arXiv subjects

Sho Sugiura

Publications and source records attributed to Sho Sugiura.

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↗

arXiv2025

Clifford circuit based heuristic optimization of fermion-to-qubit mappings

Simulation of interacting fermionic Hamiltonians is one of the most promising applications of quantum computers. However, the feasibility of analysing fermionic systems with a quantum computer hinges on the efficiency of fermion-to-qubit mappings that encode non-local fermionic degrees of freedom in local qubit degrees of freedom. While recent works have highlighted the importance of designing fermion-to-qubit mappings that are tailored to specific problem Hamiltonians, the methods proposed so far are either restricted to a narrow class of mappings or they use computationally expensive and unscalable brute-force search algorithms. Here, we address this challenge by designing a $\mathrm{\textbf{heuristic}}$ numerical optimization framework for fermion-to-qubit mappings. To this end, we first translate the fermion-to-qubit mapping problem to a Clifford circuit optimization problem, and then use simulated annealing to optimize the average Pauli weight of the problem Hamiltonian. For all fermionic Hamiltonians we have considered, the numerically optimized mappings outperform their conventional counterparts, including ternary-tree-based mappings that are known to be optimal for single creation and annihilation operators. We find that our optimized mappings yield between $15\%$ to $40\%$ improvements on the average Pauli weight when the simulation Hamiltonian has an intermediate level of complexity. Most remarkably, the optimized mappings improve the average Pauli weight for $6 \times 6$ nearest-neighbor hopping and Hubbard models by more than $40\%$ and $20\%$, respectively. Surprisingly, we also find specific interaction Hamiltonians for which the optimized mapping outperform $\mathrm{\textbf{any}}$ ternary-tree-based mapping. Our results establish heuristic numerical optimization as an effective method for obtaining mappings tailored for specific fermionic Hamiltonian.

quant-ph↗

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

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↗

arXiv2023

Power of sequential protocols in hidden quantum channel discrimination

In many natural and engineered systems, unknown quantum channels act on a subsystem that cannot be directly controlled and measured, but is instead learned through a controllable subsystem that weakly interacts with it. We study quantum channel discrimination (QCD) under these restrictions, which we call hidden system QCD (HQCD). We find that sequential protocols achieve perfect discrimination and saturate the Heisenberg limit. In contrast, depth-1 parallel and multi-shot protocols cannot solve HQCD. This suggests that sequential protocols are superior in experimentally realistic situations.

quant-ph↗

arXiv2022

Error-Robust Quantum Signal Processing using Rydberg Atoms

Rydberg atom arrays have recently emerged as one of the most promising platforms for quantum simulation and quantum information processing. However, as is the case for other experimental platforms, the longer-term success of the Rydberg atom arrays in implementing quantum algorithms depends crucially on their robustness to gate-induced errors. Here we show that, for an idealized biased error model based on Rydberg atom dynamics, the implementation of QSP protocols can be made error-robust, in the sense that the asymptotic scaling of the gate-induced error probability is slower than that of gate complexity. Moreover, using experimental parameters reported in the literature, we show that QSP iterates made out of up to a hundred gates can be implemented with constant error probability. To showcase our approach, we provide a concrete blueprint to implement QSP-based near-optimal Hamiltonian simulation on the Rydberg atom platform. Our protocol substantially improves both the scaling and the overhead of gate-induced errors in comparison to those protocols that implement a fourth-order product-formula.

quant-ph↗

arXiv2021

Quantum advantage for noisy channel discrimination

Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in many discrimination tasks compared to when only incoherent access is permitted, but it is unclear if this advantage persists when the process is noisy. Here, we show that a quantum advantage can be maintained when distinguishing between two noisy single qubit rotation channels. Numerical and analytical calculations reveal a distinct transition between optimal performance by fully coherent and fully incoherent protocols as a function of noise strength. Moreover, the size of the region of coherent quantum advantage shrinks inverse polynomially in the number of channel uses, and in an intermediate regime an improved strategy is a hybrid of fully-coherent and fully-incoherent subroutines. The fully coherent protocol is based on quantum signal processing, suggesting a generalizable algorithmic framework for the study of quantum advantage in the presence of realistic noise.

quant-ph↗

arXiv2020

Adiabatic landscape and optimal paths in ergodic systems

Whether one is interested in quantum state preparation or in the design of efficient heat engines, adiabatic (reversible) transformations play a pivotal role in minimizing computational complexity and energy losses. Understanding the structure of these transformations and identifying the systems for which such transformations can be performed efficiently and quickly is therefore of primary importance. In this paper we focus on finding optimal paths in the space of couplings controlling the system's Hamiltonian. More specifically, starting from a local Hamiltonian we analyze directions in the space of couplings along which adiabatic transformations can be accurately generated by local operators, which are both realizable in experiments and easy to simulate numerically. We consider a non-integrable 1D Ising model parametrized by two independent couplings, corresponding to longitudinal and transverse magnetic fields. We find regions in the space of couplings characterized by a very strong anisotropy of the variational adiabatic gauge potential (AGP), generating the adiabatic transformations, which allows us to define optimal adiabatic paths. We find that these paths generally terminate at singular points characterized by extensive degeneracies in the energy spectrum, splitting the parameter space into adiabatically disconnected regions. The anisotropy follows from singularities in the AGP, and we identify special robust weakly-thermalizing and non-absorbing many-body "dark" states which are annihilated by the singular part of the AGP and show that their existence extends deep into the ergodic regime.

quant-ph↗

arXiv2019

Many-body scar state intrinsic to periodically driven system: Rigorous results

The violation of the Floquet version of eigenstate thermalization hypothesis is systematically discussed with realistic Hamiltonians. Our model is based on the PXP type interactions without disorder. We exactly prove the existence of many-body scar states in the Floquet eigenstates, by showing the explicit expressions of the wave functions. Using the underlying physical mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered.

cond-mat.stat-mech↗

arXiv2019

Resonantly enhanced polariton wave mixing and Floquet parametric instability

We introduce a new theoretical approach for analyzing pump and probe experiments in non-linear acousto-optic systems. In our approach, the effect of coherently pumped polaritons is modeled as providing time-periodic modulation of the system parameters. Within this framework, propagation of the probe pulse is described by the Floquet version of Maxwell's equations and leads to such phenomena as frequency mixing and resonant parametric production of polariton pairs. We analyze light reflection from a slab of insulating material with a strongly excited phonon-polariton mode and obtain analytic expressions for the frequency-dependent reflection coefficient for the probe pulse. Our results are in agreement with recent experiments by Cartella et al. which demonstrated light amplification in resonantly excited SiC insulator. We show that, beyond a critical pumping strength, such systems should exhibit Floquet parametric instability, which corresponds to resonant scattering of the pump polaritons into pairs of finite momentum polaritons. We find that the parametric instability should be achievable in SiC using current experimental techniques and discuss its signatures, including the non-analytic frequency dependence of the reflection coefficient and the probe pulse afterglow. We discuss possible applications of the parametric instability phenomenon and suggest that similar types of instabilities can be present in other photoexcited non-linear systems.

physics.optics↗

arXiv2018

Thermal pure state path integral and emergent symmetry

We investigate a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. We formulate a path integral in terms of thermal pure states and derive an effective action for trajectories in a thermodynamic state space, where the entropy appears with its conjugate variable. In particular, for quasi-static operations, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant.

cond-mat.stat-mech↗

arXiv2018

Thermodynamical path integral and emergent symmetry

We investigate a thermally isolated quantum many-body system with an external control represented by a step protocol of a parameter. The propagator at each step of the parameter change is described by thermodynamic quantities under some assumptions. For the time evolution of such systems, we formulate a path integral over the trajectories in the thermodynamic state space. In particular, for quasi-static operations, we derive an effective action of the thermodynamic entropy and its canonically conjugate variable. Then, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant in quantum mechanics.

cond-mat.stat-mech↗

arXiv2018

Page Curves for General Interacting Systems

We calculate in detail the Renyi entanglement entropies of cTPQ states as a function of subsystem volume, filling the details of our prior work [Nature Communications 9, 1635 (2018)], where the formulas were first presented. Working in a limit of large total volume, we find universal formulas for the Renyi entanglement entropies in a region where the subsystem volume is comparable to that of the total system. The formulas are applicable to the infinite temperature limit as well as general interacting systems. For example we find that the second Renyi entropy of cTPQ states in terms of subsystem volume is written universally up to two constants, $S_2(\ell)=-\ln K(β)+\ell\ln a(β)-\ln\left(1+a(β)^{-L+2\ell}\right)$, where $L$ is the total volume of the system and $a$ and $K$ are two undetermined constants. The uses of the formulas were already presented in our prior work and we mostly concentrate on the theoretical aspect of the formulas themselves. Aside from deriving the formulas for the Renyi Page curves, the expression for the von Neumann Page curve is also derived, which was not presented in our previous work.

cond-mat.stat-mech↗

arXiv2018

Universality in volume law entanglement of pure quantum states

A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. Thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and cause a correction to this simple volume-law. To elucidate the size dependence of the entanglement entropy is of essential importance in linking quantum physics with thermodynamics, and in addressing recent experiments in ultra-cold atoms. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing thermal equilibrium. We further find that our formula applies universally to any sufficiently scrambled pure states representing thermal equilibrium, i.e., general energy eigenstates of non-integrable models and states after quantum quenches. Our universal formula can be exploited as a diagnostic of chaotic systems; we can distinguish integrable models from chaotic ones and detect many-body localization with high accuracy.

cond-mat.stat-mech↗

arXiv2018

Construction of Hamiltonians by supervised learning of energy and entanglement spectra

Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter physics, nuclear physics, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely effective Hamiltonian, is essential. Here, we propose a simple scheme of constructing Hamiltonians from given energy or entanglement spectra with machine learning. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin-1/2 model with several analytic results based on the high order perturbation theory which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the $S=1/2$ two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane phase and the Rung Singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is non-local by nature, and the locality can be restored by introducing the anisotropy and turning the system into the large-$D$ phase. Possible applications to the study of strongly-correlated systems and the model construction from experimental data are discussed.

cond-mat.str-el↗

arXiv2014

Thermal Pure Quantum States of Many-Particle Systems

We generalize the thermal pure quantum (TPQ) formulation of statistical mechanics, in such a way that it is applicable to systems whose Hilbert space is infinite dimensional. Assuming particle systems, we construct the grand-canonical TPQ (gTPQ) state, which is the counterpart of the grand-canonical Gibbs state of the ensemble formulation. A single realization of the gTPQ state gives all quantities of statistical-mechanical interest, with exponentially small probability of error. This formulation not only sheds new light on quantum statistical mechanics but also is useful for practical computations. As an illustration, we apply it to the Hubbard model, on a one-dimensional (1d) chain and on a two-dimensional (2d) triangular lattice. For the 1d chain, our results agree well with the exact solutions over wide ranges of temperature, chemical potential and the on-site interaction. For the 2d triangular lattice, for which exact results are unknown, we obtain reliable results over a wide range of temperature. We also find that finite-size effects are much smaller in the gTPQ state than in the canonical TPQ (cTPQ) state. This also shows that in the ensemble formulation the grand-canonical Gibbs state of a finite-size system simulates an infinite system much better than the canonical Gibbs state.

cond-mat.stat-mech↗

arXiv2013

New Formulation of Statistical Mechanics using Thermal Pure Quantum States

We formulate statistical mechanics based on a pure quantum state, which we call a ``thermal pure quantum (TPQ) state''. A single TPQ state gives not only equilibrium values of mechanical variables, such as magnetization and correlation functions, but also those of genuine thermodynamic variables and thermodynamic functions, such as entropy and free energy. Among many possible TPQ states, we discuss the canonical TPQ state, the TPQ state whose temperature is specified. % We also propose there are other TPQ states. In the TPQ formulation of statistical mechanics, thermal fluctuations are completely included in quantum-mechanical fluctuations. As a consequence, TPQ states have much larger quantum entanglement than the equilibrium density operators of the ensemble formulation. We also show that the TPQ formulation is very useful in practical computations, by applying the formulation to a frustrated two-dimensional quantum spin system.

cond-mat.stat-mech↗