arXiv subjects

Hirofumi Nishi

Publications and source records attributed to Hirofumi Nishi.

At least 37 records · Page 2Linked to original sources

arXiv2025

General Transform: A Unified Framework for Adaptive Transform to Enhance Representations

Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often depends on understanding the dataset's properties, making the approach less effective when such knowledge is unavailable. In this work, we propose General Transform (GT), an adaptive transform-based representation designed for machine learning applications. Unlike conventional transforms, GT learns data-driven mapping tailored to the dataset and task of interest. Here, we demonstrate that models incorporating GT outperform conventional transform-based approaches across computer vision and natural language processing tasks, highlighting its effectiveness in diverse learning scenarios.

cs.LG↗

arXiv2025

A probabilistic imaginary-time evolution quantum algorithm for advection-diffusion equation: Explicit gate-level implementation and comparisons to quantum linear system algorithms

Simulating differential equations on classical computers becomes an intractable problem if the grid size is extremely large. Quantum computers are believed to achieve a possibly exponential speedup in the matrix operation. In this paper, we propose a quantum algorithm for solving the advection-diffusion-reaction equation by employing a novel approximate probabilistic imaginary-time evolution (PITE) operator. First, the effectiveness of the proposed approximate PITE operator is justified by the theoretical evaluation of the error. Next, we construct the explicit quantum circuit to realize the imaginary-time evolution of the Hamiltonian coming from the advection-diffusion equation, whose gate complexity is logarithmic regarding the size of the discretized Hamiltonian matrix. Compared to the existing algorithms for the quantum linear system problem, our algorithm achieves an exponential speedup regarding the matrix size at the cost of a worse dependence on the error bound. Moreover, numerical simulations using gate-based quantum emulator for 1D/2D examples are also provided to verify our algorithm. Finally, we extend our algorithm to the coupled system of advection-diffusion equations to show the prospects for practical applications.

quant-ph↗

arXiv2025

Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits

In this study, we employed a quantum computer to solve a low-energy effective Hamiltonian for spin defects in diamond (so-called NV centre) and wurtzite-type aluminium nitride, which are anticipated to be qubits. The probabilistic imaginary-time evolution (PITE) method, designed for use in a fault-tolerant quantum computer (FTQC) era, was employed to calculate the ground and excited states of the spin singlet state, as represented by the effective Hamiltonian. It is difficult to compute the spin singlet state correctly using density functional theory (DFT), which should be described by multiple Slater determinants. To mitigate the effects of quantum errors inherent in current quantum computers, we implemented a $[[ n+2,n,2 ]]$ quantum error detection (QED) code called the Iceberg code. Despite the inevitable destruction of the encoded state resulting from the measurement of the ancilla qubit at each PITE step, we were able to successfully re-encode and recover the logical success state. In the implementation of the PITE, it was observed that the effective Hamiltonian comprises large components of the diagonal part and a relatively small non-diagonal part, which is frequently the case with quantum chemistry calculations. An efficient implementation of Hamiltonian simulations, in which the diagonal components dominate, was developed on a quantum computer based on the second-order Trotter-Suzuki decomposition. This is the first instance of an encoded PITE circuit being executed on a trapped-ion quantum computer. Our results demonstrate that QED effectively reduces quantum errors and that we successfully obtained both the ground and excited states of the spin singlet state. Our demonstration clearly manifests that Zr$_{\rm Al}$V$_{\rm N}$, Ti$_{\rm Al}$V$_{\rm N}$, and Hf$_{\rm Al}$V$_{\rm N}$ defects have a high potential as spin qubits for quantum sensors.

quant-ph↗

arXiv2024

Qubit encoding for a mixture of localized functions

One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit construction is not provided. Given the growing demands for practical quantum computation, we develop moderately specialized encoding techniques that generate an arbitrary linear combination of localized complex functions. We demonstrate that $n_{\mathrm{loc}}$ discrete Lorentzian functions as an expansion basis set lead to eficient probabilistic encoding, whose computational time is $\mathcal{O}( \max ( n_{\mathrm{loc}}^2 \log n_{\mathrm{loc}},n_{\mathrm{loc}}^2 \log n_q, n_q ))$ for $n_q$ data qubits equipped with $\log_2 n_{\mathrm{loc}}$ ancillae. Furthermore, amplitude amplification in combination with amplitude reduction renders it deterministic analytically with controllable errors and the computational time is reduced to $\mathcal{O}( \max ( n_{\mathrm{loc}}^{3/2} \log n_{\mathrm{loc}}, n_{\mathrm{loc}}^{3/2} \log n_q, n_q )).$ We estimate required resources for applying our scheme to quantum chemistry in real space. We also show the results on real superconducting quantum computers to confirm the validity of our techniques.

quant-ph↗

arXiv2024

Machine learning supported annealing for prediction of grand canonical crystal structures

This study investigates the application of Factorization Machines with Quantum Annealing (FMQA) to address the crystal structure problem (CSP) in materials science. FMQA is a black-box optimization algorithm that combines machine learning with annealing machines to find samples to a black-box function that minimize a given loss. The CSP involves determining the optimal arrangement of atoms in a material based on its chemical composition, a critical challenge in materials science. We explore FMQA's ability to efficiently sample optimal crystal configurations by setting the loss function to the energy of the crystal configuration as given by a predefined interatomic potential. Further we investigate how well the energies of the various metastable configurations, or local minima of the potential, are learned by the algorithm. Our investigation reveals FMQA's potential in quick ground state sampling and in recovering relational order between local minima.

cond-mat.mtrl-sci↗

arXiv2024

Orbital-free density functional theory with first-quantized quantum subroutines

In this study, we propose a quantum-classical hybrid scheme for performing orbital-free density functional theory (OFDFT) using probabilistic imaginary-time evolution (PITE), designed for the era of fault-tolerant quantum computers (FTQC), as a material calculation method for large-scale systems. PITE is applied to the part of OFDFT that searches the ground state of the Hamiltonian in each self-consistent field (SCF) iteration, while the other parts such as electron density and Hamiltonian updates are performed by existing algorithms on classical computers. When the simulation cell is discretized into $N_\mathrm{g}$ grid points, combined with quantum phase estimation (QPE), it is shown that obtaining the ground state energy of Hamiltonian requires a circuit depth of $O(\log N_\mathrm{g})$. The ground state calculation part in OFDFT is expected to be accelerated, for example, by creating an appropriate preconditioner from the estimated ground state energy for the locally optimal block preconditioned conjugate gradient (LOBPCG) method.

quant-ph↗

arXiv2024

Approximate real-time evolution operator for potential with one ancillary qubit and application to first-quantized Hamiltonian simulation

In this article, we compare the methods implementing the real-time evolution operator generated by a unitary diagonal matrix where its entries obey a known underlying real function. When the size of the unitary diagonal matrix is small, a well-known method based on Walsh operators gives a good and precise implementation. In contrast, as the number of qubits grows, the precise one uses exponentially increasing resources, and we need an efficient implementation based on suitable approximate functions. Using piecewise polynomial approximation of the function, we summarize the methods with different polynomial degrees. Moreover, we obtain the overheads of gate count for different methods concerning the error bound and grid parameter (number of qubits). This enables us to analytically find a relatively good method as long as the underlying function, the error bound, and the grid parameter are given. This study contributes to the problem of encoding a known function in the phase factor, which plays a crucial role in many quantum algorithms/subroutines. In particular, we apply our methods to implement the real-time evolution operator for the potential part in the first-quantized Hamiltonian simulation and estimate the resources (gate count and ancillary qubits) regarding the error bound, which indicates that the error coming from the approximation of the potential function is not negligible compared to the error from the Trotter-Suzuki formula.

quant-ph↗

arXiv2024

Optimized synthesis of circuits for diagonal unitary matrices with reflection symmetry

During the noisy intermediate-scale quantum (NISQ) era, it is important to optimize the quantum circuits in circuit depth and gate count, especially entanglement gates, including the CNOT gate. Among all the unitary operators, diagonal unitary matrices form a special class that plays a crucial role in many quantum algorithms/subroutines. Based on a natural gate set {CNOT, Rz}, quantum circuits for general diagonal unitary matrices were discussed in several previous works, and an optimal synthesis algorithm was proposed in terms of circuit depth. In this paper, we are interested in the implementation of diagonal unitary matrices with reflection symmetry, which has promising applications, including the realization of real-time evolution for first quantized Hamiltonians by quantum circuits. Owing to such a symmetric property, we show that the quantum circuit in the existing work can be further simplified and propose a constructive algorithm that optimizes the entanglement gate count. Compared to the previous synthesis methods for general diagonal unitary matrices, the quantum circuit by our proposed algorithm achieves nearly half the reduction in both the gate count and circuit depth.

quant-ph↗

arXiv2024

Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups

Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to perform quantum computation in good accuracy with these machines we need to develop alternative approaches for mitigating quantum computational errors. In this work, we propose quantum error mitigation (QEM) scheme for quantum computational errors which occur due to couplings with environments during gate operations, i.e., decoherence. To establish our QEM scheme, first we estimate the quantum noise effects on single-qubit states and represent them as groups of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM scheme is conducted by subtracting expectation values generated by the quantum-noise-effect circuit groups from that obtained by the quantum circuits for the quantum algorithms under consideration. As a result, the quantum noise effects are reduced, and we obtain approximately the ideal expectation values via the quantum-noise-effect circuit groups and the numbers of elementary quantum circuits composing them scale polynomial with respect to the products of the depths of quantum algorithms and the numbers of register bits. To numerically demonstrate the validity of our QEM scheme, we run noisy quantum simulations of qubits under amplitude damping effects for four types of quantum algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience processors and examine its efficacy. Consequently, the validity of our scheme is verified via both the quantum simulations and the quantum computations on the real quantum devices.

quant-ph↗

arXiv2023

First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration

We propose a novel adiabatic time evolution (ATE) method for obtaining the ground state of a quantum many-electron system on a quantum circuit based on first quantization. As a striking feature of the ATE method, it consists of only unitary operations representing real-time evolution, which means that it does not require any ancillary qubits, nor controlled real-time evolution operators. Especially, we explored the first-quantized formalism of ATE method in this study, since the implementation of first-quantized real-time evolution on quantum circuits is known to be efficient. However, when realizing the ATE quantum circuit in first-quantization formalism, obstacles are how to set the adiabatic Hamiltonian and how to prepare the corresponding initial ground state. We provide a way to prepare an antisymmetrized and non-degenerate initial ground state that is suitable as an input to an ATE circuit, which allows our ATE method to be applied to systems with any number of electrons. In addition, by considering a first-quantized Hamiltonian for quantum-mechanical electron system and classical nuclear system, we design a quantum circuit for optimal structure search based on ATE. Numerical simulations are demonstrated for simple systems, and it is confirmed that the ground state of the electronic system and optimal structure can be obtained by our method.

quant-ph↗

arXiv2023

Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer

Ground-state preparation is an important task in quantum computation. The probabilistic imaginary-time evolution (PITE) method is a promising candidate for preparing the ground state of the Hamiltonian, which comprises a single ancilla qubit and forward- and backward-controlled real-time evolution operators. The ground state preparation is a challenging task even in the quantum computation, classified as complexity-class quantum Merlin-Arthur. However, optimal parameters for PITE could potentially enhance the computational efficiency to a certain degree. In this study, we analyze the computational costs of the PITE method for both linear and exponential scheduling of the imaginary-time step size for reducing the computational cost. First, we analytically discuss an error defined as the closeness between the states acted on by exact and approximate imaginary-time evolution operators. The optimal imaginary-time step size and rate of change of imaginary time are also discussed. Subsequently, the analytical discussion is validated using numerical simulations for a one-dimensional Heisenberg chain. From the results, we find that linear scheduling works well in the case of unknown eigenvalues of the Hamiltonian. For a wide range of eigenstates, the linear scheduling returns smaller errors on average. However, the linearity of the scheduling causes problems for some specific energy regions of eigenstates. To avoid these problems, incorporating a certain level of nonlinearity into the scheduling, such as by inclusion of an exponential character, is preferable for reducing the computational costs of the PITE method. The findings of this study can make a significant contribute to the field of ground-state preparation of many-body Hamiltonians on quantum computers.

quant-ph↗

arXiv2023

Channel Attention for Quantum Convolutional Neural Networks

Quantum convolutional neural networks (QCNNs) have gathered attention as one of the most promising algorithms for quantum machine learning. Reduction in the cost of training as well as improvement in performance is required for practical implementation of these models. In this study, we propose a channel attention mechanism for QCNNs and show the effectiveness of this approach for quantum phase classification problems. Our attention mechanism creates multiple channels of output state based on measurement of quantum bits. This simple approach improves the performance of QCNNs and outperforms a conventional approach using feedforward neural networks as the additional post-processing.

quant-ph↗

arXiv2023

Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer

We propose a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver, a recently proposed framework for quantum chemistry using the probabilistic imaginary-time evolution (PITE) on a quantum computer. While the electrons in a molecule are treated in the scheme as quantum mechanical particles, the nuclei are treated as classical point charges. We encode both electronic states and candidate molecular geometries as a superposition of many-qubit states, leading to quantum advantage. The histogram formed by outcomes of repeated measurements gives the global minimum of the energy surface. We demonstrate that the circuit depth scales as O (n_e^2 poly(log n_e)) for the electron number n_e, which can be reduced to O (n_e poly(log n_e)) if extra O (n_e log n_e) qubits are available. We corroborate the scheme via numerical simulations. The new efficient scheme will be helpful for achieving scalability of practical quantum chemistry on quantum computers. As a special case of the scheme, a classical system composed only of charged particles is admitted. We also examine the scheme adapted to variational calculations that prioritize saving circuit depths for noisy intermediate-scale quantum (NISQ) devices.

quant-ph↗

arXiv2023

Annealing for prediction of grand canonical crystal structures: Efficient implementation of n-body atomic interactions

We propose an annealing scheme usable on modern Ising machines for crystal structures prediction (CSP) by taking into account the general n-body atomic interactions, and in particular three-body interactions which are necessary to simulate covalent bonds. The crystal structure is represented by discretizing a unit cell and placing binary variables which express the existence or non-existence of an atom on every grid point. The resulting quadratic unconstrained binary optimization (QUBO) or higher-order unconstrained binary optimization (HUBO) problems implement the CSP problem and is solved using simulated and quantum annealing. Using the example of Lennard-Jones clusters we show that it is not necessary to include the target atom number in the formulation allowing for simultaneous optimization of both the particle density and the configuration and argue that this is advantageous for use on annealing machines as it reduces the total amount of interactions. We further provide a scheme that allows for reduction of higher-order interaction terms that is inspired by the underlying physics. We show for a covalently bonded monolayer MoS2 crystal that we can simultaneously optimize for the particle density as well as the crystal structure using simulated annealing. We also show that we reproduce ground states of the interatomic potential with high probability that are not represented on the initial discretization of the unit cell.

quant-ph↗

arXiv2023

Quadratic acceleration of multi-step probabilistic algorithms for state preparation

For quantum state preparation, a non-unitary operator is typically designed to decay undesirable states contained in an initial state using ancilla qubits and a probabilistic action. Probabilistic algorithms do not accelerate the computational process compared to classical ones. In this study, quantum amplitude amplification (QAA) and multi-step probabilistic algorithms are combined to achieve quadratic acceleration. This method outperforms quantum phase estimation in terms of infidelity. The quadratic acceleration was confirmed by the probabilistic imaginary-time evolution (PITE) method.

quant-ph↗

arXiv2023

First-quantized eigensolver for ground and excited states of electrons under a uniform magnetic field

First-quantized eigensolver (FQE) is a recently proposed framework of quantum computation for obtaining the ground state of an interacting electronic system based on probabilistic imaginary-time evolution. In this study, we propose a method for introducing a uniform magnetic field to an FQE calculation. We demonstrate via resource estimation that the additional circuit responsible for the magnetic field can be implemented with a liner depth in terms of the number of qubits assigned to each electron, giving rise to no impact on the leading order of whole computational cost. We confirm the validity of our method via numerical simulations for ground and excited states by employing the filtration circuits for energy eigenstates. We also provide the generic construction of derivative circuits together with measurement-based formulae. As a special case of them, we can obtain the electric-current density in an electronic system to get insights into the microscopic origin of magnetic response.

quant-ph↗

arXiv2023

Quantum-Error-Mitigation Circuit Groups for Noisy Quantum Metrology

Quantum technologies work by utilizing properties inherent in quantum systems such as quantum coherence and quantum entanglement and are expected to be superior to classical counterparts for solving certain problems in science and engineering. The quantum technologies are, however, fragile against an interaction with an environment (decoherence) and in order to utilize them with high accuracy we need to develop error mitigation techniques which reduce decoherence effects. In this work, we analyze quantum error mitigation (QEM) protocol for quantum metrology in the presence of quantum noise. We demonstrate the effectiveness of our QEM protocol by analyzing three types of quantum Fisher information (QFI), ideal (error-free) QFI, noisy (erroneous) QFI, and quantum-error-mitigated QFI, and show both analytically and numerically that the scaling behaviors of quantum-error-mitigated QFI with respect to the number of probes become restored to the those exhibited in the ideal quantum metrology. Our QEM protocol is constructed by an ensemble of quantum circuits, namely QEM circuit groups, and has advantages such that it can be applied to noisy quantum metrology for any type of initial state as well as any type of the probe-system Hamiltonian, and it can be physically implemented in any type of quantum device. Furthermore, the quantum-error-mitigated QFI become approximately equal to the ideal QFI for almost any values of physical quantities to be sensed. Our protocol enables us to use quantum entanglement as a resource to perform high-sensitive quantum metrology even under the influence of quantum noise.

quant-ph↗

arXiv2022

Acceleration of probabilistic imaginary-time evolution method combined with quantum amplitude amplification

A probabilistic imaginary-time evolution (PITE) method was proposed as a nonvariational method to obtain a ground state on a quantum computer. In this formalism, the success probability of obtaining all imaginary-time evolution operators acting on the initial state decreases as the imaginary time proceeds. To alleviate the undesirable nature, we propose quantum circuits for PITE combined with the quantum amplitude amplification (QAA) method. We reduce the circuit depth in the combined circuit with QAA by introducing a pre-amplification operator. We successfully demonstrated that the combination of PITE and QAA works efficiently and reported a case in which the quantum acceleration is achieved. Additionally, we have found that by optimizing a parameter of PITE, we can reduce the number of QAA operations and that deterministic imaginary-time evolution (deterministic ITE) can be achieved which avoids the probabilistic nature of PITE. We applied the deterministic ITE procedure to multiple imaginary-time steps and discussed the computational cost for the circuits. Finally, as an example, we demonstrate the numerical results of the PITE circuit combined with QAA in the first- and second-quantized Hamiltonians.

quant-ph↗