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Dual-GSE: Resource-efficient Generalized Quantum Subspace Expansion

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arXiv 2023年

作者： Yang, Bo Yoshioka, Nobuyuki Harada, Hiroyuki Hakkaku, Shigeo Tokunaga, Yuuki Hakoshima, Hideaki Yamamoto, Kaoru Endo, Suguru LIP6 Sorbonne Université 4 Place Jussieu Paris75005 France Graduate School of Information Science and Technology The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Department of Applied Physics School of Engineering University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Wako-shi Saitama351-0198 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama332-0012 Japan Department of Applied Physics and Physico-Informatics Keio University Hiyoshi 3-14-1 Kohoku Yokohama223-8522 Japan NTT Computer and Data Science Laboratories NTT Corporation 3-9-11 Midori-cho Musashino-shi Tokyo180-8585 Japan Center for Quantum Information and Quantum Biology Osaka University 1-3 Machikaneyama Toyonaka Osaka560-8531 Japan

There are considerable obstacles against realizing practical quantum computing: a significant amount of computation errors and the restricted qubit count. As a unified method of noise-agnostic quantum error mitigation (QEM) methods, i.e., the quantum subspace expansion and virtual purification, a generalized quantum subspace expansion (GSE) has recently been proposed that is significantly robust against stochastic and coherent errors. However, GSE requires entangled measurements between copies of the quantum states, which is a significant drawback under the current situation of the restricted number of qubits and their connectivity. In this work, we propose a resource-efficient implementation of GSE, which we name "Dual-GSE", circumventing significant overheads of state copies by constructing an ansatz of error-mitigated quantum states via dual-state purification. Remarkably, Dual-GSE can further simulate larger quantum systems beyond the size of available quantum hardware with a suitable ansatz construction inspired by divide-and-conquer methods that forge entanglement classically. This also significantly reduces the measurement overhead because we only need to measure subsystems’ Pauli operators. The proposed method is demonstrated by a numerical simulation of the eight-qubit transverse-field Ising model, showing that our method estimates the ground state energy with high precision under gate noise with low mitigation overhead and practical sampling cost. Copyright © 2023, The Authors. All rights reserved.

关键词： Ground state

Error-Mitigated Quantum Metrology via Virtual Purification

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arXiv 2021年

作者： Yamamoto, Kaoru Endo, Suguru Hakoshima, Hideaki Matsuzaki, Yuichiro Tokunaga, Yuuki NTT Computer and Data Science Laboratories NTT Corporation Musashino180-8585 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama332-0012 Japan Central2 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Toyonaka560-0043 Japan Ibaraki Tsukuba305-8568 Japan

Quantum metrology with entangled resources aims to achieve sensitivity beyond the standard quantum limit by harnessing quantum effects even in the presence of environmental noise. So far, sensitivity has been mainly discussed from the viewpoint of reducing statistical errors under the assumption of perfect knowledge of a noise model. However, we cannot always obtain complete information about a noise model due to coherence time fluctuations, which are frequently observed in experiments. Such unknown fluctuating noise leads to systematic errors and nullifies the quantum advantages. Here, we propose an error-mitigated quantum metrology that can filter out unknown fluctuating noise with the aid of purification-based quantum error mitigation. We demonstrate that our protocol mitigates systematic errors and recovers superclassical scaling in a practical situation with time-inhomogeneous bias-inducing noise. Our result is the first demonstration to reveal the usefulness of purification-based error mitigation for unknown fluctuating noise, thus paving the way not only for practical quantum metrology but also for quantum computation affected by such noise. Copyright © 2021, The Authors. All rights reserved.

关键词： Purification

Perturbative quantum simulation

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arXiv 2021年

作者： Sun, Jinzhao Endo, Suguru Lin, Huiping Hayden, Patrick Vedral, Vlatko Yuan, Xiao Center on Frontiers of Computing Studies Peking University Beijing100871 China Clarendon Laboratory University of Oxford Parks Road OxfordOX1 3PU United Kingdom Quantum Advantage Research Beijing100080 China NTT Computer & Data Science Laboratories NTT Corporation Musashino Tokyo180-8585 Japan School of Computer Science Peking University Beijing100871 China Stanford Institute for Theoretical Physics Stanford University StanfordCA94305 United States Centre for Quantum Technologies National University of Singapore Singapore117543 Singapore

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to 48 qubits only using an 8 + 1 qubit quantum hardware. We experimentally demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones. Copyright © 2021, The Authors. All rights reserved.

关键词： Hamiltonians

Quantum error mitigation for rotation-symmetric bosonic codes with symmetry expansion

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Physical Review A 2025年第6期111卷 062402-062402页

作者： Suguru Endo Yasunari Suzuki Kento Tsubouchi Rui Asaoka Kaoru Yamamoto Yuichiro Matsuzaki Yuuki Tokunaga NTT Computer and Data Science Laboratories NTT Corporation Musashino 180-8585 Tokyo Japan Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-8656 Japan Research Center for Emerging Computing Technologies National Institute of Advanced Industrial Science and Technology (AIST) Central2 1-1-1 Umezono Tsukuba Ibaraki 305-8568 Japan NEC-AIST Quantum Technology Cooperative Research Laboratory National Institute of Advanced Industrial Science and Technology (AIST) Tsukuba Ibaraki 305-8568 Japan

The rotation symmetric bosonic code (RSBC) is a unified framework of practical bosonic codes that have rotation symmetries, such as cat codes and binomial codes. While cat and binomial codes achieve the breakeven point in which the coherence time of the encoded qubits exceeds that of unencoded qubits, the state preparation fidelity needs to be improved for practical quantum computing. Concerning this problem, we investigate the framework of symmetry expansion, a class of quantum error mitigation that virtually projects the state onto the noise-free symmetric subspace by exploiting the system's intrinsic symmetries and postprocessing of measurement outcomes. Although symmetry expansion has been limited to error mitigation of quantum states immediately before measurement, we successfully generalize symmetry expansion for state preparation. Then, we consider two types of stabilization: photon number and phase stabilization. Photon number stabilization can be performed by leveraging the rotation operators. On the other hand, the phase errors can be suppressed via the extension towards phase direction by leveraging the recently proposed projective squeezing method. To implement our method, we use an ancilla qubit and a randomly generated controlled gate between the bosonic code states and the ancilla qubit. Our novel error mitigation method will significantly enhance computation accuracy in the near-term bosonic quantum computing.

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Hunting for quantum-classical crossover in condensed matter problems

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arXiv 2022年

作者： Yoshioka, Nobuyuki Okubo, Tsuyoshi Suzuki, Yasunari Koizumi, Yuki Mizukami, Wataru Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Saitama Wako-shi351-0198 Japan JST PRESTO 4-1-8 Honcho Saitama Kawaguchi332-0012 Japan Institute for Physics of Intelligence University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-0033 Japan NTT Computer and Data Science Laboratories Musashino180-8585 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Osaka Toyonaka560-0043 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Osaka Toyonaka560-8531 Japan

The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: When and how will quantum computers outperform classical computers? The next milestone is undoubtedly the realization of quantum acceleration in practical problems. Here we provide a clear evidence and arguments that the primary target is likely to be condensed matter physics. Our primary contributions are summarized as follows: 1) Proposal of systematic error/runtime analysis on state-of-the-art classical algorithm based on tensor networks;2) Dedicated and high-resolution analysis on quantum resource performed at the level of executable logical instructions;3) Clarification of quantum-classical crosspoint for ground-state simulation to be within runtime of hours using only a few hundreds of thousand physical qubits for 2d Heisenberg and 2d Fermi-Hubbard models, assuming that logical qubits are encoded via the surface code with the physical error rate of p = 10−3. To our knowledge, we argue that condensed matter problems offer the earliest platform for demonstration of practical quantum advantage that is order-of-magnitude more feasible than ever known candidates, in terms of both qubit counts and total runtime. Copyright © 2022, The Authors. All rights reserved.

关键词： Condensed matter physics

Boltzmann machine learning with a variational quantum algorithm

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arXiv 2020年

作者： Shingu, Yuta Seki, Yuya Watabe, Shohei Endo, Suguru Matsuzaki, Yuichiro Kawabata, Shiro Nikuni, Tetsuro Hakoshima, Hideaki Department of Physics Faculty of Science Division I Tokyo University of Science Shinjuku Tokyo162-8601 Japan 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Department of Materials University of Oxford Parks Road OxfordOX1 3PH United Kingdom NTT Computer Data Science Laboratories NTT Corporation Musashino Tokyo180-8585 Japan

A Boltzmann machine is a powerful tool for modeling probability distributions that govern the training data. A thermal equilibrium state is typically used for the Boltzmann machine learning to obtain a suitable probability distribution. The Boltzmann machine learning consists of calculating the gradient of the loss function given in terms of the thermal average, which is the most time consuming procedure. Here, we propose a method to implement the Boltzmann machine learning by using Noisy Intermediate-Scale Quantum (NISQ) devices. We prepare an initial pure state that contains all possible computational basis states with the same amplitude, and apply a variational imaginary time simulation. Readout of the state after the evolution in the computational basis approximates the probability distribution of the thermal equilibrium state that is used for the Boltzmann machine learning. We perform the numerical simulations of our scheme and confirm that the Boltzmann machine learning works well. Our scheme leads to a significant step toward an efficient machine learning using quantum hardware. Copyright © 2020, The Authors. All rights reserved.

关键词： Probability distributions

Quantifying fermionic nonlinearity of quantum circuits

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arXiv 2021年

作者： Hakkaku, Shigeo Tashima, Yuichiro Mitarai, Kosuke Mizukami, Wataru Fujii, Keisuke Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Osaka Toyonaka560-8531 Japan NTT Computer and Data Science Laboratories NTT Corporation 3-9-11 Midoricho Musashino180-8585 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Toyonaka560-0043 Japan JST PRESTO 4-1-8 Honcho Saitama Kawaguchi332-0012 Japan Hirosawa 2-1 Saitama Wako351-0198 Japan Fujitsu Quantum Computing Joint Research Division QIQB Osaka University 1-2 Machikaneyama Toyonaka560-0043 Japan

Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Here we propose a measure, called fermionic nonlinearity, to quantify the classical simulatability of quantum circuits designed for simulating fermionic Hamiltonians. Specifically, we construct a Monte Carlo type classical algorithm based on the classical simulatability of fermionic linear optics, whose sampling overhead is characterized by the fermionic nonlinearity. As a demonstration of these techniques, we calculate the upper bound of the fermionic nonlinearity of a rotation gate generated by four fermionic modes under the dephasing noise. Moreover, we estimate the sampling costs of the unitary coupled cluster singles and doubles quantum circuits for hydrogen chains subject to the dephasing noise. We find that, depending on the error probability and atomic spacing, there are regions where the fermionic nonlinearity becomes very small or unity, and hence the circuits are classically simulatable. We believe that our method and results help to design quantum circuits for fermionic systems with potential quantum advantages. Copyright © 2021, The Authors. All rights reserved.

关键词： Timing circuits

Generalized quantum subspace expansion

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arXiv 2021年

作者： Yoshioka, Nobuyuki Hakoshima, Hideaki Matsuzaki, Yuichiro Tokunaga, Yuuki Suzuki, Yasunari Endo, Suguru Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Wako-shi Saitama351-0198 Japan 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Center for Quantum Information and Quantum Biology Osaka University 1-3 Machikaneyama Toyonaka Osaka560-8531 Japan Ibaraki Tsukuba305-8568 Japan NTT Computer and Data Science Laboratories NTT Corporation Musashino180-8585 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama332-0012 Japan

One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop practical hardware-friendly quantum error mitigation (QEM) techniques to suppress unwanted errors. Here, we propose a novel generalized quantum subspace expansion method which can handle stochastic, coherent, and algorithmic errors in quantum computers. By fully exploiting the substantially extended subspace, we can efficiently mitigate the noise present in the spectra of a given Hamiltonian, without relying on any information of noise. The performance of our method is discussed under two highly practical setups: the quantum subspaces are mainly spanned by powers of the noisy state ρm and a set of error-boosted states, respectively. We numerically demonstrate in both situations that we can suppress errors by orders of magnitude, and show that out protocol inherits the advantages of previous error-agnostic QEM techniques as well as overcoming their drawbacks. © 2021, CC BY.

关键词： Errors

Quantum Circuits for Exact Unitary t-Designs and Applications to Higher-Order Randomized Benchmarking

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PRX Quantum 2021年第3期2卷 030339-030339页

作者： Yoshifumi Nakata Da Zhao Takayuki Okuda Eiichi Bannai Yasunari Suzuki Shiro Tamiya Kentaro Heya Zhiguang Yan Kun Zuo Shuhei Tamate Yutaka Tabuchi Yasunobu Nakamura Photon Science Center Graduate School of Engineering The University of Tokyo Bunkyo-ku Tokyo 113–8656 Japan JST PRESTO 4–1–8 Honcho Kawaguchi Saitama 332–0012 Japan School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 400240 China Department of Mathematics Hiroshima University 1-3-1 Kagamiyama Higashihiroshima 739-8562 Japan Faculty of Mathematics Kyushu University (emeritus) Fukuoka 819-0385 Japan Mathematics Division National Center for Theoretical Sciences National Taiwan University Taipei 10617 Taiwan NTT Computer and Data Science Laboratories NTT Corporation Musashino 180-8585 Japan Department of Applied Physics Graduate School of Engineering The University of Tokyo 7-3-1 Hongo Bynkyo-ku Tokyo 113-8656 Japan Research Center for Advanced Science and Technology (RCAST) The University of Tokyo Meguro-ku Tokyo 153-8904 Japan RIKEN Center for Quantum Computing (RQC) Wako Saitama 351-0198 Japan

A unitary t-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general t. In this paper, we provide quantum circuits that generate exact unitary t-designs for any t on an arbitrary number of qubits. Our construction is inductive and is of practical use in small systems. We then introduce a tth-order generalization of randomized benchmarking (t-RB) as an application of exact 2t-designs. We particularly study the 2-RB in detail and show that it reveals self-adjointness of quantum noise, a metric related to the feasibility of quantum error correction (QEC). We numerically demonstrate that the 2-RB in one- and two-qubit systems is feasible, and experimentally characterize background noise of a superconducting qubit by the 2-RB. It is shown from the experiment that interactions with adjacent qubits induce the noise that may result in an obstacle toward a realization of QEC.

关键词： Quantum algorithms Quantum benchmarking Quantum gates Quantum protocols