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Methodology for replacing indirect measurements with direct measurements

Physical Review Research 2019年第1期1卷 013006-013006页

作者： Kosuke Mitarai Keisuke Fujii Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Toyonaka Osaka 560-8531 Japan QunaSys Inc. High-tech Hongo Building 1F 5-25-18 Hongo Bunkyo Tokyo 113-0033 Japan Graduate School of Science Kyoto University Kitashirakawa Oiwake-cho Sakyo-ku Kyoto 606-8302 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan

In quantum computing, the indirect measurement of unitary operators such as the Hadamard test plays a significant role in many algorithms. However, in certain cases, the indirect measurement can be reduced to the direct measurement, where a quantum state is destructively measured. Here, we investigate under what conditions such a replacement is possible and develop a general methodology for trading an indirect measurement with sequential direct measurements. The results can be applied to construct quantum circuits to evaluate the analytical gradient, metric tensor, Hessian, and even higher order derivatives of a parametrized quantum state. Also, we propose a method to measure the out-of-time-order correlator based on the presented protocol. Our protocols can significantly reduce the depth of a quantum circuit by making the controlled operation unnecessary, and thus are suitable for quantum-classical hybrid algorithms on near-term quantum computers.

关键词： quantum algorithms quantum computation quantum measurements quantum simulation

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Wave-function positivization via automatic differentiation

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Physical Review Research 2020年第3期2卷 032060(R)-032060(R)页

作者： Giacomo Torlai Juan Carrasquilla Matthew T. Fishman Roger G. Melko Matthew P. A. Fisher Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Vector Institute for Artificial Intelligence MaRS Centre Toronto Ontario Canada M5G 1M1 Department of Physics and Astronomy University of Waterloo Ontario Canada N2L 3G1 Perimeter Institute for Theoretical Physics Waterloo Ontario Canada N2L 2Y5 Department of Physics University of California Santa Barbara California 93106 USA

We introduce a procedure to systematically search for a local unitary transformation that maps a wave function with a nontrivial sign structure into a positive-real form. The transformation is parametrized as a quantum circuit compiled into a set of one- and two-qubit gates. We design a cost function that maximizes the average sign of the output state and removes its complex phases. The optimization of the gates is performed through automatic differentiation algorithms, widely used in the machine learning community. We provide numerical evidence for significant improvements in the average sign for a two-leg triangular Heisenberg ladder with next-to-nearest-neighbor and ring-exchange interactions. This model exhibits phases where the sign structure can be removed by simple local one-qubit unitaries, but also an exotic Bose-metal phase whose sign structure induces “Bose surfaces” with a fermionic character and a higher entanglement that requires deeper circuits.

关键词： Machine learning Optimization problems quantum algorithms quantum entanglement quantum protocols quantum theory quantum spin models Tensor network methods

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Experimental demonstration of a high-fidelity virtual two-qubit gate

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Physical Review Research 2024年第1期6卷 013235-013235页

作者： Akhil Pratap Singh Kosuke Mitarai Yasunari Suzuki Kentaro Heya Yutaka Tabuchi Keisuke Fujii Yasunobu Nakamura Department of Applied Physics Graduate School of Engineering The University of Tokyo Bunkyo-ku Tokyo 113-8656 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Toyonaka Osaka 560-8531 Japan NTT Computer and Data Science Laboratories NTT Corporation Musashino 180-8585 Japan RIKEN Center for Quantum Computing (RQC) Wako Saitama 351-0198 Japan

We experimentally demonstrate a virtual two-qubit gate and characterize it using quantum process tomography (QPT). The virtual two-qubit gate decomposes an actual two-qubit gate into single-qubit unitary gates and projection gates in quantum circuits for expectation-value estimation. We implement projection gates via midcircuit measurements. The deterministic sampling scheme reduces the number of experimental circuit evaluations required for decomposing a virtual two-qubit gate. We also apply quantum error mitigation to suppress the effect of measurement errors and improve the average gate fidelity of a virtual controlled-Z (CZ) gate to fav=0.9938±0.0002. Our results highlight a practical approach to implement virtual two-qubit gates with high fidelities, which are useful for simulating quantum circuits using fewer qubits and implementing two-qubit gates on a distant pair of qubits.

关键词： quantum algorithms quantum algorithms & computation quantum benchmarking quantum circuits quantum computation quantum gates quantum nondemolition measurement quantum simulation

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Scalable qubit representations of neutrino mixing matrices

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Physical Review D 2022年第5期105卷 056024-056024页

作者： M. J. Molewski B. J. P. Jones Department of Physics University of Texas at Arlington Arlington 76019 TX United States

Oscillating neutrino beams exhibit quantum coherence over distances of thousands of kilometers. Their unambiguously quantum nature suggests an appealing test system for direct quantum simulation. Such techniques may enable presently analytically intractable calculations involving multineutrino entanglements, such as collective neutrino oscillations in supernovas, but only once oscillation phenomenology is properly reexpressed in the language of quantum circuits. Here we resolve outstanding conceptual issues regarding encoding of arbitrarily mixed neutrino flavor states in the Hilbert space of an n-qubit quantum computer. We introduce algorithms to encode mixing and oscillation of any number of flavor-mixed neutrinos, both with and without CP-violation, with an efficient number of prescriptive input parameters in terms of subrotations of the Pontecorvo-Maki-Nakagawa-Sakata matrix in standard form. Examples encoded for an IBM-Q quantum computer are shown to converge to analytic predictions both with and without CP-violation.

关键词： quantum algorithms quantum gates quantum simulation

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Many-body localized hidden generative models

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Physical Review Research 2024年第4期6卷 043041页

作者： Weishun Zhong Xun Gao Susanne F. Yelin Khadijeh Najafi Department of Physics IBM Quantum MIT-IBM Watson AI Laboratory Cambridge Massachusetts 02142 USA Yorktown Heights New York 10598 USA

quantum generative models hold the promise of accelerating or improving machine learning tasks by leveraging the probabilistic nature of quantum states, but the successful optimization of these models remains a difficult challenge. To tackle this challenge, we present a new architecture for quantum generative modeling that combines insights from classical machine learning and quantum phases of matter. In particular, our model utilizes both many-body localized (MBL) dynamics and hidden units to improve the optimization of the model. We demonstrate the applicability of our model on a diverse set of classical and quantum tasks, including a toy version of MNIST handwritten digits, quantum data obtained from quantum many-body states, and nonlocal parity data. Our architecture and algorithm provide novel strategies of utilizing quantum many-body systems as learning resources and reveal a powerful connection between disorder, interaction, and learning in quantum many-body systems.

关键词： Machine learning Many-body localization quantum algorithms quantum computation quantum statistical mechanics Disordered systems

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Time evolution of uniform sequential circuits

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Physical Review Research 2023年第3期5卷 033187-033187页

作者： Nikita Astrakhantsev Sheng-Hsuan Lin Frank Pollmann Adam Smith Department of Physics University of Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland Technical University of Munich (TUM) TUM School of Natural Sciences Physics Department 85748 Garching Germany Munich Center for Quantum Science and Technology (MCQST) Schellingstr. 4 80799 Munich Germany School of Physics and Astronomy University of Nottingham Nottingham NG7 2RD United Kingdom Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems University of Nottingham Nottingham NG7 2RD United Kingdom

Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work we present a polynomially scaling hybrid quantum-classical algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. This algorithm uses a layered uniform sequential quantum circuit as a variational Ansatz to represent infinite translation-invariant quantum states. We show numerically that this Ansatz requires a number of parameters polynomial in the simulation time for a given accuracy. Furthermore, this favorable scaling of the Ansatz is maintained during our variational evolution algorithm. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind. After benchmarking the evolution algorithm on a classical computer, we demonstrate the measurement of observables of this uniform state using a finite number of qubits on a cloud-based quantum processing unit. With more efficient tensor contraction schemes, this algorithm may also offer improvements as a classical numerical algorithm.

关键词： quantum algorithms quantum circuits quantum computation

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Optimized SWAP networks with equivalent circuit averaging for QAOA

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Physical Review Research 2022年第3期4卷 033028-033028页

作者： Akel Hashim Rich Rines Victory Omole Ravi K. Naik John Mark Kreikebaum David I. Santiago Frederic T. Chong Irfan Siddiqi Pranav Gokhale Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley Berkeley California 94720 USA Graduate Group in Applied Science and Technology University of California at Berkeley Berkeley California 94720 USA Computational Research Division Lawrence Berkeley National Lab Berkeley California 94720 USA Super.tech a division of ColdQuanta Chicago Illinois 60615 USA Materials Sciences Division Lawrence Berkeley National Lab Berkeley California 94720 USA University of Chicago Chicago Illinois 60637 USA

The SWAP network is a qubit routing sequence that can be used to efficiently execute the quantum Approximate Optimization Algorithm (QAOA). Even with a minimally connected topology on an n-qubit processor, this routing sequence enables O(n2) operations to execute in O(n) steps. In this work, we optimize the execution of SWAP networks for QAOA through two techniques. First, we take advantage of an overcomplete set of native hardware operations [including 150-ns controlled-π2 phase gates with up to 99.67(1)% fidelity] to decompose the relevant quantum gates and SWAP networks in a manner which minimizes circuit depth and maximizes gate cancellation. Second, we introduce equivalent circuit averaging, which randomizes over degrees of freedom in the quantum circuit compilation to reduce the impact of systematic coherent errors. Our techniques are experimentally validated at the Advanced quantum Testbed through the execution of QAOA circuits for finding the ground state of two- and four-node Sherrington-Kirkpatrick spin-glass models with various randomly sampled parameters. We observe a ∼60% average reduction in error (total variation distance) for QAOA of depth p=1 on four transmon qubits on a superconducting quantum processor.

关键词： quantum algorithms quantum benchmarking quantum gates

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Projective cooling for the transverse Ising model

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Physical Review D 2020年第7期101卷 071504(R)-071504(R)页

作者： Erik J. Gustafson Department of Physics and Astronomy The University of Iowa Iowa City Iowa 52242 USA

We demonstrate the feasibility of ground state preparation for the transverse Ising model using projective cooling, and show that the algorithm can effectively construct the ground state in the disordered (paramagnetic) phase. On the other hand, significant temperature effects are encountered in the ordered (ferromagnetic) phase requiring larger lattices to accurately simulate.

关键词： quantum algorithms Lattice field theory

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Transversal injection for direct encoding of ancilla states for non-Clifford gates using stabilizer codes

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Physical Review Research 2023年第3期5卷 033019-033019页

作者： Jason Gavriel Daniel Herr Alexis Shaw Michael J. Bremner Alexandru Paler Simon J. Devitt Centre for Quantum Computation and Communication Technology New South Wales 2052 Australia Centre for Quantum Software and Information University of Technology Sydney Sydney New South Wales 2007 Australia d-fine GmbH An der Hauptwache 7 60213 Frankfurt Germany Department of Computer Science Aalto University 02150 Espoo Finland

Fault-tolerant, error-corrected quantum computation is commonly acknowledged to be crucial to the realization of large-scale quantum algorithms that could lead to extremely impactful scientific or commercial results. Achieving a universal set of quantum gate operations in a fault-tolerant, error-corrected framework suffers from a conservation of unpleasantness. In general, no matter what error-correction technique is employed, there is always one element of a universal gate set that carries a significant resource overhead—either in physical qubits, computational time, or both. Specifically, this is due to the application of non-Clifford gates. A common method for realizing these gates for stabilizer codes such as the surface code is a combination of three protocols: state injection, distillation, and gate teleportation. These protocols contribute to the resource overhead compared with logical operations such as a CNOT gate and contribute to the qubit resources for any error-corrected quantum algorithm. In this paper, we introduce a very simple protocol to potentially reduce this overhead for non-Clifford gates: transversal injection. Transversal injection modifies the initial physical states of all data qubits in a stabilizer code before standard encoding and results in the direct preparation of a large class of single qubit states, including resource states for non-Clifford logic gates. Preliminary results hint at high-quality fidelities at larger distances and motivate further research on this technique.

关键词： quantum algorithms quantum error correction quantum gates quantum information processing

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Gauge theory couplings on anisotropic lattices

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Physical Review D 2022年第11期106卷 114504-114504页

作者： Marcela Carena Erik J. Gustafson Henry Lamm Ying-Ying Li Wanqiang Liu Fermi National Accelerator Laboratory Batavia Illinois 60510 USA Enrico Fermi Institute University of Chicago Chicago Illinois 60637 USA Kavli Institute for Cosmological Physics University of Chicago Chicago Illinois 60637 USA Department of Physics University of Chicago Chicago Illinois 60637 USA

The advantage of simulating lattice field theory with quantum computers is hamstrung by the limited resources that induce large errors from finite volume and sizable lattice spacings. Previous work has shown how classical simulations near the Hamiltonian limit can be used for setting the lattice spacings in real time through analytical continuation, thereby reducing errors in quantum simulations. In this work, we derive perturbative relations between bare and renormalized quantities in Euclidean spacetime at any anisotropy factor—the ratio of spatial to temporal lattice spacings—and in any spatial dimension for U(N) and SU(N). This reduces the required classical preprocessing for quantum simulations. We find less than 10% discrepancy between our perturbative results and those from existing nonperturbative determinations of the anisotropy for SU(2) and U(1) gauge theories. For the discrete groups Z10, Z100 and BI, we perform lattice Monte Carlo simulations to extract anisotropy factors and observe similar agreement with our perturbative results.

关键词： Lattice gauge theory Nonperturbative effects in field theory Perturbative QCD quantum algorithms quantum simulation Lattice field theory

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