論文

It is known that effects of dissipation or measurement backreaction in postselected quantum trajectories are described by a non-Hermitian Hamiltonian, but their consequences in real-time dynamics of many-body systems are yet to be elucidated. Through a study of a non-Hermitian Hubbard model, we reveal a novel dissipation-induced dynamical phase transition in postselected quantum trajectories, where time controls the strength of postselection and becomes the intrinsic parameter inducing the phase transition. Our findings are testable in ultracold atom experiments and may open a new avenue in the dissipative engineering of quantum systems.

We study SU(3) Yang-Mills theory in (2 + 1) dimensions based on networks of Wilson lines. With the help of the q deformation, networks respect the (discretized) SU(3) gauge symmetry as a quantum group, i.e., SU(3) k, and may enable implementations of SU(3) Yang-Mills theory in quantum and classical algorithms by referring to those of the stringnet model. As a demonstration, we perform a mean-field computation of the groundstate of SU(3) k Yang-Mills theory, which is in good agreement with the conventional Monte Carlo simulation by taking sufficiently large k. The variational ansatz of the mean-field computation can be represented by the tensor networks called infinite projected entangled pair states. The success of the mean-field computation indicates that the essential features of Yang-Mills theory are well described by tensor networks, so that they may be useful in numerical simulations of Yang-Mills theory.

We study the Hamiltonian lattice Yang-Mills theory based on spin networks that provide a useful basis to represent the physical states satisfying the Gauss law constraints. We focus on SU(2) Yang-Mills theory in (2 + 1) dimensions. Following the string-net model, we introduce a regularization of the Kogut-Susskind Hamiltonian of lattice Yang-Mills theory based on the q deformation, which respects the (discretized) SU(2) gauge symmetry as quantum group, i.e., SU(2)k, and enables implementation of the lattice Yang-Mills theory both in classical and quantum algorithms by referring to those of the string-net model. Using the regularized Hamiltonian, we study quantum scars in a nonabelian gauge theory. Quantum scars are nonthermal energy eigenstates arising in the constrained quantum many-body systems. We find that quantum scars from zero modes, which have been found in abelian gauge theories arise even in a nonabelian gauge theory. We also show the spectrum of a single-plaquette model for SU(2)k and SU(3)k with naive cutoff and that based on the q-deformation to discuss cutoff dependence of the formulation.

We demonstrate a dissipative protocol for ground-state preparation of a quantum spin chain on a trapped-ion quantum computer. As a first step, we derive a Kraus representation of a dissipation channel for the protocol recently proposed by Ding et al. [Phys. Rev. Res. 6, 033147 (2024)] that still holds for arbitrary temporal discretization steps, extending the analysis beyond the Lindblad dynamics regime. The protocol guarantees that the fidelity with the ground state monotonically increases (or remains unchanged) under repeated applications of the channel to an arbitrary initial state, provided that the ground state is the unique steady state of the dissipation channel. Using this framework, we implement dissipative ground-state preparation of a transverse-field Ising chain for up to 19 spins on the trapped-ion quantum computer Reimei provided by Quantinuum. Despite the presence of hardware noise, the dynamics consistently converges to a low-energy state far away from the maximally mixed state even when the corresponding quantum circuits contain as many as 4110 entangling gates, demonstrating the intrinsic robustness of the protocol. By applying zero-noise extrapolation, the resulting energy expectation values are systematically improved to agree with noiseless simulations within statistical uncertainties.

We simulate Floquet time-evolution of a truncated SU(3) lattice Yang-Mills theory on a two-leg ladder geometry under open boundary conditions using IBM's superconducting 156-qubit device ibm\_fez. To this end, we derive the quantum spin representation of the lattice Yang-Mills theory, and compose a quantum circuit carefully tailored to hard wares, reducing the use of CZ gates. Since it is still challenging to simulate Hamiltonian evolution in present noisy quantum processors, we make the step size in the Suzuki-Trotter decomposition very large, and simulate thermalization dynamics in Floquet circuit composed of the Suzuki-Trotter evolution. We demonstrate that IBM's Heron quantum processor can simulate, by error mitigation, Floqeut thermalization dynamics in a large system consisting of $62$ qubits. Our work would be a benchmark for further quantum simulations of lattice gauge theories using real devices.

Simulating nonequilibirum dynamics of a quantum many-body system is one of the promising applications of quantum computing. We simulate the time evolution of one-dimensional ${\bf Z}_2$ lattice gauge theory on IBM's superconducting 156-qubit device ibm\_fez. We consider the Floquet circuit made of the Trotter decomposition of Hamiltonian evolution and focus on its dynamics toward thermalization. Quantum simulation with the help of error mitigation is successful in running the Floquet circuit made of $38$ and $116$ qubits up to $10$ Trotter steps in the best case. This is enough to reach the early stage of prethermalization. Our work would be a benchmark for the potential power of quantum computing for high-energy physics problems.

Nonequilibrium dynamics of quantum many-body systems is one of the main targets of quantum simulations. This focus - together with rapid advances in quantum-computing hardware - has driven increasing applications in high-energy physics, particularly in lattice gauge theories. However, most existing experimental demonstrations remain restricted to (1+1)-dimensional and/or abelian gauge theories, such as the Schwinger model and the toric code. It is essential to develop quantum simulations of nonabelian gauge theories in higher dimensions, addressing realistic problems in high-energy physics. To fill the gap, we demonstrate a quantum simulation of thermalization dynamics in a (2+1)-dimensional $q$-deformed $\mathrm{SU}(2)_3$ Yang-Mills theory using a trapped-ion quantum computer. By restricting the irreducible representations of the gauge fields to the integer-spin sector of $\mathrm{SU}(2)_3$, we obtain a simplified yet nontrivial model described by Fibonacci anyons, which preserves the essential nonabelian fusion structure of the gauge fields. We successfully simulate the real-time dynamics of this model using quantum circuits that explicitly implement $F$-moves. In our demonstrations, the quantum circuits execute up to 47 sequential $F$-moves. We identify idling errors as the dominant error source, which can be effectively mitigated using dynamical decoupling combined with a parallelized implementation of $F$-moves.

We investigate the $(2+1)$-dimensional $q$-deformed $\mathrm{SU}(N)_k$ Yang-Mills theory in the lattice Hamiltonian formalism, which is characterized by three parameters: the number of colors $N$, the coupling constant $g$, and the level $k$. By treating these as tunable parameters, we explore how key properties of the theory, such as confinement and topological order, emerge in different regimes. Employing a variational mean-field analysis that interpolates between the strong- and weak-coupling regimes, we determine the large-$N$ phase structure in terms of the 't Hooft coupling $λ_\mathrm{tH}=g^2N$ and the ratio $k/N$. We find that the topologically ordered phase remains robust at large $N$ under appropriate scalings of these parameters. This result indicates that the continuum limit of large-$N$ gauge theory may be more intricate than naively expected, and motivates studies beyond the mean-field theory, both to achieve a further understanding of confinement in gauge theories and to guide quantum simulations of large-$N$ gauge theories.

Given the rapid advances in quantum computing hardware, establishing systematic strategies for verifying the correctness of quantum computations has become increasingly important. Exploiting the fact that the axial anomaly in gauge theories is exact to all orders in perturbation theory, we propose the axial anomaly as a nontrivial benchmark for quantum simulations of lattice gauge theories. We simulate anomalous axial-charge production in ${\mathbb Z}_N$ lattice gauge theories on the trapped-ion quantum computer ``Reimei''. After taking the U(1), infinitesimal time, and infinite volume limits, we successfully reproduce the anomaly coefficient within statistical uncertainties, even without error mitigation. Our results demonstrate that the axial anomaly can be simulated on current quantum computers and serves as a verification test of quantum computations.

多自由度の粒子が相互作用する量子系は場の量子論を用いて記述することができる．現代物理学において，場の量子論は素粒子物理学・原子核物理学・物性物理学の共通言語であると言える．その中でも特に，場の量子論を素粒子物理学に応用する際には電磁場のような場の自由度の量子論を考える必要があり，そのような場の量子論はゲージ場の量子論と呼ばれる．素粒子物理学における標準模型はゲージ場の量子論を用いて記述される．量子色力学（Quantum chromodynamics, QCD）はSU（3）という非可換群をゲージ対称性とするゲージ場の量子論であり，標準模型に現れる3つの相互作用のうち，陽子や中性子（より一般にはハドロンと呼ばれる粒子）の間にはたらく強い力を，素粒子であるクォークとグルーオンを基本自由度として記述する．QCDの最も重要な性質に，短距離スケールの物理は弱結合的で，一方で，長距離スケールの物理は強結合になる漸近的自由性という性質がある．漸近的自由性により，クォークやグルーオンが高エネルギーで散乱する過程は摂動論を用いて記述することができる．一方で，クォークやグルーオンの運動から陽子や中性子ひいては我々の世界を理解するには，ゲージ場の量子論を非摂動的に解かなければならない．ゲージ場の量子論の非摂動的な解析は，現代の素粒子物理学の中心的課題の一つである．格子ゲージ理論は最も強力かつ成功した場の量子論の定式化方法の一つであり，時空を格子上に離散化することで，無限の自由度を持つゲージ場の量子論を計算可能な有限自由度の積分に正則化する．格子ゲージ理論とモンテカルロ法を組み合わせることで，ハドロンの質量，核力，有限温度の状態方程式など，QCDの重要な物理量を精密に計算することが可能になった．しかしながら，有限密度のQCDや時間発展など一部の重要な問題では，符号問題と呼ばれる困難のために，モンテカルロ法に基づく計算が破綻するという困難に直面する．符号問題はQCDに限らず大自由度の量子多体系を非摂動的に計算する際に現れる共通の困難であり，この問題を解決するために様々な試みが行われている．それらの試みの中で特に，従来の計算機では到底扱えない規模の計算を可能にするとされる量子計算を格子ゲージ理論へと応用する研究が近年注目されている．量子計算を格子ゲージ理論に応用するためには，格子ゲージ理論の計算を，量子状態にユニタリ演算子を作用させる形式で表現する必要がある．このために，従来の経路積分形式ではなく，ハミルトニアン形式に基づいて量子計算に適した計算アルゴリズムを開発する研究が行われている．ここで現れるのが表題のハミルトニアン形式の格子ゲージ理論である．様々な手法が提案され，まだ手法が確立されたわけではないが，実機を用いた検証が始まりつつある．現在の量子計算機では，連続極限の格子ゲージ理論の解析は様々な技術的制約のために実現できていないが，簡単な系での研究が着実に進展している．従来のモンテカルロ計算と同様なレベルで素粒子物理学・原子核物理学に有用な精密計算がいつできるようになるかは明らかではないが，今後量子誤り訂正技術の発展により，理論的な思考実験としては十分役に立つような計算は可能になり，量子計算はゲージ理論の非摂動ダイナミクスを解析する新しい計算道具となる期待が高い．また，量子計算の格子ゲージ理論への応用を通じて格子ゲージ理論と量子統計基礎論や量子情報理論との新しい接点が明らかになっている．量子計算は新たな計算道具を提供するのみならず，新しい融合分野を生み出すかもしれない．

We study one-flavor SU(2) and SU(3) lattice QCD in (1 + 1) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

We study $\mathrm{SU}(3)$ Yang-Mills theory in $(2+1)$ dimensions based on networks of Wilson lines. With the help of the $q$ deformation, networks respect the (discretized) $\mathrm{SU}(3)$ gauge symmetry as a quantum group, i.e., $\mathrm{SU}(3)_k$, and may enable implementations of $\mathrm{SU}(3)$ Yang-Mills theory in quantum and classical algorithms by referring to those of the stringnet model. As a demonstration, we perform a mean-field computation of the groundstate of $\mathrm{SU}(3)_k$ Yang-Mills theory, which is in good agreement with the conventional Monte Carlo simulation by taking sufficiently large $k$. The variational ansatz of the mean-field computation can be represented by the tensor networks called infinite projected entangled pair states. The success of the mean-field computation indicates that the essential features of Yang-Mills theory are well described by tensor networks, so that they may be useful in numerical simulations of Yang-Mills theory.

We study one-flavor $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ lattice QCD in ($1+1$) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

Simulating nonequilibrium dynamics of quantum many-body systems is one of the most promising applications of quantum computers. However, a faithful digital quantum simulation of the Hamiltonian evolution is very challenging in the present noisy quantum devices. Instead, nonequilibrium dynamics under the Floquet evolution realized by the Trotter decomposition of the Hamiltonian evolution with a large Trotter step size is considered to be a suitable problem for simulating in the present or near-term quantum devices. In this work, we propose simulating the many-body localization crossover as such a nonequilibrium problem in the disordered Floquet many-body systems. As a demonstration, we simulate the many-body localization crossover in a disordered kicked Ising model on a heavy-hex lattice using $60$ qubits from $156$ qubits available in the IBM Heron r2 superconducting qubit device named ibm\_fez. We compute out-of-time-ordered correlators as an indicator of the many-body localization crossover. From the late-time behavior of out-of-time-ordered correlators, we locate the quantum chaotic and many-body localized regimes as a function of the disorder strength. The validity of the results is confirmed by comparing two independent error mitigation methods, that is, the operator renormalization method and zero-noise extrapolation.

We discuss the quantum computation of dynamical chirality production in lattice gauge theory. Although the chirality of a lattice fermion is complicated in general dimensions, it can be simply formulated on a one-dimensional lattice. The chiral fermion formalism enables us to extract the physical part of the chirality production that would be interpreted as the chiral anomaly in the continuous theory. We demonstrate the computation of the Z2 lattice gauge theory on a classical emulator.

We perform real-Time lattice simulation of an open quantum system based on the Schwinger-Keldysh path integral representation of the Lindblad formalism. Although the real-Time simulation generally suffers from the sign problem, a few exceptional cases exist. We focus on a sign-problem-free system of a non-relativistic spinless fermion and analyze the time evolution under driving and dissipation.

We study the Hubbard model with non-Hermitian asymmetric hopping terms. The conjugate hopping terms are introduced for two spin components so that the negative sign is canceled out. This ensures that the quantum Monte Carlo simulation is free from the negative sign problem. We analyze the antiferromagnetic order and its suppression by the non-Hermiticity.

We theoretically investigate non-Hermitian p-wave Fermi superfluidity in one-dimensional spin-polarized Fermi gases which is relevant to recent ultracold atomic experiments. Considering an imaginary atom-dimer coupling responsible for the three-body recombination process in the Lindblad formalism, we discuss the stability of the superfluid state against the atomic loss effect. Within the two-channel non-Hermitian BCS-Eagles-Leggett theory, the atomic loss is characterized by the product of the imaginary atom-dimer coupling and the p-wave effective range. Our results indicate that for a given imaginary atom-dimer coupling, a smaller magnitude of the effective ranges of p-wave interaction is crucial for reaching the non-Hermitian p-wave Fermi superfluid state. Moreover, our theoretical framework for many-body systems with the three-body loss, which is inevitable in ultracold atoms, would promote further progress in non-Hermitian cold-atomic physics.

We introduce a two-dimensional non-Hermitian lattice model with an imaginary magnetic field and elucidate various unique features which are absent in Hermitian lattice models with real magnetic fields. To describe the imaginary magnetic field, we consider both the Landau gauge and the symmetric gauge, which are related by a generalized gauge transformation, changing not only the phase but also the amplitude of the wave function. We discuss the complex energy spectrum and the non-Hermitian Aharonov-Bohm effect as examples of properties which are due to the imaginary magnetic field independent of the generalized gauge transformation. We show that the energy spectrum does not converge as the lattice size is made larger, which comes from the intrinsic nonperiodicity of the model. However, we have found that the energy spectrum does converge if one fixes the length of one side and makes the other side longer; this asymptotic behavior can be understood in the framework of the non-Bloch band theory. We also find an analog of the Aharonov-Bohm effect; the net change of the norm of the wave function upon adiabatically forming a closed path is determined by the imaginary magnetic flux enclosed by the path, which provides an experimentally observable feature of the imaginary magnetic field.