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arXiv 2021年

作者： Bagherimehrab, Mohsen Sanders, Yuval R. Berry, Dominic W. Brennen, Gavin K. Sanders, Barry C. Institute for Quantum Science and Technology University of Calgary Alberta Canada Chemical Physics Theory Group Department of Chemistry University of Toronto ON Canada Department of Computer Science University of Toronto ON Canada Department of Physics and Astronomy Macquarie University NSW Australia Centre for Quantum Software and Information University of Technology Sydney NSW Australia Centre of Excellence in Engineered Quantum Systems Macquarie University NSW Australia

We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory (QFT). Our quantum algorithm delivers a super-quadratic speedup over the state-of-the-art quantum algorithm for ground-state generation, overcomes the ground-state-generation bottleneck of the prior approach and is optimal up to a polylogarithmic factor. Specifically, we establish two quantum algorithms-Fourier-based and wavelet-based-to generate the ground state of a free massive scalar bosonic QFT with gate complexity quasilinear in the number of discretized-QFT modes. The Fourier-based algorithm is limited to translationally invariant QFTs. Numerical simulations show that the wavelet-based algorithm successfully yields the ground state for a QFT with broken translational invariance. Furthermore, the cost of preparing particle excitations in the wavelet approach is independent of the energy scale. Our algorithms require a routine for generating one-dimensional Gaussian (1DG) states. We replace the standard method for 1DG-state generation, which requires the quantum computer to perform lots of costly arithmetic, with a novel method based on inequality testing that significantly reduces the need for arithmetic. Our method for 1DG-state generation is generic and could be extended to preparing states whose amplitudes can be computed on the fly by a quantum computer. © 2021, CC BY.

关键词： Ground state

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Provably accurate simulation of gauge theories and bosonic systems

arXiv

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arXiv 2021年

作者： Tong, Yu Albert, Victor V. McClean, Jarrod R. Preskill, John Su, Yuan Google Quantum AI VeniceCA United States Department of Mathematics University of California BerkeleyCA United States Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD United States Institute for Quantum Information and Matter Caltech PasadenaCA United States AWS Center for Quantum Computing PasadenaCA United States

quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze errors resulting from truncation, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions such as the Hubbard-Holstein, Fröhlich, and Dicke models, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then a truncation error no worse than ϵ can be achieved by choosing Λ to increase polylogarithmically with ϵ−1, an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute an upper bound on the value of Λ that achieves accuracy ϵ, finding significant improvement over previous estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes;the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our results on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with error at most ϵ by truncating local quantum numbers at Λ = polylog(ϵ−1). © 2021, CC BY.

关键词： Errors

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Optimal estimation of three parallel spins with genuine and restricted collective measurements

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Physical Review A 2025年第6期111卷 062409-062409页

作者： Changhao Yi Kai Zhou Zhibo Hou Guo-Yong Xiang Huangjun Zhu State Key Laboratory of Surface Physics Department of Physics and Center for Field Theory and Particle Physics Fudan University Shanghai 200433 China Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai 200433 China Shanghai Research Center for Quantum Sciences Shanghai 201315 China Laboratory of Quantum Information University of Science and Technology of China Hefei 230026 China CAS Center For Excellence in Quantum Information and Quantum Physics University of Science and Technology of China Hefei 230026 China Hefei National Laboratory Hefei 230088 China

Collective measurements on identical and independent quantum systems can offer advantages in information extraction compared with individual measurements. However, little is known about the distinction between restricted collective measurements and genuine collective measurements in the multipartite setting. In this work we establish a rigorous performance gap based on a simple and old estimation problem, the estimation of a random spin state given three parallel spins. Notably, we derive an analytical formula for the maximum estimation fidelity of biseparable measurements and clarify its fidelity gap from genuine collective measurements. Moreover, we clarify the structure of optimal biseparable measurements. It turns out the maximum estimation fidelity can be achieved by two- and one-copy measurements assisted by one-way communication in one direction, but not the other way. Our work reveals a rich landscape of multipartite nonclassicality in quantum measurements instead of quantum states and is expected to trigger further studies.

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Impossibility of cloning of quantum coherence

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Physical Review A 2021年第2期103卷 022422-022422页

作者： Dhrumil Patel Subhasree Patro Chiranjeevi Vanarasa Indranil Chakrabarty Arun Kumar Pati Department of Computer Science and Engineering Louisiana State University Baton Rouge 70803 LA United States QuSoft CWI Amsterdam and University of Amsterdam Amsterdam 1098 XG Netherlands Center for Security Theory and Algorithmic Research International Institute of Information Technology-Hyderabad Gachibowli Telangana 500032 India Center for Security Theory and Algorithmic Research International Institute of Information Technology-Hyderabad Gachibowli Telangana 500032 India Quantum Information and Computation Group Harish-Chandra Research Institute HBNI Allahabad 211019 India

It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no cloning of quantum coherence. Here, in this article, we show that it is impossible to clone the coherence of an arbitrary quantum state. In particular, with an ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states. Lastly, we generalize the impossibility of cloning of coherence in terms of dimension of the quantum state and coherence measure taken into consideration.

关键词： quantum coherence & coherence measures quantum information processing

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Twirling channels have minimal mixed-unitary rank

arXiv

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arXiv 2020年

作者： Girard, Mark Levick, Jeremy Institute for Quantum Computing University of Waterloo School of Computer Science University of Waterloo Department of Mathematics & Statistics University of Guelph

For a positive integer d and a unitary representation ρ : G → U(d) of a compact group G, the twirling channel for this representation is the linear mapping Φ: Md → Md defined as Φ(X) = RG dµ(g) ρ(g)Xρ(g−1) for every X ∈ Md, where µ is the Haar measure on G. Such channels are examples of mixed-unitary channels, as they are in the convex hull of the set of unitary channels of a fixed size. By Carathéodory’s theorem, these channels can always be expressed as a finite linear combination of unitary channels. We consider the mixed-unitary rank twirling channels—which is the minimum number of distinct unitary conjugations required to express the channel as a convex combination of unitary channels—and show that the mixed-unitary rank of every twirling channel is always equal to its Choi rank, both of which are equal to the dimension of the von Neumann algebra generated by the representation. Moreover, we show how to explicitly construct minimal mixed-unitary decompositions for these types of channels and provide some examples. Copyright © 2020, The Authors. All rights reserved.

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quantum Simulation with Hybrid Tensor Networks

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Physical Review Letters 2021年第4期127卷 040501-040501页

作者： Xiao Yuan Jinzhao Sun Junyu Liu Qi Zhao You Zhou Center on Frontiers of Computing Studies Department of Computer Science Peking University Beijing 100871 China Stanford Institute for Theoretical Physics Stanford University Stanford California 94305 USA Clarendon Laboratory University of Oxford Parks Road Oxford OX1 3PU United Kingdom Walter Burke Institute for Theoretical Physics California Institute of Technology Pasadena California 91125 USA Institute for Quantum Information and Matter California Institute of Technology Pasadena California 91125 USA Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA

Tensor network theory and quantum simulation are, respectively, the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions. With the example of hybrid tree tensor networks, we demonstrate efficient quantum simulation using a quantum computer whose size is significantly smaller than the one of the target system. We numerically benchmark our method for finding the ground state of 1D and 2D spin systems of up to 8×8 and 9×8 qubits with operations only acting on 8+1 and 9+1 qubits, respectively. Our approach sheds light on simulation of large practical problems with intermediate-scale quantum computers, with potential applications in chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.

关键词： quantum algorithms quantum computation quantum networks quantum simulation

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quantum advantage in learning from experiments

arXiv

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arXiv 2021年

作者： Huang, Hsin-Yuan Broughton, Michael Cotler, Jordan Chen, Sitan Li, Jerry Mohseni, Masoud Neven, Hartmut Babbush, Ryan Kueng, Richard Preskill, John McClean, Jarrod R. Institute for Quantum Information and Matter Caltech PasadenaCA United States Department of Computing and Mathematical Sciences Caltech PasadenaCA United States Google Quantum AI 340 Main Street VeniceCA90291 United States Cambridge MA02138 United States Black Hole Initiative CambridgeMA02138 United States Department of Electrical Engineering and Computer Science University of California Berkeley BerkeleyCA United States Simons Institute for the Theory of Computing BerkeleyCA United States Microsoft Research AI RedmondWA98052 United States Institute for Integrated Circuits Johannes Kepler University Linz Austria AWS Center for Quantum Computing PasadenaCA91125 United States

quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest;for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature. © 2021, CC BY.

关键词： Principal component analysis

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Optimal Verification of the Bell State and Greenberger-Horne-Zeilinger States in Untrusted quantum Networks

arXiv

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arXiv 2021年

作者： Han, Yun-Guang Li, Zihao Wang, Yukun Zhu, Huangjun State Key Laboratory of Surface Physics Department of Physics Fudan University Shanghai 200433 China Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai 200433 China Center for Field Theory and Particle Physics Fudan University Shanghai 200433 China Department of Computer Science and Technology China University of Petroleum Beijing102249 China

Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted quantum network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger-Horne-Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger-Horne-Zeilinger states and for detecting genuine multipartite entanglement. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum entanglement

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Long-lived topological time-crystalline order on a quantum processor

arXiv

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arXiv 2024年

作者： Xiang, Liang Jiang, Wenjie Bao, Zehang Song, Zixuan Xu, Shibo Wang, Ke Chen, Jiachen Jin, Feitong Zhu, Xuhao Zhu, Zitian Shen, Fanhao Wang, Ning Zhang, Chuanyu Wu, Yaozu Zou, Yiren Zhong, Jiarun Cui, Zhengyi Zhang, Aosai Tan, Ziqi Li, Tingting Gao, Yu Deng, Jinfeng Zhang, Xu Dong, Hang Zhang, Pengfei Jiang, Si Li, Weikang Lu, Zhide Sun, Zheng-Zhi Li, Hekang Wang, Zhen Song, Chao Guo, Qiujiang Liu, Fangli Gong, Zhe-Xuan Gorshkov, Alexey V. Yao, Norman Y. Iadecola, Thomas Machado, Francisco Wang, H. Deng, Dong-Ling School of Physics ZJU-Hangzhou Global Scientific and Technological Innovation Center Zhejiang Province Key Laboratory of Quantum Technology and Device Zhejiang University Hangzhou China Center for Quantum Information IIIS Tsinghua University Beijing100084 China Hefei National Laboratory Hefei230088 China Joint Quantum Institute Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD United States QuEra Computing Inc. BostonMA United States Department of Physics Colorado School of Mines GoldenCO United States National Institute of standards and Technology BoulderCO United States Department of Physics Harvard University Cambridge02138 MA United States Department of Physics and Astronomy Iowa State University AmesIA United States Ames Laboratory AmesIA United States ITAMP Harvard-Smithsonian Center for Astrophysics CambridgeMA02138 United States Shanghai Qi Zhi Institute 41th Floor AI Tower No. 701 Yunjin Road Xuhui District Shanghai200232 China

Topologically ordered phases of matter [1–3] elude Landau’s symmetry-breaking theory [4], featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium [5, 6]. Here, we report the observation of signatures of such a phenomenon—a prethermal topologically ordered time crystal—with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface-code Hamiltonian [7, 8], we observe discrete time-translation symmetry breaking dynamics [9–16] that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy [17, 18] and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors [19]. Copyright © 2024, The Authors. All rights reserved.

关键词： Dynamics

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Low-depth quantum state preparation

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Physical Review Research 2021年第4期3卷 043200-043200页

作者： Xiao-Ming Zhang Man-Hong Yung Xiao Yuan Center on Frontiers of Computing Studies Department of Computer Science Peking University Beijing 100871 China Department of Physics City University of Hong Kong Tat Chee Avenue Kowloon Hong Kong SAR China Department of Physics Southern University of Science and Technology Shenzhen 518055 China Shenzhen Institute for Quantum Science and Engineering Southern University of Science and Technology Shenzhen 518055 China Guangdong Provincial Key Laboratory of Quantum Science and Engineering Southern University of Science and Technology Shenzhen 518055 China

A crucial subroutine in quantum computing is to load the classical data of N complex numbers into the amplitude of a superposed n=⌈log2N⌉-qubit state. It has been proven that any algorithm universally implementing this subroutine would need at least O(N) constant weight operations. However, the proof assumes that only n qubits are used, whereas the circuit depth could be reduced by extending the space and allowing ancillary qubits. Here we investigate this space-time tradeoff in quantum state preparation with classical data. We propose quantum algorithms with O(n2) circuit depth to encode any N complex numbers using only single- and two-qubit gates, and local measurements with ancillary qubits. Different variances of the algorithm are proposed with different space and runtime. In particular, we present a scheme with O(N2) ancillary qubits, O(n2) circuit depth, and O(n2) average runtime, which exponentially improves the conventional bound. While the algorithm requires more ancillary qubits, it consists of quantum circuit blocks that only simultaneously act on a constant number of qubits, and at most O(n) qubits are entangled. We also prove a fundamental lower bound Ω(n) for the minimum circuit depth and runtime with an arbitrary number of ancillary qubits, aligning with our scheme with O(n2). The algorithms are expected to have wide applications in both near-term and universal quantum computing.

关键词： quantum algorithms quantum computation

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