Percy Deift, Mary Beth Ruskai, Wolfgang Spitzer
We use elementary variational arguments to prove, and improve on, gap estimates which arise in simulating quantum circuits by adiabatic evolution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Simulating Circuit Layout for Distributed Quantum Computing
本文提出了一种用于分布式量子计算的电路布局模拟工具，通过分而治之的方法实现电路的编译和组装。
We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of $L$ gates we can construct a quantum adiabatic algorithm with time complexity of $O(L)$. Additionally, our construction shows that one may exponentially speed up some quantum adiabatic algorithms by properly choosing an evolution path.
Quantum algorithm for simulating non-adiabatic dynamics at metallic surfaces
本研究提出了一种量子算法，用于高效模拟分子-金属界面的非绝热动力学，展示了其在现实模型系统中的低实现成本和应用潜力。
Towards adiabatic quantum computing using compressed quantum circuits
本研究提出基于张量网络的固定深度参数化量子电路经典优化方法，结合反绝热驱动抑制非绝热跃迁，在量子伊辛链基态制备任务中性能优于传统Trotter乘积公式，可应用于组合优化。
A Toffoli gate ($C^{n}$-NOT gate) is regarded as an important unitary gate in quantum computation, and is simulated by a quantum circuit composed of $C^{2}$-NOT gates. This paper presents a quantum circuit with a new configuration of $C^{2}$-NOT gates simulating a $C^{2m+1}$-NOT operation under the condition $m=2^{n}$ ($n=1,2,...$). The circuit is composed of units called multi-qubits gates (MQGs), each of which performs $m$ $C^{2}$-NOT operations simultaneously on $3m$ qubits. Simultaneous operations eliminate the need to manipulate qubits individually, as required in conventional quantum cir…
We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient.
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will poin…
Recently, constant-depth quantum circuits are proved more powerful than their classical counterparts at solving certain problems, e.g., the two-dimensional (2D) hidden linear function (HLF) problem regarding a symmetric binary matrix. To further investigate the boundary between classical and quantum computing models, in this work we propose a high-performance two-stage classical scheme to solve a full-sampling variant of the 2D HLF problem, which combines traditional classical parallel algorithms and a gate-based classical circuit model together for exactly simulating the target shallow quantu…
Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard circuit model. However, it can be shown that the two models are computationally equivalent. The key to the proof is a mapping of a quantum circuit to an an adiabatic evolution, and then showing that the minimum spectral gap of the adiabatic Hamiltonian is at least inverse polynomial in the number of computational steps $L$. In this paper we provide two simplified proofs that the gap is inverse polynomial. Both proofs result in the same lower bound for the minimum gap, which for…
We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the protocol can efficiently simulate a large set of multi-qubit mixed states that are not mixtures of stabilizer states. The existence of these 'bound states' was previously only known for odd-dimensional systems like qutrits. The algorithm also has the favorable property that circuits with depolarizing noise are simulated much faster than unitary circuits. Th…
Superconducting quantum circuits is one of the leading candidates for a universal quantum computer. Designing novel qubit and multiqubit superconducting circuits requires the ability to simulate and analyze the properties of a general circuit. In particular, going outside the transmon approach, we cannot make assumptions on anharmonicity, thus precluding blackbox quantization approaches and necessitating the formal circuit quantization approach. We consider and solve two issues involved in simulating general superconducting circuits. One of the issues is the handling of free modes in the circu…
Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits
本文提出一种新的量子绝热定理，消除了绝热时间尺度中的 2^n 因子和截断依赖，并将其应用于超导电路，给出通量量子比特的绝热时间尺度对电路参数的显式依赖，同时证明量子退火末段泄漏不可避免。
We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building blocks in the construction of arbitrary `adiabatic circuits', analogously to the manner in which gates are used in the circuit model. One implication of the above construction is that arbitrary classical boolean circuits as well as gate model circuits may be directly translated to adiabatic algorithms with no additional resources or complexities. We show that …
We generalize the quasi-diabatic (QD) propagation scheme to simulate the non-adiabatic polariton dynamics in molecule-cavity hybrid systems. The adiabatic-Fock states, which are the tensor product states of the adiabatic electronic states of the molecule and photon Fock states, are used as the locally well-defined diabatic states for the dynamics propagation. These locally well-defined diabatic states allow using any diabatic quantum dynamics methods for dynamics propagation, and the definition of these states will be updated at every nuclear time step. We use several recently developed non-ad…
Method for simulating open-system dynamics using mid-circuit measurements on a quantum computer
提出一种利用中间电路测量和重置在量子计算机上模拟开放电子系统动力学的方法，无需额外量子比特，并在IBM量子计算机上验证，可普遍适用。
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the `shortcut to adiabaticity' (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting …
Quantum circuits for simulating linear interferometers
受量子工作量证明协议启发，研究人员提出基于二次量子化的数字量子线路模拟线性光学干涉仪的方法，给出资源复杂度，还推出可生成对应线路的Aquinas软件包并给出实例。
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several efficient strong simulation techniques are known for restricted families of quantum circuits and we develop an additional technique in this article. Further, we show that strong simulation algorithms perform another fundamental task: solving search problems. Efficient strong simulation techniques allow solutions to a class of search problems to be counted and found …
Coherent population transfer with polariton states in circuit QED
本文提出利用绝热捷径方法加速超导电路中的STIRAP过程，在电路QED极化激元Λ系统中实现快速高保真的超绝热相干布居转移。
Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
本文将DMRG量子电路模拟从MPS扩展到TTN，通过变分压缩近似演化态，并在随机电路和QAOA上验证其内存与保真度优势。
Simulating dynamics of RLC circuits with a quantum differential-algebraic equations solver
本文提出一种量子算法，用于模拟包含电阻、电感和电容的RLC电路动力学，通过量子态编码电压和电流值，实现指数级加速，证明了该问题的BQP难性。
We examine a proposed auction using quantum states to represent bids and distributed adiabatic search to find the winner. When the auctioneer follows the protocol, the final measurement giving the outcome of the auction also destroys the bid states, thereby preserving privacy of losing bidders. We describe how a dishonest auctioneer could alter the protocol to violate this privacy guarantee, and present methods by which bidders can counter such attacks. We also suggest possible quantum circuit implementations of the auctions protocol, and quantum circuits to perpetrate and to counter attacks b…
We propose how to engineer the longitudinal coupling to accelerate the measurement of a qubit longitudinally coupled to a cavity, motivated by the concept of shortcuts to adiabaticity. Different modulations are inversely designed from two methods of inverse engineering and counter-diabatic driving, for achieving larger values of the signal-to-noise ratio (SNR) at nanosecond scale. By comparison, we demonstrate that our protocols outperform the usual periodic modulations on the pointer state separation and SNR. Finally, we show a possible implementation considering state-of-the-art circuit quan…
We introduce a method to speed up adiabatic protocols for creating entanglement between two qubits dispersively coupled to a transmission line, while keeping fidelities high and maintaining robustness to control errors. The method takes genuinely adiabatic sweeps, ranging from a simple Landau-Zener drive to boundary cancellation methods and local adiabatic drivings, and adds fast oscillations to speed up the protocol while canceling unwanted transitions. We compare our protocol with existing adiabatic methods in a state-of-the-art parameter range and show substantial gains. Numerical simulatio…
Shortcuts to adiabaticity in superconducting circuits for fast multi-partite state generation
本文提出用逆向工程方法设计量子比特与场模间的纵向耦合，借助绝热捷径在超导电路中快速生成多体量子门，生成时间达纳秒级且不受组件数和耗散显著影响。
Linear canonical transformations of bosonic modes correspond to Gaussian unitaries, which comprise passive linear-optical transformations as effected by a multiport passive interferometer and active Bogoliubov transformations as effected by a nonlinear amplification medium. As a consequence of the Bloch-Messiah theorem, any Gaussian unitary can be decomposed into a passive interferometer followed by a layer of single-mode squeezers and another passive interferometer. Here, it is shown how to circumvent the need for active transformations. Namely, we provide a technique to simulate sampling fro…
We present a quantum algorithm for implementing $ϕ^4$ lattice scalar field theory on qubit computers. The field is represented in the discretized field amplitude basis. The number of qubits and elementary gates required by the implementation of the evolution operator is proportional to the lattice size. The algorithm allows efficient $ϕ^4$ state preparation for a large range of input parameters in both the normal and broken-symmetry phases. The states are prepared using a combination of variational and adiabatic evolution methods. First, the ground state of a local Hamiltonian, which includes …
Practical framework for simulating permutation-equivariant quantum circuits
本文提出一种高效模拟置换等变量子电路的算法，利用k-局部门生成器假设，将时间复杂度降至O(n^{ω+1})，并通过Lipkin-Meshkov-Glick模型验证，证明在n=512时可在两分钟内计算纠缠度。
Simulating quantum circuits with a neural statebank
提出神经状态库，通过自回归Transformer沿电路轨迹学习波函数，以紧凑表示评估振幅和生成样本，在34量子比特上达到约10^{-2}的保真度，优于其他近似模拟器且内存远少于精确模拟。
Simulating quantum circuit expectation values by Clifford perturbation theory
本文提出基于海森堡绘景泡利项截断的克利福德微扰方法，用于高效近似大型近克利福德电路的期望值，并在QAOA基准上验证了其有效性及误差量化能力。
Simulating quantum circuits using the multi-scale entanglement renormalization ansatz
提出基于多尺度纠缠重整化假设（MERA）和黎曼优化的可扩展技术，用于中等规模量子电路的近似模拟，并在243量子比特电路上验证了有效性。
Shortcuts to adiabaticity (STA) are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various STA protocols have been demonstrated in closed systems. However, realizing STA for open quantum systems has presented a greater challenge, due to complex controls required in existing proposals. Here we present the first experimental demonstration of STA for open quantum systems, using a superconducting circuit QED system consisting of two coupled bosonic oscillators…
Studying out-of-equilibrium physics in quantum systems under quantum quench is of vast experimental and theoretical interests. Using periodic quantum quenches, we present an experimentally accessible scheme to simulate the quantum Zeno and anti-Zeno effects in an open quantum system of a single superconducting qubit interacting with an array of transmission line resonators. The scheme is based on the following two observations: Firstly, compared with conventional systems, the short-time non-exponential decay in our superconducting circuit system is readily observed; and secondly, a quench-off …
Co-designed Quantum Discrete Adiabatic Linear System Solver Via Dynamic Circuits
提出一种结合动态电路与实时经典处理的协同设计框架，将量子离散绝热演化分段优化，把电路深度从O(steps×depth(U))降至O(depth(U))，在真实噪声下保持超80%保真度。
Classically Simulating Quantum Supremacy IQP Circuits through a Random Graph Approach
本文提出改进的经典算法模拟随机IQP电路，通过振幅计算和稳定子分解将稠密电路模拟复杂度优化至O(((log n)^(4-β))/n^(2-β)*2^n)，并实现笔记本上模拟50量子比特、集群可达70量子比特。
We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap ΔE between the ground state and the first excited state is any constant independent of n, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from eac…
Stimulated Raman adiabatic passage is a quantum protocol that can be used for robust state preparation in a three-level system. It has been commonly employed in quantum optics, but recently this technique has drawn attention also in circuit quantum electrodynamics. The protocol relies on two slowly varying drive pulses that couple the initial and the target state via an intermediate state, which remains unpopulated. Here we study the detrimental effect of the parasitic couplings of the drives into transitions other than those required by the protocol. The effect is most prominent in systems wi…
We propose a scheme for simulating 3+1, 2+1, 1+1 Dirac equation for a free spin-1/2 particle with superconducting josephson circuits consisting of five qubits, four qubits, two qubits respectively. In 3+1D and 2+1D, the flux qubit1 driven by a resonant pulse is in the superposition state of its own two eigenstatesis, and it is used as a bus to induce the (blue)red-sideband excitation consisting of a magnetic pulse acting resonantly on two levels of the flux qubit2 and the energy levels of one phase qubit, which yields two (Anti)Jaynes-Cummings interactions with one driving pulse and reduces th…
The time or cost of simulating a quantum circuit by adiabatic evolution is determined by the spectral gap of the Hamiltonians involved in the simulation. In "standard" constructions based on Feynman's Hamiltonian, such a gap decreases polynomially with the number of gates in the circuit, L. Because a larger gap implies a smaller cost, we study the limits of spectral gap amplification in this context. We show that, under some assumptions on the ground states and the cost of evolving with the Hamiltonians (which apply to the standard constructions), an upper bound on the gap of order 1/L follows…
We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the `sum-of-stabilisers' method with an automated simplification strategy based on the ZX-calculus. Recently it was shown that quantum circuits can be classically simulated by expressing the non-stabiliser gates in a circuit as magic state injections and decomposing them in chunks of 2-6 states at a time, obtaining sums of (efficiently-simulable) stabiliser states with many fewer terms than the naive approach. We adapt these techniques from the original setting of Clifford circuits with magic …
We analyze the optical selection rules of the microwave-assisted transitions in a flux qubit superconducting quantum circuit (SQC). We show that the parities of the states relevant to the superconducting phase in the SQC are well-defined when the external magnetic flux $Φ_{e}=Φ_{0}/2$, then the selection rules are same as the ones for the electric-dipole transitions in usual atoms. When $Φ_{e}\neq Φ_{0}/2$, the symmetry of the potential of the artificial "atom'' is broken, a so-called $Δ$-type "cyclic" three-level atom is formed, where one- and two-photon processes can coexist. We study how th…
Simulation of materials by using quantum processors is envisioned to be a major direction of development in quantum information science. Here we exploit the mathematical analogies between a triangular spin lattice with Dzyaloshinskii-Moriya coupling on one edge and a three-level system driven by three fields in a loop configuation to emulate spin-transport effects. We show that the spin transport efficiency, seen in the three-level system as population transfer, is enhanced when the conditions for superadiabaticity are satisfied. We demonstrate experimentally that phenomena characteristic to s…
Revisiting Quantum Supremacy: Simulating Sycamore-Class Circuits Using Hybrid CPU/GPU HPC Workloads
通过混合CPU/GPU HPC工作负载模拟Sycamore级电路，实现量子霸权的高效仿真并展示其持续性。
We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.
The numerical simulation of quantum circuits is an indispensable tool for development, verification and validation of hybrid quantum-classical algorithms on near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. We present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) which serves as a quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the general purpose, scalable tensor n…
The finite-time isothermal process is fundamental in quantum thermodynamics yet complicated with combination of changing control parameters and the interaction with the thermal bath. Such complexity prevents the direct application of the traditional thermodynamics measurement of the relevant quantities. In this paper, we provide a discrete-step method to separate the work done and the heat exchange in the isothermal process by decomposing the process into piecewise adiabatic and isochoric processes. The piecewise control scheme makes it possible to simulate the whole process on a generic quant…
Simulating quantum circuits with arbitrary local noise using Pauli Propagation
本文提出一种多项式时间经典算法，用于高效模拟典型量子电路在任意非相干局部噪声下的可观测量期望值，通过Pauli路径方法证明了在高概率下截断策略可实现反多项式小的模拟误差。
Shortcuts to adiabaticity is a general method for speeding up adiabatic quantum protocols, and has many potential applications in quantum information processing. Unfortunately, analytically constructing shortcuts to adiabaticity for systems having complex interactions and more than a few levels is a challenging task. This is usually overcome by assuming an idealized Hamiltonian [e.g., only a limited subset of energy levels are retained, and the rotating-wave approximation (RWA) is made]. Here we develop an $analytic$ approach that allows one to go beyond these limitations. Our method is genera…
Matrix Product Evolution: A Method for Simulating Quantum Circuits Using Tensor Networks
针对量子电路经典模拟受希尔伯特空间指数增长限制的问题，提出沿电路深度构建的矩阵乘积演化（MPE）方法，开发拉链式收缩策略，经随机量子电路和多体态演化模拟验证，可作为MPS模拟的补充方法。
Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters $K$ and $d$ of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most $d$ with at most $K$ qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any $(K,d)$-clust…
We propose a general tensor network method for simulating quantum circuits. The method is massively more efficient in computing a large number of correlated bitstring amplitudes and probabilities than existing methods. As an application, we study the sampling problem of Google's Sycamore circuits, which are believed to be beyond the reach of classical supercomputers and have been used to demonstrate quantum supremacy. Using our method, employing a small computational cluster containing 60 graphical processing units (GPUs), we have generated one million correlated bitstrings with some entries f…
Simulating Time Evolution with Fully Optimized Single-Qubit Gates on Parameterized Quantum Circuits
本研究提出一种可同时优化参数化量子电路中单量子比特门转轴与角度的时间演化模拟新方法，可扩展至特定双量子比特门优化，数值实验验证了其在哈密顿量基态求解等场景的有效性，还分析了精度与硬件效率的权衡。
Simulating the quantum switch with quantum circuits is computationally hard
研究证明，用量子电路模拟量子开关在计算上具有指数难度，且无法通过增加调用次数实现
Geometric phases are noise-resilient, and thus provide a robust way towards high fidelity quantum manipulation. Here we experimentally demonstrate arbitrary non-adiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmark…
Characterization and Optimization of Tunable Couplers via Adiabatic Control in Superconducting Circuits
本研究通过绝热控制技术实现超导电路中可调耦合器的高效表征与优化，解决了耦合器校准和控制的难题。
Mechanism of Efficacy in QAOA for Random k-SAT: From Adiabatic Manifold to Sublinear Parameter Optimization
本文研究了QAOA在随机k-SAT问题中的有效性机制，揭示了绝热态转移与QAOA算法之间的对应关系，并提出了一种基于绝热流形的参数优化策略，实现了亚线性参数优化和鲁棒初始化。
BosonSampling is a well-defined scheme for demonstrating quantum supremacy with photons in near term. Although relying only on multi-photon interference in nonadaptive linear-optical networks, it is hard to simulate classically. Here we study BosonSampling using matrix product states, a powerful method from quantum many-body physics. This method stores the instantaneous quantum state during the evolution of photons in the optical quantum circuit, which allows us to reveal the dynamical features of single photons in BosonSampling devices, such as entanglement entropy growth. We show the flexibl…
Simulating adiabatic quantum computation with a variational approach
针对经典资源难以模拟大型量子器件幺正动力学的难题，提出结合含时变分蒙特卡洛方法与关联含时Jastrow拟设的变分方法，可在多种量子问题中实现准确的绝热量子计算模拟。
We propose a scheme for generating SU(2) adiabatic geometric phases in a circuit consisting of three capacitively coupled flux-biased Josephson phase qubits.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。