Julio Gea-Banacloche
A lower bound on the amount of energy needed to carry out an elementary logical operation on a qubit system, with a given accuracy and in a given time, has been recently postulated. This paper is an attempt to formalize this bound and explore the conditions under which it may be expected to hold. This is a work in progress and any contributions will be appreciated.
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Demonstrating a universal logical gate set in error-detecting surface codes on a superconducting quantum processor
本研究针对超导系统中表面码逻辑量子比特两量子比特门缺失的问题，用处理器\textit{Wukong}在距离-2表面码上实现通用逻辑门集合，含横向CNOT与任意单量子比特旋转门，还容错制备逻辑贝尔态，证实纠缠，推动超导容错量子计算发展。
A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one obtains for arity-one a complete family of logical operators corresponding to all the one-argument logical connectives. Scaling-up to n-arity gates is obtained by using the Kronecker product and unitary transformations. The quantum version of the Fourier transform of Boolean functions is presented and a Reed-Muller decomposition for quantum logical gates is de…
Topologically quantum error corrected logical gates are complex. Chains of errors can form in space and time and diagonally in spacetime. It is highly nontrivial to determine whether a given logical gate is free of low weight combinations of errors leading to failure. We report a new tool Nestcheck capable of analyzing an arbitrary topological computation and determining the minimum number of errors required to cause failure.
Transversal Logical Clifford gates on rotated surface codes with reconfigurable neutral atom arrays
提出利用可重构中性原子阵列在旋转表面码上横向实现逻辑 H、S 门的方案，并结合 CNOT 完善 Clifford 门集，S 门性能在电路噪声下与量子存储器相当。
Partitioning qubits in hypergraph product codes to implement logical gates
研究超图积码中的横向门，通过构建辛正则基证明横向门可实现Hadamard和控制-Z门，结合纠错可实现任意逻辑比特间的纠缠门，为LDPC码上的通用容错量子计算奠定基础。
Composable logical gate error in approximate quantum error correction: reexamining gate implementations in Gottesman-Kitaev-Preskill codes
本文研究了近似GKP码中逻辑门误差的可组合性，发现Pauli门精度随压缩量增加而提高，而某些Clifford门在近似情况下存在恒定误差。
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from a…
Efficient encoding of the 2D toric code logical state using local Clifford gates
提出一种仅用局域 $CX$ 和 $H$ 门、深度 $2L+1$ 的电路高效编码二维环面码逻辑态的算法。
Kerr-effect-based quantum logical gates in decoherence-free subspace
针对消相干效应影响量子逻辑门高效实现的问题，提出在无消相干子空间中利用交叉克尔非线性构建CNOT、Toffoli、Fredkin量子控制门的方案，无需复杂电路与辅助光子，成功概率近1且抗光子损耗，具备实用可行性。
Color code with a logical control-$S$ gate using transversal $T$ rotations
本文提出一种颜色码，利用横向T和T†旋转实现逻辑控制-S门，展示了非克莱因门的实现方法。
An implementation is proposed of single qubit gates, e.g., phase, NOT, \sqrt{NOT} and Hadamard, operating on polarized photons and based on light storage. Instead of processing photons themselves, qubit transformations are performed on atomic excitations due to photon storage in a medium of atoms in the tripod configuration.
Addressable gate-based logical computation with quantum LDPC codes
本文提出一种基于门的可寻址协议，利用辅助Bacon-Shor码和量子隐形传态在量子LDPC码上实现单量子比特及多量子比特Clifford操作，并可结合魔态培养实现通用容错量子计算。
Fault-tolerant quantum computation using quantum error-correcting codes requires fault-tolerant constructions of nontransversal gates. Shor proposed a fault-tolerant construction of a nontransversal gate, i.e., the Toffoli gate for a family of the Calderbank-Shor-Steane codes which has even-weight stabilizer generators and odd-weight logical operators. In fact, as shown in this paper, error propagations in the ancilla preparation of Shor's construction lead to logical errors. This work provides a solution to this problem through the insertion of bit flip error correction. Finally, error rates …
We derive a set of composite pulse sequences that generates CNOT gates and correct all systematic errors within the logical subspace to arbitrary order. These sequences are applicable for any two-qubit interaction Hamiltonian, and make no assumptions about the underlying noise mechanism except that it is constant on the timescale of the operation. We do assume access to error-free single-qubit gates, so single-qubit gate imperfections eventually limit the achievable fidelity. However, since single-qubit gates generally have much higher fidelities than two-qubit gates in practice, these pulse s…
Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding are of particular interest because their QEC protection is hardware efficient, but gate operations on QEC protected logical qubits remain elusive. Here, we experimentally demonstrate full control on a single logical qubit with a binomial bosonic code, including encoding, decoding, repetitive QEC, and …
We propose a way for realizing a two-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. In this proposal, the two lowest levels of each SQUID serve as the logical states and two intermediate levels of each SQUID are used for the gate realization. We show that neither adjustment of SQUID level spacings during the gate operation nor uniformity in SQUID parameters is required by this proposal. In addition, this proposal does not require the adiabatic passage or a second-order detuning and thus the gate is much faster.
Finding diagonal logical gates in CSS codes and circuits
本文提出高效算法，可从给定ansatz门中找出CSS码与电路的所有对角逻辑门，其运行时间为O(n³)，还讨论了该方法向其他门及量子位的推广，为容错量子计算提供支持。
Optimizing Rydberg Gates for Logical Qubit Performance
本文提出一类对强度不均匀性和多普勒频移具有鲁棒性的中性原子里德伯阻塞门，并证明其在擦除偏置量子比特中可维持擦除错误偏置，从而降低容错量子计算对激光稳定性和原子温度的要求。
Logical gate set tomography
本研究提出逻辑门集断层扫描，对Quantinuum H1处理器上7量子比特Steane码实现的通用单量子比特逻辑门集完成完整表征，识别逻辑误差特征并揭示物理误差源对逻辑误差的影响。
The concrete schemes to realize three types of basic quantum logical gates using linear quadripartite cluster states of optical continuous variables are proposed. The influences of noises and finite squeezing on the computation precision are analyzed in terms of the fidelity of propagated quantum information through the continuous variable cluster states. The proposed schemes provide direct references for the design of experimental systems of one-way quantum computer based on the cluster entanglement of amplitude and phase quadratures of light.
Scalable Constant-Time Logical Gates for Large-Scale Quantum Computation Using Window-Based Correlated Decoding
本文提出一种结合延迟修复线路与窗口相关解码的架构，实现可扩展常数时间逻辑门，降低解码频率和持续时间，并支持时间最优容错量子计算，适用于离子阱等大规模量子计算系统。
Logical gates on Floquet codes via folds and twists
本文通过折叠和扭转技术在Floquet码上实现逻辑门，展示了其在纠错码中的应用和性能优势。
Efficient characterization of qudit logical gates with gate set tomography using an error-free Virtual-Z-gate model
针对传统门集层析成像（GST）数据收集和计算成本高的问题，提出一种高效qudit GST方法，利用qudit Hadamard门与无误差虚拟Z门构建基准态以降低计算成本，并在超导transmon qutrit上验证了适用性。
We use the "modes of the universe" approach to study a cavity-mediated two-photon logical gate recently proposed by Koshino, Ishizaka and Nakamura. We clarify the relationship between the more commonly used input-output formalism, and that of Koshino et al., and show that some elements of this gate had been anticipated by other authors. We conclude that their proposed gate can work both in the good and bad cavity limits, provided only that the pulses are long enough. Our formalism allows us to estimate analytically the size of the various error terms, and to follow the spectral evolution of th…
Quantum error correction and fault-tolerant quantum computation are two fundamental concepts which make quantum computing feasible. While providing a theoretical means with which to ensure the arbitrary accuracy of any quantum circuit, fault-tolerant error correction is predicated upon the robust preparation of logical states. An optimal direct circuit and a more complex fault-tolerant circuit for the preparation of the [[7,1,3]] Steane logical-zero are simulated in the presence of discrete quantum errors to quantify the regime within which fault-tolerant preparation of logical states is prefe…
Quantum computation with logical gates between hot systems
研究热量子比特间的量子计算问题，提出逻辑编码门方法以提升对位置波动等不完美因素的鲁棒性，显著提高门保真度，为减轻热噪声提供平台无关工具。
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such limits, but imperfect gate operations introduce errors to the correction procedure as well. The additional gate operations required due to the physical layout of qubits exacerbate the situation. Here, we use density-matrix simulations to investigate the performance change of logical qubits according to quantum error correction codes and qubit layouts and the expe…
We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates used in the approximation. However, for the specific case of arbitrary single-qubit gates and the fault-tolerant gates permitted by the concatenated 7-qubit Steane code, we find gate sequences sufficiently long and accurate to permit the fault-tolerant factoring of numbers thousands of bits long. A general scaling law of how rapidly these fault-tolerant app…
Suppression of Universal Errors in DFS-Encoded Superconducting Geometric Logical \emph{T} Gate
本文提出一种超导几何逻辑T门方案，通过整合去相干自由子空间编码与多环优化复合几何脉冲工程，实现对通用误差的高阶抑制，提升了对多种噪声源的鲁棒性。
No-go theorems for logical gates on product quantum codes
本研究基于Bravyi--König定理的推广，证明超图乘积码上非Clifford逻辑门无法横向实现，且维度限制Clifford层级门的可达性，揭示了qLDPC码容错计算的代数结构限制。
Protecting logical qubits with dynamical decoupling
提出一种在最近邻物理量子比特上实现iSWAP门的新颖动力学解耦方案，仅需两个物理量子比特编码一个逻辑量子比特，实验证明逻辑量子比特相干时间最多延长366%，并首次在超导量子比特中实现多逻辑量子比特优于物理对应物。
A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from linear optical quantum computation in order to perform high fidelity quantum gates across a quantum network. The error-detecting properties of the heralded operations ensure high fidelity while the encoding makes it possible to correct for failed attempts such that deterministic and high-quality gates can be achieved. Importantly, this is robust to photon los…
A measurement-induced continuous-variable logical gate is able to prepare Schrödinger cat states if the gate uses a non-Gaussian resource state, such as cubic phase state [I. V. Sokolov, Phys. Lett. A 384, 126762 (2020)]. Our scheme provides an alternative to hybrid circuits which use photon subtraction and (or) Fock resource states and photon number detectors. We reveal the conditions under which the gate conditionally prepares quantum superposition of two undistorted "copies" of an arbitrary input state that occupies a finite area in phase space. A detailed analysis of the fidelity between t…
A $\boldsymbol{2d \times d \times d}$ Spacetime Volume Implementation of a Logical S Gate in the Surface Code
本文提出一种减少时空体积的逻辑S门实现方法，通过改进的扭缺陷编织协议，利用邻近两量子比特门实现，提升了近似容错性能。
Clifford gates with logical transversality for self-dual CSS codes
本文针对自对偶CSS码，证明了存在辛基使横向Hadamard和相位门可实现的充要条件，并推广到级联码，为低开销容错量子计算提供多种横向Clifford门实现。
Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates
本文构造了一族恒定速率、稳定子权重亚对数增长的量子码，仅用横向和折叠横向门即可实现完整逻辑Clifford群，为低空间开销容错量子计算提供路径。
Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can be prepared by a single recovery operation in any state whose stabilizer generator separates into X and Z parts. Optimized methods to move logical qubits around and to achieve controlled-not and Toffoli gates are discussed. It is found that the number of time-steps required to complete a fault-tolerant quantum computation is the same when k>1 as when k=1.
We simulate the implementation of a T-gate, or $\fracπ{8}$-gate, for a [7,1,3] encoded logical qubit in a non-equiprobable error environment. We demonstrate that the use of certain non-fault tolerant methods in the implementation may nevertheless enable reliable quantum computation while reducing basic resource consumption. Reliability is determined by calculating gate fidelities for the one-qubit logical gate. Specifically, we show that despite using a non-fault tolerant procedures in constructing a logical zero ancilla to implement the T-gate the gate fidelity of the logical gate, after perf…
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single qubit errors. We perform quantum process tomography of the encoded gate…
Construction of the full logical Clifford group for high-rate quantum Reed-Muller codes using only transversal and fold-transversal gates
针对自对偶量子Reed-Muller码族，仅用横向和折叠横向门构造完整逻辑Clifford群的生成集，实现任意可寻址Clifford门，无需辅助量子比特。
Deterministic Universal Logical Gates for Finite-Energy GKP Qubits in Trapped Neutral Atoms
该研究提出了囚禁中性原子中有限能量GKP量子比特的通用逻辑门集，采用魔阱条件实现无测量的逻辑控制，基于⁸⁸Sr原子的实验显示门保真度达0.985以上，为相关量子控制提供了可行途径。
We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.
Fault-tolerant and fully addressable unitary logical gates via round-robin sparsification
本研究针对量子LDPC码，提出基于轮询稀疏化的低深度酉电路，实现完全可寻址且容错的两量子比特克利福德门，并通过多种码的数值模拟验证其普遍适用性。
Universal Quantum Gate Set for Gottesman-Kitaev-Preskill Logical Qubits
本研究在囚禁离子机械运动的有限能量 GKP 态上，通过动态调制自旋-运动耦合的最优控制，实验实现含单比特门和首个双比特纠缠门的通用逻辑门集合。
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in p…
Logical blocks for fault-tolerant topological quantum computation
本文提出逻辑块框架，以时空统一方式描述拓扑逻辑门，并基于表面码与LDPC码级联及FBQC实现通用容错量子计算，验证阈值一致性并探索减少资源开销的新方案。
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for these codes, the disjointness, which, roughly speaking, is the number of mostly non-overlapping representatives of any given non-trivial logical Pauli operator. We use the disjointness to prove that transversal gates on error-detecting stabilizer codes are necessarily in a finite level of the Clifford hierarchy. We also apply our techniques to topological code…
We simulate four quantum error correcting codes under error models inspired by realistic noise sources in near-term ion trap quantum computers: $T_2$ dephasing, gate overrotation, and crosstalk. We use this data to find preferred codes for given error parameters along with logical error biases and a pseudothreshold which compares the physical and logical gate failure rates for a CNOT gate. Using these results we conclude that Bacon-Shor-13 is the most promising near term candidate as long as the impact of crosstalk can be mitigated through other means.
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we demonstrate that a small but useful error detecting code improves the fidelity of the fault-tolerant gates implemented in the code space as compared to the fidelity of physically equivalent gates implemented on physical qubits. By running a randomized benchmarking protocol in the logical code space of the [4,2,2] code, we observe an order of magnitude improveme…
Fault-Tolerant Constant-Depth Clifford Gates on Toric Codes
针对2D环面码，提出并模拟了结合折叠横向门、Dehn扭转和单次逻辑Pauli测量的容错常深度逻辑门组，其能生成完整Clifford群并具备容错性与常深度特性。
Suppressing errors in analog logical rotation gates via balanced fusion
研究早期容错量子算法中模拟逻辑旋转门的误差问题，提出‘平衡融合’技术，通过改进对相干误差项积累的分析，将误差缩放提升至$O(p \phi^{1.5})$，提高小角度模拟逻辑旋转的可行性。
Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design which, in general, increases the complexity of the implementation. Here, we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In…
Stesso: A reconfigurable decomposition of $n$-bit Toffoli gates using symmetrical logical structures and adjustable support qubits
针对当代量子计算机对称结构下$(n+1)$位Toffoli门分解难以重构且辅助量子比特消耗多的问题，提出名为Stesso的分解方法，利用可调辅助量子比特构建不同极性算子，显著降低了量子成本。
Genuine Multipartite Entanglement between Logical Qubits via Cross-Code Lattice Surgery
研究利用交叉码晶格手术在俘获离子量子处理器中实验生成并验证逻辑真正多方纠缠，介绍了通过不同码实现的通用逻辑门集，展示了多方纠缠态及单逻辑量子比特任意旋转，为容错量子计算架构提供核心构建块。
Fault-Tolerant Logical Clifford Gates from Code Automorphisms
本文提出利用稳定子码的自同构群构造容错逻辑 Clifford 门，通过将码映射为二元线性码并用 MAGMA 计算自同构，给出严格算法、Python 实现及多种码上的门构造示例。
Fault-tolerant multi-qubit gates in Parity Codes
该研究提出在正交码中高效实现容错多量子比特门的方法，通过交换门实现任意数量逻辑量子比特的奇偶性控制NOT操作，无需复杂路由或晶格手术。
The three-spin-$1/2$ decoherence-free subsystem defines a logical qubit protected from collective noise and supports exchange-only universal gates. Such logical qubits are well-suited for implementation with electrically-defined quantum dots. Exact exchange-only entangling logical gates exist but are challenging to construct and understand. We use a decoupling strategy to obtain straightforward approximate entangling gates. A benefit of the strategy is that if the physical spins are aligned, then it can implement evolution under entangling Hamiltonians. Hamiltonians expressible as linear combi…
High-Fidelity Controlled-Phase Gate for Binomial Codes via Geometric Phase Engineering
提出利用几何相位工程实现二项式编码逻辑量子比特的受控相位门，实验演示了97.4%的受控Z门过程保真度，超越了所有先前报道的玻色子码双逻辑量子比特门。
Transversal Diagonal Logical Operators for Stabiliser Codes
本研究针对CSS码，提出识别所有横向对角逻辑算子的更通用或更低复杂度算法，并给出构造具有所需对角逻辑克利福德层级算子的CSS码的方法，以推进容错量子计算。
Liquid phase NMR is a general purpose test-bed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherence free subspaces that protect the quantum information from fully correlated dephasing.
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