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Information-Theoretic Bounds on quantum Advantage in Machine Learning

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Physical Review Letters 2021年第19期126卷 190505-190505页

作者： Hsin-Yuan Huang Richard Kueng John Preskill Institute for Quantum Information and Matter Caltech Pasadena California 91125 USA Department of Computing and Mathematical Sciences Caltech Pasadena California 91125 USA Institute for Integrated Circuits Johannes Kepler University Linz Linz 4040 Austria Walter Burke Institute for Theoretical Physics Caltech Pasadena California 91125 USA AWS Center for Quantum Computing Pasadena California 91125 USA

We study the performance of classical and quantum machine learning (ML) models in predicting outcomes of physical experiments. The experiments depend on an input parameter x and involve execution of a (possibly unknown) quantum process E. Our figure of merit is the number of runs of E required to achieve a desired prediction performance. We consider classical ML models that perform a measurement and record the classical outcome after each run of E, and quantum ML models that can access E coherently to acquire quantum data; the classical or quantum data are then used to predict the outcomes of future experiments. We prove that for any input distribution D(x), a classical ML model can provide accurate predictions on average by accessing E a number of times comparable to the optimal quantum ML model. In contrast, for achieving an accurate prediction on all inputs, we prove that the exponential quantum advantage is possible. For example, to predict the expectations of all Pauli observables in an n-qubit system ρ, classical ML models require 2Ω(n) copies of ρ, but we present a quantum ML model using only O(n) copies. Our results clarify where the quantum advantage is possible and highlight the potential for classical ML models to address challenging quantum problems in physics and chemistry.

关键词： Machine learning quantum information processing

The randomized measurement toolbox

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arXiv 2022年

作者： Elben, Andreas Flammia, Steven T. Huang, Hsin-Yuan Kueng, Richard Preskill, John Vermersch, Benoît Zoller, Peter Institute For Quantum Information And Matter Caltech PasadenaCA United States Walter Burke Institute For Theoretical Physics Caltech PasadenaCA United States Institute For Theoretical Physics University Of Innsbruck InnsbruckA-6020 Austria Institute For Quantum Optics Quantum Information Of The Austrian Academy Of Sciences InnsbruckA-6020 Austria AWS Center For Quantum Computing PasadenaCA United States Department Of Computing And Mathematical Sciences Caltech PasadenaCA United States Institute For Integrated Circuits Johannes Kepler University Linz Altenbergerstrasse 69 Linz4040 Austria Univ. Grenoble Alpes CNRS LPMMC Grenoble38000 France

Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of their power, but also makes them difficult to control precisely or characterize accurately using measured classical data. We review recently developed protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In all these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis;then a classical computer processes the measurement outcomes to estimate the desired property. The randomization of the measurement procedure has distinct advantages;for example, a single data set can be employed multiple times to pursue a variety of applications, and imperfections in the measurements are mapped to a simplified noise model that can more easily be mitigated. We discuss a range of use cases that have already been realized in quantum devices, including Hamiltonian simulation tasks, probes of quantum chaos, measurements of nonlocal order parameters, and comparison of quantum states produced in distantly separated laboratories. By providing a workable method for translating a complex quantum state into a succinct classical representation that preserves a rich variety of relevant physical properties, the randomized measurement toolbox strengthens our ability to grasp and control the quantum world. Copyright © 2022, The Authors. All rights reserved.

关键词： Qubits

Provably efficient machine learning for quantum many-body problems

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arXiv 2021年

作者： Huang, Hsin-Yuan Kueng, Richard Torlai, Giacomo Albert, Victor V. Preskill, John Institute for Quantum Information and Matter Department of Computing and Mathematical Sciences Caltech PasadenaCA United States Institute for Integrated Circuits Johannes Kepler University Linz Austria AWS Center for Quantum Computing PasadenaCA United States Joint Center for Quantum Information and Computer Science National Institute of Standards and Technology University of Maryland College ParkMD United States

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases. © 2021, CC BY.

关键词： Machine learning

Bright photon-pair source based on a silicon dual-Mach-Zehnder microring

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Science China(Physics,Mechanics & Astronomy) 2020年第2期63卷 3-6页

作者： Chao Wu YingWen Liu XiaoWen Gu XinXin Yu YueChan Kong Yang Wang XiaoGang Qiang JunJie Wu ZhiHong Zhu XueJun Yang Ping Xu Institute for Quantum Information and State Key Laboratory of High Performance Computing College of ComputerCollege of Advanced Interdisciplinary StudiesNational University of Defense TechnologyChangsha 410073China Science and Technology on Monolithic Integrated Circuits and Modules Laboratory Nanjing Electronic Devices InstituteNanjing 210016China National Laboratory of Solid State Microstructures and School of Physics Nanjing UniversityNanjing 210093China

Single photons and photon pairs are typically generated by spontaneous parametric down conversion or quantum dots;however,spontaneous four-wave mixing(SFWM)in silicon microring resonators[1]is also an appealing source of entangled photons,offering a strong cavity-enhanced nonlinear interactions while maintaining features,such as compact,simple to fabricate,and allowing for thermal ***,silicon ring-resonators usually suffer from a trade-off between providing a high pair generation rate(PGR)and high extraction *** achieve high PGR,devices are generally operated with the signal and idler photons in the undercoupling regime and pump photons at the critical coupling point,while high extraction rates require the converted photons to be ***,the optimal conditions for achieving maximal output photon pair flux are critical coupling for the pump photons and overcoupling for the converted photons[2,3].

关键词： coupling photon converted

Information-theoretic bounds on quantum advantage in machine learning

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arXiv 2021年

作者： Huang, Hsin-Yuan Kueng, Richard Preskill, John Institute for Quantum Information and Matter Caltech PasadenaCA United States Department of Computing and Mathematical Sciences Caltech PasadenaCA United States Institute for Integrated Circuits Johannes Kepler University Linz Austria Walter Burke Institute for Theoretical Physics Caltech PasadenaCA United States AWS Center for Quantum Computing PasadenaCA United States

We study the performance of classical and quantum machine learning (ML) models in predicting outcomes of physical experiments. The experiments depend on an input parameter x and involve execution of a (possibly unknown) quantum process E. Our figure of merit is the number of runs of E required to achieve a desired prediction performance. We consider classical ML models that perform a measurement and record the classical outcome after each run of E, and quantum ML models that can access E coherently to acquire quantum data;the classical or quantum data is then used to predict outcomes of future experiments. We prove that for any input distribution D(x), a classical ML model can provide accurate predictions on average by accessing E a number of times comparable to the optimal quantum ML model. In contrast, for achieving accurate prediction on all inputs, we prove that exponential quantum advantage is possible. For example, to predict expectations of all Pauli observables in an n-qubit system ρ, classical ML models require 2Ω(n) copies of ρ, but we present a quantum ML model using only O(n) copies. Our results clarify where quantum advantage is possible and highlight the potential for classical ML models to address challenging quantum problems in physics and chemistry. © 2021, CC BY.

关键词： Forecasting

Efficient estimation of Pauli observables by derandomization

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arXiv 2021年

We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements with fixed Pauli measurements;the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any L low-weight Pauli observables, a deterministic measurement on only of order log(L) copies of a quantum state suffices. In some cases, for example when some of the Pauli observables have a high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules. © 2021, CC BY.

关键词： quantum theory

Non-Hermitian Waveguide Cavity QED with Tunable Atomic Mirrors

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arXiv 2023年

作者： Nie, Wei Shi, Tao Liu, Yu-Xi Nori, Franco Center for Joint Quantum Studies and Department of Physics School of Science Tianjin University Tianjin300350 China Institute of Theoretical Physics Chinese Academy of Sciences P.O. Box 2735 Beijing100190 China CAS Center for Excellence in Topological Quantum Computation University of Chinese Academy of Sciences Beijing100049 China School of Integrated Circuits Tsinghua University Beijing100084 China Theoretical Quantum Physics Laboratory Cluster for Pioneering Research RIKEN Wakoshi Saitama351-0198 Japan Center for Quantum Computing RIKEN Wakoshi Saitama351-0198 Japan Physics Department The University of Michigan Ann ArborMI48109-1040 United States

Optical mirrors determine cavity properties by means of light reflection. Imperfect reflection gives rise to open cavities with photon loss. We study an open cavity made of atom-dimer mirrors with a tunable reflection spectrum. We find that the atomic cavity shows anti-PT symmetry. The anti-PT phase transition controlled by atomic couplings in mirrors indicates the emergence of two degenerate cavity supermodes. Interestingly, a threshold of mirror reflection is identified for realizing strong coherent cavity-atom coupling. This reflection threshold reveals the criterion of atomic mirrors to produce a good cavity. Moreover, cavity quantum electrodynamics with a probe atom shows mirror-tuned properties, including reflection-dependent polaritons formed by the cavity and probe atom. Our work presents a non-Hermitian theory of an anti-PT atomic cavity, which may have applications in quantum optics and quantum computation. © 2023, CC BY-NC-ND.

关键词： Atoms

Undoped Strained Ge quantum Well with Ultrahigh Mobility Grown by Reduce Pressure Chemical Vapor Deposition

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arXiv 2022年

作者： Kong, Zhenzhen Li, Zonghu Cao, Gang Su, Jiale Zhang, Yiwen Liu, Jinbiao Liu, Jingxiong Ren, Yuhui Wei, Laiming Guo, Guoping Wu, Yuanyuan Radamson, Henry H. Li, Junfeng Wu, Zhenhua Li, Haiou Yang, Jiecheng Zhao, Chao Wang, Guilei Integrated Circuit Advanced Process R&D Center Institute of Microelectronics Chinese Academy of Sciences Beijing100029 China School of Integrated Circuits University of Chinese Academy of Sciences Beijing100049 China CAS Key Laboratory of Quantum Information University of Science and Technology of China Hefei230026 China Hefei National Laboratory Hefei230088 China School of Advanced Manufacturing Engineering Hefei University Hefei230601 China Origin Quantum Computing Company Limited Hefei230026 China Research and Development Center of Optoelectronic Hybrid IC Guangdong Greater Bay Area Institute of Integrated Circuit and System Guangzhou510535 China Beijing Superstring Academy of Memory Technology 100176 China

We fabricate an undoped Ge quantum well under a 30 nm relaxed Ge0.8Si0.2 shallow barrier. The bottom barrier contains Ge0.8Si0.2 (650 ℃) followed by Ge0.9Si0.1 (800 ℃) such that variation of Ge content forms a sharp interface that can suppress the threading dislocation density (TDD) penetrating into the undoped Ge quantum well. The Ge0.8Si0.2 barrier introduces enough in-plane parallel strain (Ε strain -0.41%) in the Ge quantum well. The heterostructure field-effect transistors with a shallow buried channel obtain an ultrahigh two-dimensional hole gas (2DHG) mobility over 2×106 cm2/Vs and a very low percolation of 5.625 × 1010cm−2. A tunable fractional quantum Hall effect at high densities and high magnetic fields has also been observed. This approach defines strained germanium as providing the material basis for tuning the spin-orbit coupling strength for fast and coherent quantum *** Codes 81-05, 81V70 © 2022, CC BY-NC-ND.

关键词： Germanium

Fast generation of Schrödinger cat states in a Kerr-tunable superconducting resonator

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arXiv 2023年

作者： He, X.L. Lu, Yong Bao, D.Q. Xue, Hang Jiang, W.B. Wang, Z. Roudsari, A.F. Delsing, Per Tsai, J.S. Lin, Z.R. National Key Laboratory of Materials for Integrated Circuits Shanghai Institute of Microsystem and Information Technology Chinese Academy of Sciences Shanghai200050 China University of Chinese Academy of Science Beijing100049 China 3rd Physikalisches Institut University of Stuttgart Stuttgart70569 Germany Microtechnology and Nanoscience Chalmers University of Technology GöteborgSE-412 96 Sweden Graduate School of Science Tokyo University of Science Shinjuku Tokyo162-0825 Japan Center for Quantum Computing RIKEN Saitama Wako351-0198 Japan

Schrödinger cat states, quantum superpositions of macroscopically distinct classical states, are an important resource for quantum communication, quantum metrology and quantum computation. Especially, cat states in a phase space protected against phase-flip errors can be used as a logical qubit. However, cat states, normally generated in three-dimensional cavities, are facing the challenges of scalability and controllability. Here, we present a novel strategy to generate and store cat states in a coplanar superconducting circuit by the fast modulation of Kerr nonlinearity. At the Kerr-free work point, our cat states are passively preserved due to the vanishing Kerr effect. We are able to prepare a 2-component cat state in our chip-based device with a fidelity reaching 89.1% under a 96 ns gate time. Our scheme shows an excellent route to constructing a chip-based bosonic quantum processor. Copyright © 2023, The Authors. All rights reserved.

关键词： Superconducting resonators