Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation
BlueQubit Inc.（BlueQubit公司）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算科学联合中心，美国国家标准与技术研究院/马里兰大学）；Joint Quantum Institute, NIST/University of Maryland（量子联合研究所，美国国家标准与技术研究院/马里兰大学）
我们利用泡利路径模拟来变分地获得用于制备各种量子多体哈密顿量基态的参数化电路。这些包括一维的量子各向同性模型、在正方形和重六边形晶格上的二维模型，以及凯它夫蜂窝模型，所有系统规模均达到100个量子比特或更多——这是通用量子电路无法通过精确的态向量模拟达到的规模——从而达到实用规模。我们通过精确基态能量进行基准测试，当可用时，否则通过密度矩阵重整化群计算进行比较，发现有很强的一致性。为进一步评估变分态的质量，我们评估了量子各向同性模型在x和z方向的磁化率，并计算了凯它夫蜂窝模型的拓扑纠缠熵。最后，我们使用参数化电路，通过泡利路径模拟在Quantinuum的System Model H2量子计算机上制备了凯它夫蜂窝模型的近似基态，分别在有隙和无隙区域，使用48个量子比特。我们实现了约5%的相对能量误差，没有误差缓解，并在量子设备上展示了超越固定点模型的任何子的编织。
英文摘要：
We use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more -- sizes at which generic quantum circuits are beyond the reach of exact state-vector simulation -- thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately $5\%$ without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.
A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we propose a general and robust protocol to decompose any target unitary into a sequence of Pauli rotations. The procedure involves identifying a commuting subset of Pauli operators having a high trace overlap with the target unitary, followed by a numerical optimization of their corresponding rotation angles. The protocol is demonstrated by decomposing several…
TARE: Block Encoding Linear Combinations of Pauli Strings Without Ancilla State Preparation
Fraunhofer-Institut für Arbeitswirtschaft und Organisation IAO（弗劳恩霍夫工作经济与组织研究所）；Universität Stuttgart, Institut für Arbeitswissenschaft und Technologiemanagement IAT（斯图加特大学劳动科学与技术管理研究所）；Fraunhofer-Institut für Angewandte Festkörperphysik IAF（弗劳恩霍夫应用固体物理研究所）；Albert-Ludwigs-Universität Freiburg（弗赖堡阿尔伯特·路德维希大学）
Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource requirements both by co-processing with a classical processor and by structuring computation into many subproblems. Each quantum subproblem involves a separate state preparation terminated by the measurement of one Pauli string. However, the number of such Pauli strings scales as $N^4$ for typical problems of interest--a daunting growth rate that poses a serious li…
We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are tensor products of single-qubit operators drawn from the group $\langle αI, X,S\rangle$, where $α=e^{iπ/4}$ and $S=\operatorname{diag}(1,i)$. We provide techniques to efficiently compute various properties related to bipartite entanglement, expectation values of local observables, preparation by means of quantum circuits, parent Hamiltonians etc. We also highligh…
Recently, several quantum benchmarking algorithms have been developed to characterize noisy quantum gates on today's quantum devices. A well-known issue in benchmarking is that not everything about quantum noise is learnable due to the existence of gauge freedom, leaving open the question of what information about noise is learnable and what is not, which has been unclear even for a single CNOT gate. Here we give a precise characterization of the learnability of Pauli noise channels attached to Clifford gates, showing that learnable information corresponds to the cycle space of the pattern tra…
Collective Quantum State Preparation Is Nonadditive
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area（粤港澳大湾区量子科学中心）
Direct fidelity estimation through joint fiducial grouping
ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科技研究院）；Centre for Quantum Technologies, National University of Singapore（量子技术中心，新加坡国立大学）
With continuing improvements on the quality of fabricated quantum devices, it becomes increasingly crucial to analyze noisy quantum process in greater details such as characterizing the non-Markovianity in a quantitative manner. In this work, we propose an experimental protocol, termed Spectral Transfer Tensor Maps (SpecTTM), to accurately predict the RHP non-Markovian measure of any Pauli channels without state-preparation and measurement (SPAM) errors. In fact, for Pauli channels, SpecTTM even allows the reconstruction of highly-precised noise power spectrum for qubits. At last, we also disc…
Unitary fault-tolerant encoding of Pauli states in surface codes
Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich（于利希研究中心）；Institute for Quantum Information, RWTH Aachen University（亚琛工业大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；School of Physics and Astronomy, Monash University（蒙纳士大学）；NVIDIA Corporation（英伟达公司）；Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）
Toward Quantum Utility in Correlated Topological Matter: Variational Preparation of Fractional Quantum Hall Manifolds
Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；University of the Basque Country (UPV/EHU)（巴斯克大学）；Mondragon Unibertsitatea（蒙德拉贡大学）；TECNALIA（泰克纳利亚研究中心）；IMDEA Nanoscience（IMDEA纳米科学研究所）；Centro de Física de Materiales (CFM-MPC), CSIC-UPV/EHU（材料物理中心（CSIC-巴斯克大学））
Characterization of Unlearnable Noise with Mid-Circuit-Measurement-Based Cycle Benchmarking
Imperial College London（帝国理工学院）；Fraunhofer Institute for Industrial Mathematics（弗劳恩霍夫工业数学研究所）；Algorithmiq Ltd（Algorithmiq有限公司）；University of Helsinki（赫尔辛基大学）；Fraunhofer Center for Maritime Logistics（弗劳恩霍夫海事物流中心）
Pauli channels are ubiquitous in quantum information, both as a dominant noise source in many computing architectures and as a practical model for analyzing error correction and fault tolerance. Here we prove several results on efficiently learning Pauli channels, and more generally the Pauli projection of a quantum channel. We first derive a procedure for learning a Pauli channel on $n$ qubits with high probability to a relative precision $ε$ using $O\bigl(ε^{-2} n 2^n\bigr)$ measurements, which is efficient in the Hilbert space dimension. The estimate is robust to state preparation and measu…
A High-Performance Pauli-Algebra Framework for Large-Scale Quantum Simulations
State Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China（精密与智能化学国家重点实验室，中国科学技术大学）；Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（合肥微尺度物质科学国家研究中心，中国科学技术大学）；Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）
We present a study on preparing and manipulating path-like temporal-mode (TM) qubits based on third-order nonlinear interactions. Specifically, we consider the process of frequency conversion via difference frequency generation. To prepare a qubit, we aim to use Gaussian input states to a nonlinear waveguide. The coupling between the input state and a specific TM is maximized, obtaining qubits prepared with fidelities close to one. TMs evolve linearly within the medium; therefore, it is possible to define rotations around any axis contained in the $xy$ plane, allowing spanning the full Bloch s…
Stochastic Pauli-path simulator for large-scale quantum optimization
Generative AI Lab, College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院生成式人工智能实验室）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学学院）；Hon Hai (Foxconn) Research Institute（鸿海（富士康）研究院）
IBM Research Europe - Zurich（IBM 欧洲苏黎世研究中心）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）
We address measurement schemes where certain observables are chosen at random within a set of non-degenerate isospectral observables and then measured on repeated preparations of a physical system. Each observable has a given probability to be measured, and the statistics of this generalized measurement is described by a positive operator-valued measure (POVM). This kind of schemes are referred to as quantum roulettes since each observable is chosen at random, e.g. according to the fluctuating value of an external parameter. Here we focus on quantum roulettes for qubits involving the measureme…
Distinct Feedback-Strength Requirements for Quantum-State Ensemble Preparation under Channel-Equivalent Monitoring
School of Computer Science and Engineering, Macau University of Science and Technology（澳门科技大学计算机科学与工程学院）；Zhuhai MUST Science and Technology Research Institute（珠海澳门科技大学研究院）；School of Information and Software Engineering, University of Electronic Science and Technology of China（电子科技大学信息与软件工程学院）
Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly prepare arbitrary CSS stabilizer states for general CSS stabilizer codes is still unknown, and their preparation can be highly costly in computational resources. In this paper, we show how to prepare a large class of CSS stabilizer states useful for FTQC. We propose distillation protocols using syndrome …
We propose a fault tolerant loading scheme to produce an array of fermions in an optical lattice of the high fidelity required for applications in quantum information processing and the modelling of strongly correlated systems. A cold reservoir of Fermions plays a dual role as a source of atoms to be loaded into the lattice via a Raman process and as a heat bath for sympathetic cooling of lattice atoms. Atoms are initially transferred into an excited motional state in each lattice site, and then decay to the motional ground state, creating particle-hole pairs in the reservoir. Atoms transferre…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group of a quantum code. First, we show how to measure a Pauli operator acting on physical qubits using a single coherent state with large average photon number, displacement operations, and photon detection. Second, we show how to measure the stabilizer operators fault-tolerantly by the deterministic preparation of coherent cat states along with one-bit teleportat…
In recent years substantial research effort has been devoted to quantum algorithms for ground state energy estimation (GSEE) in chemistry and materials. Given the many heuristic and non-heuristic methods being developed, it is challenging to assess what combination of these will ultimately be used in practice. One important metric for assessing utility is runtime. For most GSEE algorithms, the runtime depends on the ground state preparation (GSP) method. Towards assessing the utility of various combinations of GSEE and GSP methods, we asked under which conditions a GSP method should be accepte…
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…
The Hamiltonian operator plays a central role in quantum theory being a generator of unitary quantum dynamics. Its expectation value describes the energy of a quantum system. Typically being a non-unitary operator, the action of the Hamiltonian is either encoded using complex ancilla-based circuits, or implemented effectively as a sum of Pauli string terms. Here, we show how to approximate the Hamiltonian operator as a sum of propagators using a differential representation. The proposed approach, named Hamiltonian operator approximation (HOA), is designed to benefit analog quantum simulators, …
Efficient self-consistent learning of gate set Pauli noise
Pritzker School of Molecular Engineering, The University of Chicago（芝加哥大学普里茨克分子工程学院）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Department of Computer Science, Virginia Tech（弗吉尼亚理工大学计算机科学系）；Phasecraft Inc.（Phasecraft公司）
We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli "depolarization" channel via the Pauli twirl approximation, and obtain the logical error rate as a function of the qubit T1, T2 and state preparation, gate, and readout errors. A numerical Monte Carlo simulation is performed to obtain the logical error rates and a leading-order analytic formula is derived to estimate their behavior below threshold. Our resu…
