Alexei Kitaev, William A. Webb
We present an algorithm that prepares multidimensional Gaussian wavefunctions on qubit arrays and an application of such wavefunctions to multidimensional resampling, a technique useful in quantum digital simulation.
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Quantum computation with the eigenstate thermalization hypothesis instead of wavefunction preparation
提出利用量子电路在时间演化下的热化能力来求解线性代数问题，通过本征态热化假说和完全遍历性产生本征态的等概率叠加，结合量子相位估计实现输入算符函数的计算，从而在多项式对数时间内避免复杂的波函数制备。
Adiabatic state preparation from general initial states
本文提出从一般初始波函数出发的绝热态制备启发式方法，通过近似父哈密顿量构造绝热路径，并成功应用于水和亚甲基基态模拟。
Clifford-efficient sparse state preparation for molecular wavefunctions
该研究提出一种面向分子波函数的稀疏量子态制备方法，利用GF(2)上仿射关系减少非克利福德门与辅助量子比特，在分子基准测试中辅助量子比特用量最少且非克利福德门数量相当。
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important instrument, to classify relevant many-particle wavefunctions, and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions ba…
This paper contains initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves dualising a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the Pusey-Barrett-Rudolph theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable p…
Quantum state preparation and readout with modulated electrons
本文全面研究了调制电子波函数在与量子发射体相互作用时制备和读出其量子态的能力，揭示了周期性电子梳和非理想调制电子波包在诱导类拉比动力学、实现量子态制备及量子态层析方面的潜力，并确立了实验可行平台需满足的参数平衡。
Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires ${\cal O}(2^{n_Q})$ entangling gates on a quantum computer with $n_Q$ qubits per site. It is conceivable that, instead, initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a non-interacting scalar field theory, initializing to a symmetric exponential wavefunction requires $n_Q-1$ entangling gates, compared with the $2^{n_Q-1} + n_Q-3 + δ_{n_Q,1}…
Efficient classical representation and quantum state preparation of complete active space wavefunctions
针对强电子关联分子，提出基于量子Paldus变换的完全活性空间波函数高效经典表示（矩阵乘积态，键维O(d^2)）和量子态制备方法，复杂度O(d^3)，较现有方法指数级改进。
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory. We demonstrate a general method for obtaining the exact functional as a machine learned model from a sufficiently powerful quantum computer. Only existing assumptions for the current feasibility of solutions on the quantum computer are used. Several known algorithms including quantum phase estimation, quantum amplitude estimation, and quantum gradient methods…
We introduce a protocol capable of generating a general measurement operator for a mechanical resonator. The technique requires a qubit-resonator interaction and uses a coherent pulse to drive qubit transitions. This is followed by projective measurement of the qubit's energy, constraining the resonator in a state that depends on the pulse shape. The freedom to choose a pulse shape for the coherent drive enables an arbitrary position-basis measurement operator. Using this measurement operator, we outline a two pulse protocol that probabilistically generates a pure mechanical state with a desir…
Minimizing state preparation times in pulse-level variational molecular simulations
针对NISQ设备相干时间短的限制，本文研究了ctrl-VQE变分脉冲整形算法在耦合transmon量子比特设备上制备分子波函数的最短脉冲，发现时间最优脉冲呈bang-bang形式，且计算子空间外的泄漏能加速态制备并降低相干时间要求。
Information versus Physicality: On the Nature of the Wavefunctions of Quantum Mechanics
该研究指出PBR定理关于波函数与物理态分布关联的初始假设存在缺陷，违背量子力学线性结构与玻恩定则，证明其论证无法解答波函数的时空本体论地位问题。
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum states on a lattice in real space. In particular, the present algorithm is able to prepare general pure and mixed many-particle states of any number of particles. It relies on a procedure for converting from a second-quantized state to its first-quantized counterpart. The algorithm is efficient in that it operates in time that is polynomial in all the essentia…
Efficient Preparation of Quantum States via Randomized Truncation
本文提出一种随机化量子态制备方法，通过概率放大小振幅以减少门操作数量，显著提升复杂态初始化的效率和可行性。
Quantum state preparation for multivariate functions
本文提出通过线性组合傅里叶与切比雪夫基函数的块编码来制备多元函数量子态，无需算术电路或量子傅里叶变换，并在离子阱处理器上验证了高斯分布制备。
As we enter a new era of quantum technology, it is increasingly important to develop methods to aid in the accurate preparation of quantum states for a variety of materials, matter, and devices. Computational techniques can be used to reconstruct a state from data, however the growing number of qubits demands ongoing algorithmic advances in order to keep pace with experiments. In this paper, we present an open-source software package called QuCumber that uses machine learning to reconstruct a quantum state consistent with a set of projective measurements. QuCumber uses a restricted Boltzmann m…
Status of quantum wavefunction is one of the most debated issues in quantum foundations -- whether it corresponds directly to the reality or just represents knowledge or information about some aspect of reality. In this letter we propose a {\it $ψ$-ontology} theorem that excludes a class of ontological explanations where quantum wavefunction is treated as mere information. Our result, unlike the acclaimed Pusey-Barrett-Rudolph's theorem, does not presume the absence of holistic ontological properties for product quantum preparations. At the core of our derivation we utilize the seminal no-go r…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while unnecessary states are projected out of the Hilbert space. We provide a bijective mapping using combinatoric ranking to bijectively map fermion basis states to qubit basis states and express operators in the standard spin representation. We then evaluate compact mapping using the Variational Quantum Eigensolver (VQE) with the unitary coupled cluster singles and d…
Quantum State Preparation Of Multiconfigurational States For Quantum Chemistry
本文提出了一种利用Givens旋转制备多配置态的量子电路方法，并比较了其与利用化学状态向量稀疏性的替代技术，展示了在量子化学应用中的优势。
Advancing Practical Quantum Embedding Simulations via Operator Commutativity Based State Preparation for Complex Chemical Systems
本文提出基于算符交换性的动态ansatz构造策略，结合密度矩阵嵌入理论框架，提升大分子系统模拟的准确性和效率，减少量子门需求。
Shallow Electronic State Preparation for Quantum Chemistry with Quantum Monte Carlo Pre-Selection
提出一种量子蒙特卡洛预筛选程序，构建紧凑的Givens旋转拟设，在保持数对称性的同时生成比传统方法更浅的量子电路，并在Quantinuum H1上验证其在高噪声下优于复杂拟设。
Simulating 2D topological quantum phase transitions on a digital quantum computer
本研究提出基于等距张量网络的线性深度参数化量子电路设计方法，可在数字量子计算机上高效制备二维拓扑相变多体基态，并验证了其相变特性与全息模拟可行性。
State preparation of AGP on a quantum computer without number projection
本文提出一种在量子计算机上确定性、多项式代价制备 AGP/ESP 态的算法，无需粒子数对称性破缺与恢复，并揭示其可由解纠缠幺正配对耦合簇与 Jastrow 层实现。
We construct a local $ψ$-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state $|ψ_e(t)\rangle$ as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state $|ψ_o(t)\rangle$ which is different from the prepared quantum state $|ψ_e(t)\rangle$ and has an ontic status. The ontic state of a single particle consists of two parts. First, a single particle ontic quantum state $χ(\vec{x},t)|i…
Tailored and Externally Corrected Coupled Cluster with Quantum Inputs
本文提出利用量子计算的波函数重叠改进经典耦合簇方法，以更准确地处理分子电子结构中的静态和动态相关效应。
The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized circuits, but this becomes increasingly challenging with circuit size. As a consequence, the utility of large-scale circuit optimization is relatively unknown. In this work we demonstrate that purely classical resources can be used to optimize quantum circuits in an approximate but robust manner such that we can bridge the resources that we have from high perfo…
We implement and characterize a numerical algorithm inspired by the $s$-source framework [Phys. Rev.~B 93, 045127 (2016)] for building a quantum many-body ground state wavefunction on a lattice of size $2L$ by applying adiabatic evolution to the corresponding ground state at size $L$, along with $L$ interleaved ancillae. The procedure can in principle be iterated to repeatedly double the size of the system. We implement the algorithm for several one dimensional spin model Hamiltonians, and find that the construction works particularly well when the gap is large and, interestingly, at scale inv…
A Euclidean Monte-Carlo-informed route to ground-state preparation for quantum simulation of scalar field theory
针对量子场论量子模拟中非平凡初始态制备的难题，本研究利用欧几里得时间蒙特卡洛的经典信息，提出可高效转化为多项式门复杂度量子线路的变分拟设族，搭建了欧几里得与闵可夫斯基描述的桥梁。
Spin coupling is all you need: Encoding strong electron correlation in molecules on quantum computers
本文提出在量子计算机上通过自旋耦合初始态直接编码强关联分子系统的纠缠结构，避免指数级行列式开销，并提供高效制备电路，显著降低量子相位估计等算法的运行时间，为可扩展量子模拟奠定关键基础。
Vibrational ADAPT-VQE: Critical points leads to problematic convergence
本研究构建振动ADAPT-VQE（vADAPT-VQE）理论框架，验证其算法性能时发现波函数制备过程频繁出现临界点，提示该方法制备振动波函数效用会衰减，需进一步研究规避方案。
Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
提出基于序率截断的 SeqHT 方法，推导算子贡献上界，并在 ibm_sherbrooke 上验证其可将 λϕ⁴ 绝热态制备电路深度降低约30%。
Dissipative ground state preparation in ab initio electronic structure theory
本研究提出了一种基于利恩布兰德动力学的耗散方法，用于在量子计算机上高效准备从头电子结构问题的基态，通过两种通用类型的跳跃算符实现，且不依赖变分参数。
The negative hydrogen ion is the first three body quantum problem whose ground state energy is calculated using the `Chandrasekhar Wavefunction' that accounts for the electron-electron correlation. Solving multi-body systems is a daunting task in quantum mechanics as it includes choosing a trial wavefunction and the calculation of integrals for the system that becomes almost impossible for systems with three or more particles. This difficulty can be addressed by quantum computers. They have emerged as a tool to address different electronic structure problems with remarkable efficiency. They ha…
We present a new geometry of spacetime where events may be positive dimensional. This geometry is obtained by applying the identity of indiscernibles, which is a fundamental principle of quantum statistics, to time. Quantum nonlocality arises as a natural consequence of this geometry. We also examine the ontology of the wavefunction in this framework. In particular, we show how entanglement swapping in spacetime invalidates the preparation assumption of the PBR theorem.
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard QM picture, the proposed model only uses integer-valued quantities and arithmetic operations. In particular, it assumes a discrete spacetime under the form of an euclidean lattice. The proposed approach describes individual particle trajectories as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associa…
Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. Due to long experimental preparation times, obtaining projective measurement data can be relatively slow for large arrays, which poses a challenge for state reconstruction methods such as tomography. Today, novel groundstate wavefunction ansätze like recurrent neural networks (RNNs) can be efficiently trained not only from projective measurement data, but also through Hamiltonian-guided variational Monte Carlo (VMC). In this paper, we demonstrate how pretrainin…
Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, and in-situ tuning of parameters. We show how to realise strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realised by dynamic tuning of the cavity resonances. We demonstrate the existence of Fractional Quantum Hall states by com- puting topological invariants, phase transitions between topologically distinct states, and Laughlin wavefunction overlap.
Quantum sensing with critical systems: impact of symmetry, imperfections, and decoherence
研究借助量子临界波函数开发干涉传感协议，与GHZ态等比较性能，并基于对称性引入算法识别最优测量策略，研究其在多种情况下的鲁棒性，发现临界系统优势及非酉变形可提高精度，结合相关成果，干涉传感前景良好。
Operator Commutativity Screening and Progressive Operator Block Reordering toward Many-body Inspired Quantum State Preparation
针对VQE拟设设计难题，提出通过交换性筛选和渐进式算符块重排的动态构建策略，以更少参数实现精确能量并绕过局部陷阱，在强关联体系成功再现基态。
The observation of quantum phenomena in macroscopic mechanical oscillators has been a subject of interest since the inception of quantum mechanics. Prerequisite to this regime are both preparation of the mechanical oscillator at low phonon occupancy and a measurement sensitivity at the scale of the spread of the oscillator's ground state wavefunction. It has been widely perceived that the most promising approach to address these two challenges are electro nanomechanical systems. Here we approach for the first time the quantum regime with a mechanical oscillator of mesoscopic dimensions--discer…
Amplitude Encoding of Slater-Type Orbitals via Matrix Product States: Efficient State Preparation and Integral Evaluation on Quantum Hardware
本文研究了利用矩阵积态在量子计算机上实现Slater型轨道的振幅编码，展示了在量子硬件上高效的状态制备和积分计算方法，验证了在三维空间中多中心积分的计算精度。
End-to-End Simulation of Chemical Dynamics on a Quantum Computer
本文提出一种端到端量子算法，无需近似方法，实现非绝热化学动力学的高效模拟，具有子线性复杂度，适用于光化学等应用。
A Grid-Based Quantum Algorithm for the Time-Dependent Simulation of Infrared Spectra
本文提出一种基于网格的量子算法，用于在量子计算机上模拟红外光谱，通过概率策略应用非幺正偶极子算符，并采用Split Operator-量子傅里叶变换时间演化方案，实现了对水分子振动模型的准确模拟。
Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of non-linear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resona…
It is believed that one of the first useful applications for a quantum computer will be the preparation of groundstates of molecular Hamiltonians. A crucial task involving state preparation and readout is obtaining physical observables of such states, which are typically estimated using projective measurements on the qubits. At present, measurement data is costly and time-consuming to obtain on any quantum computing architecture, which has significant consequences for the statistical errors of estimators. In this paper, we adapt common neural network models (restricted Boltzmann machines and r…
Rapidly Achieving Chemical Accuracy with Quantum Computing Enforced Language Model
本研究提出量子计算增强的transformer语言模型QiankunNet-VQE，融合经典与量子资源，在12量子比特下实现媲美经典最优方法的精度，无需误差缓解即可克服VQE局限，为求解多电子薛定谔方程提供实用量子优势新路径。
Multi-QIDA method for VQE state preparation in molecular systems
针对VQE态制备的可扩展性与高电路深度等挑战，本研究将Multi-QIDA方法应用于分子系统，通过结合QMI矩阵、最小/最大生成树与逐层优化及SO(4)相关器，构建了浅层高效量子电路，有效恢复了分子相关性。
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and inter-electronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born-Oppenheimer approximation, but faster and more efficient as well, for al…
Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The problem of speeding up these processes has garnered a large amount of interest, resulting in a menagerie of approaches, most notably quantum optimal control and shortcuts to adiabaticity. The two approaches are complementary: optimal control manipulates control fields to steer the dynamics in the minimum allowed time while shortcut…
Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. The same goes for Ansätze on a quantum computer. We develop a unitary coupled cluster method on the antisymmetrized geminal power (AGP) -- a state formally equivalent to the number-projected Bardeen--Cooper--Schrieffer wavefunction. We demonstrate our method for the single-band Fermi--Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than $\mathcal{O}(…
Generative Circuit Design for Quantum-Selected Configuration Interaction
本文提出基于生成量子本征求解器的框架，通过Transformer策略优化ansatz结构，实现高精度子空间设计，在N2分子中验证，优化电路在门数上显著优于时间演化电路，达到化学精度。
Beyond VQE and QPE: A Noise- and Sampling-Error-Tolerant Quantum Algorithm with Heisenberg-Limited Precision
本文提出Witnessed Quantum Time Evolution算法，通过单个辅助量子比特控制实时演算算符并利用傅里叶分析，实现任意量子系统的本征能谱高效计算，具有海森堡极限精度和抗噪声能力。
The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmica…
Enhancing Accuracy of Quantum-Selected Configuration Interaction Calculations using Multireference Perturbation Theory: Application to Aromatic Molecules
本研究提出基于多参考微扰理论改进量子选择组态相互作用（QSCI）的精度，以QSCI波函数为参考，应用于萘和并四苯的基态和激发态计算，显著提高精度。
Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the form of the wavefunction ansatz. Recently in Nat. Commun. 10, 3007 (2019), an algorithm termed ADAPT-VQE was introduced to build system-adapted ansätze with substantially fewer variational parameters compared to other approaches. This algorithm relies heavily on a predefined operator pool with which it builds the ansatz. However, Nat. Commun. 10, 3007 (2019) d…
Boson-fermion universality of mesoscopic entanglement fluctuations in free systems
本文研究耦合谐振子链远离平衡时的长时间纠缠动力学，发现其纠缠涨落统计与自由费米子模型严格一致，表现出玻色子-费米子普适性，并揭示了涨落分布的不对称尾部及方差标度交叉行为。
A Novel Quantum-Classical Hybrid Algorithm for Determining Eigenstate Energies in Quantum Systems
提出新型量子算法XZ24，通过辅助量子比特和傅里叶变换高效计算任意量子系统的本征能谱，免去本征态制备且降低测量开销，实现多本征能量同时计算。
We reformulate the continuous space Schrödinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. Binary encoding of position produces a Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code, and a Hamming distance 2 Gray code yields the additional effect of reducing the spin model down to the XZ and transverse Ising model respectively. We also identify the bijective m…
Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits
提出SC-ADAPT-VQE算法，利用关联指数衰减和经典计算确定可扩展电路，在IBM量子计算机上成功制备100量子比特施温格模型真空态，精度随电路深度指数收敛。
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