）
Duke Quantum Center, Duke University（杜克大学量子中心）；Department of Physics, Duke University（杜克大学物理系）；Department of Electrical and Computer Engineering, Duke University（杜克大学电气与计算机工程系）；Department of Chemistry, Duke University（杜克大学化学系）
Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing
QuTech, Delft University of Technology（代尔夫特理工大学 QuTech）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学 卡弗里纳米科学研究所）；Delft Institute of Applied Mathematics, Delft University of Technology（代尔夫特理工大学 应用数学研究所）
Optimized Compilation of Logical Clifford Circuits
Fraunhofer IIS, Fraunhofer Institute for Integrated Circuits IIS（弗劳恩霍夫集成电路研究所）；University of Würzburg（维尔茨堡大学）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·阿历克西斯大学）
In an effort to overcome the limitations of random spin-glass benchmarks for quantum annealers, focus has shifted to carefully-crafted gadget-based problems whose logical structure has typically a planar topology. Recent experiments on these gadget problems using a commercially-available quantum annealer have demonstrated an impressive performance over a selection of commonly-used classical optimization heuristics. Here we show that efficient classical optimization techniques, such as minimum-weight perfect matching, can solve these gadget problems exactly and in polynomial time. We present ap…
Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and high-fidelity non-Clifford rotation gates. To address this issue, we propose a postselection-based algorithm to efficiently prepare resource states for gate teleportation. Our algorithm achieves fault tolerance, demonstrating the exponential suppression of logical errors with code distance, and it applies to any stabilizer codes. We provide analytical derivat…
One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface code, based on either boundary defects, holes, or bulk twist defects. However proposed fault-tolerant implementations of the Clifford group in these schemes are limited and often require unnecessary overhead. For example, the Clifford phase gate in certain planar and hole encodings has been proposed to be implemented using costly state injection and distillation…
