arXiv subjects

Tatsuhiko N. Ikeda

Publications and source records attributed to Tatsuhiko N. Ikeda.

At least 19 recordsLinked to original sources

arXiv2026

Demonstration of a quantum comparator on an ion-trap quantum device

Quantum computers are believed to solve a class of computational problems that are based on modular arithmetic faster than classical computers. Among the arithmetic building blocks, comparison of integer pairs is a primitive. Here we report its demonstration in the Reimei quantum computer at RIKEN, whose trapped-ion architecture provides all-to-all qubit connectivity together with high gate fidelities. We observe high success probabilities for bit widths n = 3, 5, 7, and 9: Under a conventional output-only success criterion we obtain 95% at n=9; under a stricter criterion additionally requiring the ancilla to be correct, the success is 69% at n=9. These results demonstrate reliable quantum comparison at scales far beyond those previously achieved experimentally, not only for comparators but also in the broader context of quantum arithmetic circuits.

quant-ph↗

arXiv2026

Gyromagnetic Quantum Friction in Rayleigh Vorticity Baths

We identify an intrinsic zero-temperature relaxation channel for near-surface spins gyromagnetically coupled to Rayleigh-wave vorticity. This surface-mode contribution requires no thermal phonons, unlike Raman relaxation, and is fixed by Rayleigh vorticity rather than material-specific $g$-factor modulation. The Rayleigh-vorticity bath is super-Ohmic and evanescent with depth, producing field and depth scalings of spin relaxation. These scalings establish shallow spin sensors and hybrid surface-acoustic-wave spin interfaces as detectors of Rayleigh-wave acoustic quantum friction in solids.

cond-mat.mes-hall↗

arXiv2025

Explicit error bounds with commutator scaling for time-dependent product and multi-product formulas

Product formula (PF), which approximates the time evolution under a many-body Hamiltonian by the product of local time evolution operators, is one of the central approaches for simulating quantum dynamics by quantum computers. It has been of great interest whether PFs have a bound of the error from the exact time evolution, which is expressed by commutators among local terms (called commutator scaling), since it brings the substantial suppression of the computational cost in the system size. Although recent studies have revealed the presence and the explicit formulas of the PF error bounds for time-independent systems, those for time-dependent Hamiltonians remain to be a difficult problem except for low-order PFs. In this paper, we derive an explicit error bound of generic PFs for smooth time-dependent Hamiltonians, which is expressed by commutators among local terms and their time derivatives. This error bound can also host the substantial suppression in the system size for generic local Hamiltonians with finite-, short-, and long-ranged interactions, thereby giving a much better estimate of gate counts. Our derivation employs Floquet theory; Embedding generic smooth time-dependent Hamiltonians into time-periodic ones, we map the time-dependent PF error to the time-independent one defined on an infinite-dimensional space. This approach allows to obtain the error bounds not only for the ordinary time-dependent PF but also for its various family. In particular, we also clarify the explicit error bound of a time-dependent multi-product formula, with which we can achieve much smaller error by a linear combination of time-dependent PFs. Our results will shed light on various applications of quantum computers, ranging from quantum simulation of nonequilibrium materials to faster algorithms exploiting time-dependent Hamiltonians like adiabatic state preparation.

quant-ph↗

arXiv2025

Unpolarized prethermal discrete time crystal

Prethermal discrete time crystals (DTCs) are a novel phase of periodically driven matter that exhibits robust subharmonic oscillations without requiring disorder. However, previous realizations of prethermal DTCs have relied on the presence of polarization, either spontaneous or induced. Here, we introduce a new class of prethermal DTCs termed ``unpolarized prethermal discrete time crystals'' (UPDTCs) that arise without any uniform/staggered polarization and propose an experiment to observe them in current trapped-ion quantum simulators. By studying a model of trapped ions using a quantum circuit simulator, we demonstrate that robust period-doubled dynamics can persist in the autocorrelation function of the staggered magnetization, even though its expectation value does not exhibit such dynamics. The period-doubled dynamics is not explained by the classical picture of flipping spins but by quantum fluctuations. We establish that UPDTCs are exponentially long-lived in the high-frequency driving regime, a hallmark of prethermalization. These results expand the known phenomenology and mechanism of prethermal time crystals and underscore the role of quantum effects in stabilizing novel nonequilibrium phases.

cond-mat.quant-gas↗

arXiv2025

Floquet theory and applications in open quantum and classical systems

This article reviews theoretical methods for analyzing Floquet engineering (FE) phenomena in open (dissipative) quantum or classical systems, with an emphasis on our recent results. In many theoretical studies for FE in quantum systems, researchers have used the Floquet theory for closed (isolated) quantum systems, that is based on the Schrödinger equation. However, if we consider the FE in materials driven by an oscillating field like a laser, a weak but finite interaction between a target system and an environment (bath) is inevitable. In this article, we describe these periodically driven dissipative systems by means of the quantum master (GKSL) equation. In particular, we show that a nonequilibrium steady state appears after a long driving due to the balance between the energy injection by the driving field and the release to the bath. In addition to quantum systems, if we try to simply apply Floquet theory to periodically driven classical systems, it failed because the equation of motion (EOM) is generally nonlinear, and the Floquet theorem can be applied only to linear differential equations. Instead, by considering the distribution function of the classical variables (i.e., Fokker-Planck equation), one can arrive at the effective EOM for the driven systems. We illustrate the essence of the Floquet theory for classical systems. On top of fundamentals of the Floquet theory, we review representative examples of FEs (Floquet topological insulators, inverse Faraday effects in metals and magnets, Kapitza pendulum, etc.) and dissipation-assisted FEs.

cond-mat.str-el↗

arXiv2024

Exact spectral form factors of non-interacting fermions with Dyson statistics

The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed \textit{exactly}. These ensembles describe the evolution of non-interacting fermions in the presence of correlated on-site potentials drawn from the eigenvalue distribution of a circular ensemble. For disorder parameters drawn from the circular unitary ensemble (CUE), we derive an exact closed form for the SFF, valid for any choice of system size $L$ and integer time $t$. When the disorder is drawn from the circular orthogonal or symplectic ensembles (COE and CSE, respectively), we carry out the disorder averages analytically and reduce the computation of the SFF at integer times to a combinatorial problem amenable to transfer matrix methods. In each of these cases the SFF grows exponentially in time, which we argue is a signature of random matrix universality at the single-particle level. Finally, we develop matchgate circuit representations of our circuit ensembles, enabling their experimental realization in quantum simulators.

cond-mat.stat-mech↗

arXiv2024

Single-Particle Universality of the Many-Body Spectral Form Factor

We consider systems of fermions evolved by non-interacting unitary circuits with correlated on-site potentials. When these potentials are drawn from the eigenvalue distribution of a circular random matrix ensemble, the single-particle sector exhibits chaotic dynamics. We study the corresponding many-body spectral statistics and show that the spectral form factor (SFF) can be computed \textit{exactly}. Due to the absence of interactions the SFF grows exponentially in time, a result which we demonstrate through simple arguments, scaling collapses, and closed-form evaluation of the SFF. We study the role of interactions by numerically analyzing a kicked Ising model and find that the SFF crosses over to a linear growth regime consistent with many-body random matrix universality. Our exact results for the SFF provide a baseline for future studies of the crossover between single-particle and many-body random matrix behavior.

cond-mat.stat-mech↗

arXiv2024

A Quantum-Resistant Photonic Hash Function

We propose a quantum hash function based on Gaussian boson sampling on a photonic quantum computer, aiming to provide quantum-resistant security. Extensive simulations demonstrate that this hash function exhibits strong properties of preimage, second preimage, and collision resistance, which are essential for cryptographic applications. Notably, the estimated number of attempts required for a successful collision attack increases exponentially with the mode counts of the photonic quantum computer, suggesting robust resistance against birthday attacks. We also analyze the sampling cost for physical implementation and discuss potential applications to blockchain technologies, where the inherent quantum nature of the hash computation could provide quantum-resistant security. The high dimensionality of the quantum state space involved in the hashing process poses significant challenges for quantum attacks, indicating a path towards quantum security. Our work lays the foundation for a new paradigm of quantum-resistant hashing with applications in emerging quantum-era information systems.

quant-ph↗

arXiv2024

Floquet systems with continuous dynamical symmetries: characterization, time-dependent Noether charge, and solvability

We study quantum Floquet (periodically-driven) systems having continuous dynamical symmetry (CDS) consisting of a time translation and a unitary transformation on the Hilbert space. Unlike the discrete ones, the CDS strongly constrains the possible Hamiltonians $H(t)$ and allows us to obtain all the Floquet states by solving a finite-dimensional eigenvalue problem. Besides, Noether's theorem leads to a time-dependent conservation charge, whose expectation value is time-independent throughout evolution. We exemplify these consequences of CDS in the seminal Rabi model, an effective model of a nitrogen-vacancy center in diamonds without strain terms, and Heisenberg spin models in rotating fields. Our results provide a systematic way of solving for Floquet states and explain how they avoid hybridization in quasienergy diagrams.

cond-mat.mes-hall↗

arXiv2024

Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations

Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a method for measuring the Trotter error without ancillary qubits on quantum circuits by combining the $m$th- and $n$th-order ($m<n$) Trotterizations rather than consulting with mathematical error bounds. Using this method, we make Trotterization precision-guaranteed, developing an algorithm named Trotter$(m,n)$, in which the Trotter error at each time step is within an error tolerance $ε$ preset for our purpose. Trotter$(m,n)$ is applicable to both time- independent and dependent Hamiltonians, and it adaptively chooses almost the largest stepsize $\mathrm{d}t$, which keeps quantum circuits shallowest within the error tolerance. Benchmarking it in a quantum spin chain, we find the adaptively chosen $\mathrm{d}t$ to be about ten times larger than that inferred from known upper bounds of Trotter errors.

quant-ph↗

arXiv2024

Robust effective ground state in a nonintegrable Floquet quantum circuit

An external periodic (Floquet) drive is believed to bring any initial state to the featureless infinite temperature state in generic nonintegrable isolated quantum many-body systems in the thermodynamic limit, irrespective of the driving frequency $Ω$. However, numerical or analytical evidence either proving or disproving this hypothesis is very limited and the issue has remained unsettled. Here, we study the initial state dependence of Floquet heating in a nonintegrable kicked Ising chain of length up to $L=30$ with an efficient quantum circuit simulator, showing a possible counterexample: The ground state of the effective Floquet Hamiltonian is exceptionally robust against heating, and could stay at finite energy density even after infinitely many Floquet cycles, if the driving period is shorter than a threshold value. This sharp energy localization transition/crossover does not happen for generic excited states. The exceptional robustness of the ground state is interpreted by (i) its isolation in the energy spectrum and (ii) the fact that those states with $L$-independent $\hbarΩ$ energy above the ground state energy of any generic local Hamiltonian, like the approximate Floquet Hamiltonian, are atypical and viewed as a collection of noninteracting quasipartiles. Our finding paves the way for engineering Floquet protocols with finite driving periods realizing long-lived, or possibly even perpetual, Floquet phases by initial state design.

quant-ph↗

arXiv2023

Minimum Trotterization Formulas for a Time-Dependent Hamiltonian

When a time propagator $e^{δt A}$ for duration $δt$ consists of two noncommuting parts $A=X+Y$, Trotterization approximately decomposes the propagator into a product of exponentials of $X$ and $Y$. Various Trotterization formulas have been utilized in quantum and classical computers, but much less is known for the Trotterization with the time-dependent generator $A(t)$. Here, for $A(t)$ given by the sum of two operators $X$ and $Y$ with time-dependent coefficients $A(t) = x(t) X + y(t) Y$, we develop a systematic approach to derive high-order Trotterization formulas with minimum possible exponentials. In particular, we obtain fourth-order and sixth-order Trotterization formulas involving seven and fifteen exponentials, respectively, which are no more than those for time-independent generators. We also construct another fourth-order formula consisting of nine exponentials having a smaller error coefficient. Finally, we numerically benchmark the fourth-order formulas in a Hamiltonian simulation for a quantum Ising chain, showing that the 9-exponential formula accompanies smaller errors per local quantum gate than the well-known Suzuki formula.

quant-ph↗

arXiv2022

Stimulated Rayleigh Scattering Enhanced by a Longitudinal Plasma Mode in a Periodically Driven Dirac Semimetal Cd$_3$As$_2$

Using broadband (12-45 THz) multi-terahertz spectroscopy, we show that stimulated Rayleigh scattering dominates the transient optical conductivity of cadmium arsenide, a Dirac semimetal, under an optical driving field at 30 THz. The characteristic dispersive lineshape with net optical gain is accounted for by optical transitions between light-induced Floquet subbands, strikingly enhanced by the longitudinal plasma mode. Stimulated Rayleigh scattering with an unprecedentedly large refractive index change may pave the way for slow light generation in conductive solids at room temperature.

cond-mat.mtrl-sci↗

arXiv2022

Conformality of Charge Density Wave

New quantum phenomena are continuously being discovered in 2D systems. In particular, the charge density wave (CDW) has the aspect of a quantum crystal with a macroscopic wave function (order parameter), so unlike quantum liquids (superconductivity, quantum Hall liquids $^3$He, $^4$He), new ground states such as supersolid and Moiré solids can be expected. However, it is difficult to describe these states because of their quantum aspect, hence there is still no theory that can explain CDW phases in a unified way. The best way to describe a quantum crystal seems to be a conformal transformation that allows local deformation (wave properties) and preserves local angles (crystal properties). Here, we propose a unifying conformal description of 2D CDW phases in the typical 2D CDW material transition metal dichalcogenides (MX$_2$). We discover that the discommensurate CDW phases in MX$_2$ can be explained beautifully by a discrete conformal transformation of CDW wavevectors. This conformality is due to commensurability of CDW with the MX$_2$ lattice. In other words, interference of harmonic wavefunction induces conformality. Using this new conformal formulation, we explain experimental nearly-commensurate/stripe/T CDW phases in 1$T$-TaS$_2$ ($\sqrt{13}\times\sqrt{13}$ structure), 2$H$-TaSe$_2$ ($\sqrt{9}\times\sqrt{9}$ structure), and explain the origin of a new experimental nearly-commensurate phase in TaSe$_2$ thin-film ($\sqrt{7}\times\sqrt{7}$ structure). This theory is very simple in the sense that it includes only discommensuration and comprises physics as rich as quantum Hall liquids. This new description will broaden our perspective of quantum crystals.

cond-mat.str-el↗

arXiv2022

Criticality and Rigidity of Dissipative Discrete Time Crystals in Solids

We consider a dissipative quantum Ising model periodically driven by a train of $π$-pulses and investigate dissipative discrete time crystals (DTCs) in solids. In this model, the interaction between the spins spontaneously breaks the discrete time translation symmetry, giving rise to a dissipative DTC, where two ferromagnetic states are switched alternately by each pulse. We microscopically describe the generic dissipation due to thermal contact to an equilibrium heat bath using the Bloch-Redfield equation. In contrast to other DTC studies, this dissipation stabilizes, rather than destroys, the DTC order without fine-tuning as long as the temperature is low enough. Invoking the time-dependent mean-field theory and solving self-consistently the periodic drive, dissipation, and DTC order parameter, we investigate the nonequilibrium DTC phase transition and determine the critical exponents, including a dynamical one. We also find phase transitions without equilibrium counterpart: a nontrivial interplay of the periodic drive and dissipation gives rise to reentrant DTC transition when changing the pulse interval at a fixed temperature. Besides, to demonstrate the rigidity of the DTC, we consider imperfect $π$-pulses, showing that the DTC is robust against the small imperfections and finding that discrete time quasicrystals (DTQC) can appear for the larger imperfections. Together with experimental proposals in magnetic materials, our results pave the ways for realizing the DTC and for uncovering nonequilibrium critical phenomena in real solid-state materials.

cond-mat.stat-mech↗

arXiv2022

Exciton-coherence generation through diabatic and adiabatic dynamics of Floquet state

Floquet engineering of electronic systems is a promising way of controlling quantum material properties on an ultrafast time scale. So far, the energy structure of Floquet states in solids has been observed through time and angle-resolved photoelectron spectroscopy or pump-probe measurement techniques. However, the dynamical aspects of the photon-dressed states under ultrashort pulse driving have not been explored yet. Their dynamics become highly sensitive to the envelope of the driving field when the light-matter interaction enters non-perturbative regime, and thus, understanding of them is crucial for ultrafast manipulation of quantum state. Here, we observed coherent exciton emissions under intense and non-resonant mid-infrared fields in monolayer WSe2 at room temperature, which is unexpected in perturbative nonlinear optics. Together with numerical calculations, our measurements revealed that the coherent exciton emission reflects the diabatic and adiabatic dynamics of Floquet states. Our results provide a new approach to probing the dynamics of the Floquet state and lead to control of quantum materials through pulse shaping of the driving field.

cond-mat.other↗

arXiv2022

Floquet-Landau-Zener interferometry: Usefulness of the Floquet theory in pulse-laser-driven systems

We develop the Landau-Zener transfer matrix theory for the instantaneous Floquet states (IFSs) for quantum systems driven by strong pulse lasers. Applying this theory to the pulse excitation probability in two-level quantum systems, we show unexpectedly good quantitative agreements for few-cycle pulses. This approach enables us to qualitatively understand the probability's peculiar behaviors as quantum path interference between IFSs. We also study the pulse-width dependence, finding that this Floquet-state interpretation remains useful for shorter pulses down to 2-cycle ones in the present model. These results imply that the Floquet theory is meaningful in experimental few-cycle lasers if applied appropriately in the sense of IFSs.

cond-mat.mes-hall↗

arXiv2021

Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach

Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital in Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs based on the high-frequency (HF) expansion with linear algebraic numerics and without numerically solving the time evolution. This theory shows that NESSs can deviate from the Floquet-Gibbs state depending on the dissipation type. We show the validity and usefulness of the HF-expansion approach in concrete models for a diamond nitrogen-vacancy (NV) center, a kicked open XY spin chain with topological phase transition under boundary dissipation, and the Heisenberg spin chain in a circularly-polarized magnetic field under bulk dissipation. In particular, for the isotropic Heisenberg chain, we propose the dissipation-assisted terahertz (THz) inverse Faraday effect in quantum magnets. Our theoretical framework applies to various time-periodic Lindblad equations that are currently under active research.

cond-mat.mes-hall↗