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Towards optimization of photonic-crystal surface-emitting lasers via quantum annealing

Inoue T., Seki Y., Tanaka S., Togawa N., Ishizaki K., Noda S.

Optics Express （Optics Express） 30 （ 24 ） 43503 - 43512 2022年11月

査読有り, ISSN 1094-4087

Photonic-crystal surface-emitting lasers (PCSELs), which utilize a two-dimensional (2D) optical resonance inside a photonic crystal for lasing, feature various outstanding functionalities such as single-mode high-power operation and arbitrary control of beam polarizations. Although most of the previous designs of PCSELs employ spatially uniform photonic crystals, it is expected that lasing performance can be further improved if it becomes possible to optimize the spatial distribution of photonic crystals. In this paper, we investigate the structural optimization of PCSELs via quantum annealing towards high-power, narrow-beam-divergence operation with linear polarization. The optimization of PCSELs is performed by the iteration of the following three steps: (1) time-dependent 3D coupled-wave analysis of lasing performance, (2) formulation of the lasing performance via a factorization machine, and (3) selection of optimal solution(s) via quantum annealing. By using this approach, we discover an advanced PCSEL with a non-uniform spatial distribution of the band-edge frequency and injection current, which simultaneously enables higher output power, a narrower divergence angle, and a higher linear polarization ratio than conventional uniform PCSELs. Our results potentially indicate the universal applicability of quantum annealing, which has been mainly applied to specific types of discrete optimization problems so far, for various physics and engineering problems in the field of smart manufacturing.

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Quantum annealing with twisted fields

Imoto T., Seki Y., Matsuzaki Y., Kawabata S.

New Journal of Physics （New Journal of Physics） 24 （ 11 ） 113009 - 113009 2022年11月

査読有り, ISSN 13672630

Quantum annealing (QA) is a promising method for solving combinational optimization problems and performing quantum chemical calculations. The main sources of errors in QA are the effects of decoherence and non-adiabatic transition. We propose a method for suppressing both these effects using inhomogeneous twist operators corresponding to the twist angles of transverse fields applied to qubits. Furthermore, we adopt variational methods to determine the optimal inhomogeneous twist operator for minimizing the energy of the state after QA. Our approach is useful for increasing the energy gap and/or making the quantum states robust against decoherence during QA. In summary, our results can pave the way to a new approach for realizing practical QA.

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Guaranteed-accuracy quantum annealing

Imoto T., Seki Y., Matsuzaki Y., Kawabata S.

Physical Review A （Physical Review A） 106 （ 4 ） 2022年10月

査読有り, ISSN 24699926

Quantum chemistry calculations constitute an important application of quantum annealing (QA). For practical applications in quantum chemistry, it is essential to estimate the ground-state energy of the Hamiltonian with chemical accuracy. However, there is no known method for guaranteeing the accuracy of the energy estimated via QA. Here, we propose a method for guaranteeing the accuracy of the energy estimated via QA using the Weinstein and Temple bounds. In our scheme, before QA is performed, the energies of the ground state and first excited state must be preestimated with some error bars (corresponding to the possible estimation error) via classical computation with some approximations. We show that, if the expectation value and standard deviation of the energy of the state after QA are lower than certain threshold values (that we can calculate from the preestimation), the ground-state energy estimated by QA is closer to the ground-state energy than the preestimation. As the expectation value and standard deviation of the energy can be experimentally measured via QA, our results pave the way for accurate estimation of the ground-state energy using QA.

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Obtaining Ground States of the XXZ Model Using the Quantum Annealing with Inductively Coupled Superconducting Flux Qubits

Imoto T., Seki Y., Matsuzaki Y.

Journal of the Physical Society of Japan （Journal of the Physical Society of Japan） 91 （ 6 ） 2022年06月

査読有り, ISSN 00319015

Obtaining ground states of Hamiltonians is important in the condensed matter physics and the quantum chemistry. The interaction Hamiltonians typically contain not only diagonal but also off-diagonal elements. Although quantum annealing provides a way to obtain a ground state of a Hamiltonian, we can only use the Hamiltonian with Ising interaction by using currently available commercial quantum annealing devices. In this work, we propose a quantum annealing for the XXZ model, which contains both Ising interaction and energy-exchange interaction, by using inductively coupled superconducting flux qubits. The key idea is to use a recently proposed spin-lock quantum annealing where the qubits are driven by microwave fields. As long as the rotating wave approximation is valid, the inductive coupling between the superconducting flux qubits produces the desired Hamiltonian in the rotating frame, and we can use such an interaction for the quantum annealing while the microwave fields driving play a role of the transverse fields. To quantify the performance of our scheme, we implement numerical simulations, and show that we can obtain ground states of the two-dimensional Heisenberg model with a high fidelity.

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Quantum remote sensing under the effect of dephasing

Okane H., Hakoshima H., Takeuchi Y., Seki Y., Matsuzaki Y.

Physical Review A （Physical Review A） 104 （ 6 ） 2021年12月

査読有り, ISSN 24699926

The quantum remote sensing (QRS) is a scheme to add security about the measurement results of a qubit-based sensor. A client delegates a measurement task to a remote server that has a quantum sensor, and eavesdropper (Eve) steals every classical information stored in the server side. By using quantum properties, the QRS provides an asymmetricity about the information gain where the client gets more information about the sensing results than Eve. However, quantum states are fragile against decoherence, and so it is not clear whether such a QRS is practically useful under the effect of realistic noise. Here, we investigate the performance of the QRS with dephasing during the interaction with the target fields. In the QRS, the client and server need to share a Bell pair, and an imperfection of the Bell pair leads to a state preparation error in a systematic way on the server side for the sensing. We consider the effect of both dephasing and state preparation error. The uncertainty of the client side decreases with the square root of the repetition number M for small M, which is the same scaling as the standard quantum metrology. On the other hand, for large M, the state preparation error becomes as relevant as the dephasing, and the uncertainty decreases logarithmically with M. We compare the information gain between the client and Eve. This leads us to obtain the conditions for the asymmetric gain to be maintained even under the effect of dephasing. Then, we can quantify how much information the client can gain while preserving the information asymmetricity.

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Boltzmann machine learning with a variational quantum algorithm

Shingu Y., Seki Y., Watabe S., Endo S., Matsuzaki Y., Kawabata S., Nikuni T., Hakoshima H.

Physical Review A （Physical Review A） 104 （ 3 ） 2021年09月

査読有り, ISSN 24699926

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 devices. We prepare an initial pure state that contains all possible computational basis states with the same amplitude, and we 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.

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Excited state search using quantum annealing

Seki Y., Matsuzaki Y., Kawabata S.

Journal of the Physical Society of Japan （Journal of the Physical Society of Japan） 90 （ 5 ） 054002 - 054002 2021年05月

査読有り, ISSN 00319015

Quantum annealing (QA) is one of the ways of finding ground states of problem Hamiltonians. We initially apply transverse fields corresponding to a driver Hamiltonian and adiabatically change the Hamiltonian to the problem Hamiltonian to obtain the target ground state. However, for some purposes such as quantum chemistry, both ground and excited states are needed to understand the properties of the molecules. Here, we describe a scheme based on QA to search arbitrary excited states of problem Hamiltonians. By splitting the degeneracy of the driver Hamiltonian with inhomogeneous transverse fields, we can prepare a nondegenerate excited state as the initial state, and an adiabatic change of the Hamiltonian provides a target excited state as long as the adiabatic condition holds. We also show that our scheme enables us to find a desired excited state by designing the driver Hamiltonian suitably even in the presence of weak decoherence. These results are important for quantum chemistry and post-quantum cryptography.

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Direct estimation of the energy gap between the ground state and excited state with quantum annealing

Matsuzaki Y., Hakoshima H., Sugisaki K., Seki Y., Kawabata S.

Japanese Journal of Applied Physics （Japanese Journal of Applied Physics） 60 （ SB ） SBBI02 - SBBI02 2021年05月

査読有り, ISSN 00214922

In quantum chemistry, it is important to estimate an energy gap between a ground state and an excited state of molecular Hamiltonians. In previous researches, it was necessary to measure the energy of the ground state and that of the excited state separately, and the energy gap was estimated from the subtraction between them. Here, we show a novel scheme to estimate such an energy gap in a more direct manner. We use a concept of a Ramsey type measurement in the quantum annealing (QA) for such a direct estimation of the energy gap. In our scheme, the measured signal oscillates with a frequency of the energy gap. To study the performance of our scheme, we perform numerical simulations. The results show our scheme is robust against non-adiabatic transitions between the ground state and first excited state. Our scheme paves the way for the practical application of QA in quantum chemistry.

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Quantum annealing with capacitive-shunted flux qubits

Yuichiro Matsuzaki, Hideaki Hakoshima, Yuya Seki, Shiro Kawabata

Japanese Journal of Applied Physics （Japan Society of Applied Physics） 2020年01月

査読有り, ISSN 0021-4922

Quantum annealing (QA) provides us with a way to solve combinatorial
optimization problems. In the previous demonstration of the QA, a
superconducting flux qubit (FQ) was used. However, the flux qubits in these
demonstrations have a short coherence time such as tens of nano seconds. For
the purpose to utilize quantum properties, it is necessary to use another qubit
with a better coherence time. Here, we propose to use a capacitive-shunted flux
qubit (CSFQ) for the implementation of the QA. The CSFQ has a few order of
magnitude better coherence time than the FQ used in the QA. We theoretically
show that, although it is difficult to perform the conventional QA with the
CSFQ due to the form and strength of the interaction between the CSFQs, a
spin-lock based QA can be implemented with the CSFQ even with the current
technology. Our results pave the way for the realization of the practical QA
that exploits quantum advantage with long-lived qubits.

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Enhancing quantum annealing performance by a degenerate two-level system

Shohei Watabe, Yuya Seki, Shiro Kawabata

Scientific Reports 10 146 2020年01月

査読有り

Quantum annealing is an innovative idea and method for avoiding the increase
of the calculation cost of the combinatorial optimization problem. Since the
combinatorial optimization problems are ubiquitous, quantum annealing machine
with high efficiency and scalability will give an immeasurable impact on many
fields. However, the conventional quantum annealing machine may not have a high
success probability for finding the solution because the energy gap closes
exponentially as a function of the system size. To propose an idea for finding
high success probability is one of the most important issues. Here we show that
a degenerate two-level system provides the higher success probability than the
conventional spin-1/2 model in a weak longitudinal magnetic field region. The
physics behind this is that the quantum annealing in this model can be reduced
into that in the spin-1/2 model, where the effective longitudinal magnetic
field may open the energy gap, which suppresses the Landau--Zener tunneling
providing leakage of the ground state. We also present the success probability
of the $\Lambda$-type system, which may show the higher success probability
than the conventional spin-1/2 model.

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Quantum Phase Transition in Fully Connected Quantum Wajnflasz-Pick Model

Seki, Yuya, Tanaka, Shu, Kawabata, Shiro

Journal of the Physical Society of Japan 88 054006 2019年01月

査読有り

We construct a quantum Wajnflasz-Pick model that is a generalized quantum
Ising model, and investigate a nature of quantum phase transitions of the model
with infinite-range interactions. Quantum phase transition phenomena have drawn
attention in the field of quantum computing as well as condensed matter
physics, since the phenomena are closely related to the performance of quantum
annealing (QA) and adiabatic quantum computation (AQC). We add a quantum driver
Hamiltonian to the Hamiltonian of classical Wajnflasz-Pick model. The classical
Wajnflasz-Pick model consists of two-level systems as with the usual Ising
model. Unlike the usual Ising spin, each of the upper and the lower levels of
the system can be degenerate. The states in the upper level and the lower level
are referred to as upper states and lower states, respectively. The quantum
driver Hamiltonian we introduced causes spin flip between the upper and the
lower states and state transitions within each of the upper and the lower
states. Numerical analysis showed that the model undergoes first-order phase
transitions whereas a corresponding quantum Ising model, quantum Curie-Weiss
model, does not undergo first-order phase transitions. In particular, we
observed an anomalous phenomenon that the system undergoes successive
first-order phase transitions under certain conditions. The obtained results
indicate that the performance of QA and AQC by using degenerate two-level
systems can be controlled by the parameters in the systems.

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Quantum annealing with antiferromagnetic transverse interactions for the Hopfield model

Yuya Seki, Hidetoshi Nishimori

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL （IOP PUBLISHING LTD） 48 （ 33 ） 335301 2015年08月

査読有り, ISSN 1751-8113

We investigate quantum annealing (QA) with antiferromagnetic transverse interactions for the generalized Hopfield model with k-body interactions. The goal is to study the effectiveness of antiferromagnetic interactions, which were shown to help us avoid problematic first-order quantum phase transitions in pure ferromagnetic systems, in random systems. We estimate the efficiency of QA by analyzing phase diagrams for two cases where the number of embedded patterns is finite or extensively large. The phase diagrams of the model with finite patterns show that there exist annealing paths that avoid first-order transitions at least for 5 <= k <= 21. The same is true for the extensive case with k = 4 and 5. In contrast, it is impossible to avoid first-order transitions for the case of finite patterns with k = 3 and the case of extensive number of patterns with k = 2 and 3. The spin-glass phase hampers the QA process in the case of k = 2 and extensive patterns. These results indicate that QA with antiferromagnetic transverse interactions is efficient also for certain random spin systems.

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Quantum annealing with antiferromagnetic fluctuations for mean-field models

Yuya Seki, Hidetoshi Nishimori

Kinki University Series on Quantum Computing 9 121 2014年05月

Quantum annealing with antiferromagnetic fluctuations

Yuya Seki, Hidetoshi Nishimori

PHYSICAL REVIEW E （AMER PHYSICAL SOC） 85 （ 5 ） 051112 2012年05月

査読有り, ISSN 1539-3755

We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic p-spin model, for which the conventional quantum annealing has been shown to have difficulties in finding the ground state efficiently due to a first-order transition. We study the phase diagram of this system both analytically and numerically. Using the static approximation, we find that there exists a quantum path to reach the final ground state from the trivial initial state that avoids first-order transitions for intermediate values of p. We also study numerically the energy gap between the ground state and the first excited state and find evidence for intermediate values of p for which the time complexity scales polynomially with the system size at a second-order transition point along the quantum path that avoids first-order transitions. These results suggest that quantum annealing would be able to solve this problem with intermediate values of p efficiently, in contrast to the case with only simple transverse-field fluctuations.

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