Indian Institute of Engineering Science And Technology（印度工程科学理工学院）；University of Waterloo（滑铁卢大学）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Indian Institute of Science Education and Research, Thiruvananthapuram（特鲁万纳姆拉浦尔印度科学教育与研究学院）；Wilfrid Laurier University（威尔弗里德·劳雷尔大学）
Amit Anand, Sanchit Srivastava, Sayan Gangopadhyay, Shohini Ghose
We show that currently available noisy intermediate-scale quantum (NISQ) computers can be used for versatile quantum simulations of chaotic systems. We introduce a novel classical-quantum hybrid approachfor exploring the dynamics of the chaotic quantum kicked top (QKT) on a universal quantum computer. The programmability of this approach allows us to experimentally explore the complete range of QKT chaoticity parameter regimes inaccessible to previous studies. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer (IBMQ), we observe periodicities in the evolution of the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit entanglement. We also demonstrate a connection between entanglement and delocalization in the 2-qubit QKT, confirming theoretical predictions.
We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by…
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.
Noise dominates every aspect of near-term quantum computers, rendering it exceedingly difficult to carry out even small computations. In this paper we are concerned with the modelling of noise in Noisy Intermediate-Scale Quantum (NISQ) computers. We focus on three error groups that represent the main sources of noise during a computation and present quantum channels that model each source. We engineer a noise model that combines all three noise channels and simulates the evolution of the quantum computer using its calibrated error rates. We run various experiments of our model, showcasing its …
It is well known that a quantum circuit on $N$ qubits composed of Clifford gates with the addition of $k$ non Clifford gates can be simulated on a classical computer by an algorithm scaling as $\text{poly}(N)\exp(k)$[1]. We show that, for a quantum circuit to simulate quantum chaotic behavior, it is both necessary and sufficient that $k=O(N)$. This result implies the impossibility of simulating quantum chaos on a classical computer.
Quantum computing is an emerging technology, promising a paradigm shift in computing, and allowing for speedups in many different problems. However, quantum devices are still in their early stages, most with only a small number qubits. This places a reliance on simulation to develop quantum algorithms and to verify these devices. While there exists many algorithms for the simulation of quantum circuits, there is (at the time of writing) no tools which use OpenCL to parallelize this simulation, thereby taking advantage of devices such as GPUs while still remaining portable. In this paper, such …
Accurate quantum chemistry simulations remain challenging on classical computers for problems of industrially relevant sizes and there is reason for hope that quantum computing may help push the boundaries of what is technically feasible. While variational quantum eigensolver (VQE) algorithms may already turn noisy intermediate scale quantum (NISQ) devices into useful machines, one has to make all efforts to use the scarce quantum resources as efficiently as possible. We combine the so-called seniority-zero, or paired-electron, approximation of computational quantum chemistry with techniques f…
Simulating Electron Transfer on Noisy Quantum Computers
Institute of Engineering Thermodynamics, German Aerospace Center (DLR)（德国航空航天中心工程热力学研究所）；Helmholtz Institute Ulm（乌尔姆亥姆霍兹研究所）；Institute of Software Technology, German Aerospace Center (DLR)（德国航空航天中心软件技术研究所）；HQS Quantum Simulations GmbH（HQS量子模拟有限公司）；Department of Physics, Ulm University（乌尔姆大学物理系）
Two qubit density matrices, which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initi…
The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE algorithm for simulating extended systems. However, the numerical study of an one-dimensional (1D) infinite hydrogen chain using existing VQE algorithms shows a remarkable deviation of the ground state energy with respect to the exact full configuration interaction (FCI) result. Here, we present two schemes to improve the accuracy of quantum simulations for ex…
Quantum computers are a promising candidate to radically expand computational science through increased computing power and more effective algorithms. In particular quantum computing could have a tremendous impact in the field of quantum cosmology. The goal of quantum cosmology is to describe the evolution of the Universe through the Wheeler-DeWitt equation or path integral methods without having to first formulate a full theory of quantum gravity. The quantum computer provides an advantage in this endeavor because it can perform path integrals in Lorentzian space and does not require construc…
Variational quantum eigensolver (VQE) is promising to show quantum advantage on near-term noisy-intermediate-scale quantum (NISQ) computers. One central problem of VQE is the effect of noise, especially the physical noise on realistic quantum computers. We study systematically the effect of noise for the VQE algorithm, by performing numerical simulations with various local noise models, including the amplitude damping, dephasing, and depolarizing noise. We show that the ground state energy will deviate from the exact value as the noise probability increase and normally noise will accumulate as…
Comments on `Stable Quantum Computation of Unstable Classical Chaos,' `Efficient Quantum Computing Insensitive to Phase Errors,' and `Quantum Computer Inverting Time Arrow for Macroscopic Systems'
最近，论文B。乔治和D.L. Shepelyansky，Phys. Rev. 86_，5393（2001）中提出的[C. Zalka，quant-ph/0110019; L. Di'osi，quant-ph/0110026]。这封信声称，当在量子计算机上执行Arnold猫映射下的相空间密度演化时，误差敏感性将呈指数级加速和降低。一方面，有些观点以前的答复者尚未提出。另一方面，作者的反应[quant-ph/0110142]提出了新的问题。本说明述及这两个问题。
We simulate the dynamics of braiding Majorana zero modes on an IBM Quantum computer. We find the native quantum gates introduce too much noise to observe braiding. Instead, we use Qiskit Pulse to develop scaled two-qubit quantum gates that better match the unitary time evolution operator and enable us to observe braiding. This work demonstrates that quantum computers can be used for simulation, and highlights the use of pulse-level control for programming quantum computers and constitutes the first experimental evidence of braiding via dynamical Hamiltonian evolution.
We present a novel method for solving eigenvalue problems on a quantum computer based on spectroscopy. The method works by coupling a "probe" qubit to a set of system simulation qubits and then time evolving both the probe and the system under Hamiltonian dynamics. In this way, we simulate spectroscopy on a quantum computer. We test our method on the IBM quantum hardware for a simple single spin model and an interacting Kitaev chain model. For the Kitaev chain, we trace out the pseudo-topological phase boundary for a two-site model.
Error mitigation is likely to be key in obtaining near term quantum advantage. In this work we present one of the first implementations of several Clifford data regression based methods which are used to mitigate the effect of noise in real quantum data. We explore the dynamics of the 1-D Ising model with transverse and longitudinal magnetic fields, highlighting signatures of confinement. We find in general Clifford data regression based techniques are advantageous in comparison with zero-noise extrapolation and obtain quantitative agreement with exact results for systems of 9 qubits with circ…
Simulating the Dynamics of Markovian Quantum Processes by Quantum Collision Models on Quantum Computers
RIKEN Center for Computational Science（理化学研究所计算科学中心）；Q-CTRL；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；RIKEN Pioneering Research Institute（理化学研究所先导研究本部）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）
The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples, with experimental demonstrations and potential for obtaining a quantum computer to solve problems believed classically impossible. This introduces a challenge: how does one design or understand such photonic networks? One must be able to calculate observables using general methods capable of treating arbitrary inputs, dissipation and noise. We develop novel com…
Open systems dynamics: Simulating master equations in the computer
主方程可能是任何研究耗散量子光学的人最基本的方程。在这种情况下，在计算机中编码和模拟这些方程的有效方法是非常有用的，在这篇笔记中，我试图以一种全面的方式介绍我是如何做到这一点的，重点是Matlab，但使其足够通用，以便可以直接翻译为任何其他语言或软件的选择。我的大部分方法都是从胡安·何塞·加西亚-里波尔（Juan José García-Ripoll）那里继承来的（他的数学能力我怎么称赞都不为过），我在这里和那里改变它们，以适应我（相当有限的）数字大脑的工作方式，并尽可能地将它们与我如何理解它们背后的理论联系起来。目前，笔记集中在如何编码主方程并找到它们的稳态，但我希望很快我就能用时间演化方法更新它们，包括如何处理依赖于时间的主方程。在过去的4年里，我在各种不同的背景下测试了这些方法，包括电路量子电动力学，激光问题，光学参量振荡器和光机系统。评论和（建设性的）批评是非常欢迎的，并将适当的信贷和承认。
The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin system in the presence of magnetic field can be obtained from the Ising model. We simulate the above Hamiltonian by designing a quantum circuit with precise gate measurement and execute with the IBMQ experience platform through different $N$ states with controlled energy separation where we can check quantum synchronization in a dissipative lattice system. Our r…
ArQTiC is an open-source, full-stack software package built for the simulations of materials on quantum computers. It currently can simulate materials that can be modeled by any Hamiltonian derived from a generic, one-dimensional, time-dependent Heisenberg Hamiltonain. ArQTiC includes modules for generating quantum programs for real- and imaginary-time evolution, quantum circuit optimization, connection to various quantum backends via the cloud, and post-processing of quantum results. By enabling users to seamlessly perform and analyze materials simulations on quantum computers by simply provi…
Quantum materials exhibit a wide array of exotic phenomena and practically useful properties. A better understanding of these materials can provide deeper insights into fundamental physics in the quantum realm as well as advance technology for entertainment, healthcare, and sustainability. The emergence of digital quantum computers (DQCs), which can efficiently perform quantum simulations that are otherwise intractable on classical computers, provides a promising path forward for testing and analyzing the remarkable, and often counter-intuitive, behavior of quantum materials. Equipped with the…
Quantum computers have the potential to efficiently simulate large-scale quantum systems for which classical approaches are bound to fail. Even though several existing quantum devices now feature total qubit numbers of more than one hundred, their applicability remains plagued by the presence of noise and errors. Thus, the degree to which large quantum systems can successfully be simulated on these devices remains unclear. Here, we report on cloud simulations performed on several of IBM's superconducting quantum computers to simulate ground states of spin chains having a wide range of system s…
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…
Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics -- we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous time dynamics of observables and reachable system sizes are small …
