arXiv subjects

Hirotaka Oshima

Publications and source records attributed to Hirotaka Oshima.

33 records · Page 2Linked to original sources

arXiv2025

Molecular Quantum Transformer

The Transformer model, renowned for its powerful attention mechanism, has achieved state-of-the-art performance in various artificial intelligence tasks but faces challenges such as high computational cost and memory usage. Researchers are exploring quantum computing to enhance the Transformer's design, though it still shows limited success with classical data. With a growing focus on leveraging quantum machine learning for quantum data, particularly in quantum chemistry, we propose the Molecular Quantum Transformer (MQT) for modeling interactions in molecular quantum systems. By utilizing quantum circuits to implement the attention mechanism on the molecular configurations, MQT can efficiently calculate ground-state energies for all configurations. Numerical demonstrations show that in calculating ground-state energies for H2, LiH, BeH2, and H4, MQT outperforms the classical Transformer, highlighting the promise of quantum effects in Transformer structures. Furthermore, its pretraining capability on diverse molecular data facilitates the efficient learning of new molecules, extending its applicability to complex molecular systems with minimal additional effort. Our method offers an alternative to existing quantum algorithms for estimating ground-state energies, opening new avenues in quantum chemistry and materials science.

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arXiv2025

Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks

Quantum neural networks (QNNs) require an efficient training algorithm to achieve practical quantum advantages. A promising approach is gradient-based optimization, where gradients are estimated by quantum measurements. However, QNNs currently lack general quantum algorithms for efficiently measuring gradients, which limits their scalability. To elucidate the fundamental limits and potentials of efficient gradient estimation, we rigorously prove a trade-off between gradient measurement efficiency (the mean number of simultaneously measurable gradient components) and expressivity in deep QNNs. This trade-off indicates that more expressive QNNs require higher measurement costs per parameter for gradient estimation, while reducing QNN expressivity to suit a given task can increase gradient measurement efficiency. We further propose a general QNN ansatz called the stabilizer-logical product ansatz (SLPA), which achieves the trade-off upper bound by exploiting the symmetric structure of the quantum circuit. Numerical experiments show that the SLPA drastically reduces the sample complexity needed for training while maintaining accuracy and trainability compared to well-designed circuits based on the parameter-shift method.

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arXiv2025

Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution

Simulating thermal-equilibrium properties at finite temperature is crucial for studying quantum many-body systems. Quantum computers are expected to enable us to simulate large systems at finite temperatures, overcoming challenges faced by classical computers, like the sign problem of the quantum Monte-Carlo technique. Conventional methods suitable for fault-tolerant quantum computing (FTQC) devices are designed for studying large-scale quantum many-body systems but require a large number of ancilla qubits and a deep quantum circuit with many basic gates, making them unsuitable for the early stage of the FTQC era, at which the availability of qubits and quantum gates is limited. In this paper, we propose a method suitable for quantum devices in this early stage to calculate the thermal-equilibrium expectation value of an observable at finite temperatures. Our proposal, named the Markov-chain Monte Carlo with sampled pairs of unitaries (MCMC-SPU) algorithm, involves sampling simple quantum circuits and generating the corresponding statistical ensembles. This approach addresses the issues of resource demand and the decay in probability associated with postselection of measurement outcomes on ancilla qubits. We validate our proposal with numerical simulation on the one-dimensional transverse-field Ising model as an illustrative example.

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arXiv2024

Compilation of Trotter-Based Time Evolution for Partially Fault-Tolerant Quantum Computing Architecture

Achieving practical quantum speedup with limited resources is a crucial challenge in both academic and industrial communities. To address this, a partially fault-tolerant quantum computing architecture called ``space-time efficient analog rotation quantum computing architecture (STAR architecture)'' has been recently proposed. This architecture focuses on minimizing resource requirements while maximizing the precision of non-Clifford gates, essential for universal quantum computation. However, non-deterministic processes such as the repeat-until-success (RUS) protocol and state injection can introduce significant computational overhead. Therefore, optimizing the logical circuit to minimize this overhead by using efficient fault-tolerant operations is essential. This paper presents an efficient method for simulating the time evolution of the 2D Hubbard model Hamiltonian, a promising application of the STAR architecture. We present two techniques, parallel injection protocol and adaptive injection region updating, to reduce unnecessary time overhead specific to our architecture. By integrating these with the existing fSWAP technique, we develop an efficient Trotter-based time evolution operation for the 2D Hubbard model. Our analysis reveals an acceleration of over 10 times compared to naive serial compilation. This optimized compilation enables us to estimate the computational resources required for quantum phase estimation of the 2D Hubbard model. For devices with a physical error rate of $p_{\rm phys} = 10^{-4}$, we estimate that approximately $6.5 \times 10^4$ physical qubits are required to achieve faster ground state energy estimation of the $8\times8$ Hubbard model compared to classical computation.

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arXiv2024

Practical quantum advantage on partially fault-tolerant quantum computer

Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited scalability of current near-term algorithms. Meanwhile, assuming a typical architecture for fault-tolerant quantum computing (FTQC), realistic applications inevitably require a vast number of qubits, typically exceeding $10^6$, which seems far beyond near-term realization. In this work, to bridge the gap between the NISQ and FTQC eras, we propose an alternative approach to achieve practical quantum advantages on early-FTQC devices. Our framework is based on partially fault-tolerant logical operations to minimize spatial overhead and avoids the costly distillation techniques typically required for executing non-Clifford gates. To this end, we develop a space-time efficient state preparation protocol to generate an ancillary non-Clifford state consumed for implementing an analog rotation gate with an arbitrary small angle $θ$ and a remarkably low worst-case error rate below $\mathcal{O}(|θ| p_{\text{ph}})$, where $p_{\text{ph}}$ is the physical error rate. Furthermore, we propose several error suppression schemes tailored to our preparation protocol, which are essential to minimize the overhead for mitigating errors. Based on this framework, we present several promising applications that leverage the potential of our framework, including the Trotter simulation and quantum phase estimation (QPE). Notably, we demonstrate that our framework allows us to perform the QPE for $(8\times 8)$-site Hubbard model with fewer than $4.9\times 10^4$ qubits and an execution time of 9 days (or 12 minutes with full parallelization) under $p_{\text{ph}}=10^{-4}$, which is significantly faster than recent classical estimation with tensor network techniques (DMRG and PEPS).

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arXiv2024

Subspace-Based Local Compilation of Variational Quantum Circuits for Large-Scale Quantum Many-Body Simulation

Simulation of quantum many-body systems is a promising application of quantum computers. However, implementing the time-evolution operator as a quantum circuit efficiently on near-term devices with limited resources is challenging. Standard approaches like Trotterization often require deep circuits, making them impractical. This paper proposes a hybrid quantum-classical algorithm called Local Subspace Variational Quantum Compilation (LSVQC) for compiling the time-evolution operator. The LSVQC uses variational optimization to reproduce the action of the target time-evolution operator within a physically reasonable subspace. Optimization is performed on small local subsystems based on the Lieb-Robinson bound, allowing for cost function evaluation using small-scale quantum devices or classical computers. Numerical simulations on a spin-lattice model and an $\mathit{\text{ab initio}}$ effective model of strongly correlated material Sr$_2$CuO$_3$ demonstrate the algorithm's effectiveness. It is shown that the LSVQC achieves a 95% reduction in circuit depth compared to Trotterization while maintaining accuracy. The subspace restriction also reduces resource requirements and improves accuracy. Furthermore, we estimate the gate count needed to execute the quantum simulations using the LSVQC on near-term quantum computing architectures in the noisy intermediate-scale or early fault-tolerant quantum computing era. Our estimation suggests that the acceptable physical gate error rate for the LSVQC can be significantly larger than for Trotterization.

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arXiv2024

Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data

The quantum convolutional neural network (QCNN) is a promising quantum machine learning (QML) model that is expected to achieve quantum advantages in classically intractable problems. However, the QCNN requires a large number of measurements for data learning, limiting its practical applications in large-scale problems. To alleviate this requirement, we propose a novel architecture called split-parallelizing QCNN (sp-QCNN), which exploits the prior knowledge of quantum data to design an efficient model. This architecture draws inspiration from geometric quantum machine learning and targets translationally symmetric quantum data commonly encountered in physics and quantum computing science. By splitting the quantum circuit based on translational symmetry, the sp-QCNN can substantially parallelize the conventional QCNN without increasing the number of qubits and improve the measurement efficiency by an order of the number of qubits. To demonstrate its effectiveness, we apply the sp-QCNN to a quantum phase recognition task and show that it can achieve comparable classification accuracy to the conventional QCNN while considerably reducing the measurement resources required. Due to its high measurement efficiency, the sp-QCNN can mitigate statistical errors in estimating the gradient of the loss function, thereby accelerating the learning process. These results open up new possibilities for incorporating the prior data knowledge into the efficient design of QML models, leading to practical quantum advantages.

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arXiv2023

Comparative study of decoding the surface code using simulated annealing under depolarizing noise

We explored decoding methods for the surface code under depolarizing noise by mapping the problem into the Ising model optimization. We consider two kinds of mapping with and without a soft constraint and also various optimization solvers, including simulated annealing implemented on a CPU, "Fujitsu Digital Annealer" (DA), a hardware architecture specialized for the Ising problems, and CPLEX, an exact integer programming solver. We find that the proposed Ising-based decoding approaches provide higher accuracy compared to the minimum-weight perfect matching (MWPM) algorithm for depolarizing noise and comparable to minimum distance decoding using CPLEX. While decoding time is longer than MWPM when we compare it with a single core CPU, our method is amenable to parallelization and easy to implement on dedicated hardware, suggesting potential future speedups. Regarding the mapping methods to the Ising model with and without a soft constraint, the SA decoder yielded higher accuracy without a soft constraint. In contrast, the DA decoder shows less difference between the two mapping methods, which indicates that DA can find a better solution with smaller number of iterations even under the soft constraint. Our results are important for devising efficient and fast decoders feasible with quantum computer control devices.

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arXiv2023

Synergetic quantum error mitigation by randomized compiling and zero-noise extrapolation for the variational quantum eigensolver

We propose a quantum error mitigation strategy for the variational quantum eigensolver (VQE) algorithm. We find, via numerical simulation, that very small amounts of coherent noise in VQE can cause substantially large errors that are difficult to suppress by conventional mitigation methods, and yet our proposed mitigation strategy is able to significantly reduce these errors. The proposed strategy is a combination of previously reported techniques, namely randomized compiling (RC) and zero-noise extrapolation (ZNE). Intuitively, randomized compiling turns coherent errors in the circuit into stochastic Pauli errors, which facilitates extrapolation to the zero-noise limit when evaluating the cost function. Our numerical simulation of VQE for small molecules shows that the proposed strategy can mitigate energy errors induced by various types of coherent noise by up to two orders of magnitude.

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arXiv2023

Variational Denoising for Variational Quantum Eigensolver

The variational quantum eigensolver (VQE) is a hybrid algorithm that has the potential to provide a quantum advantage in practical chemistry problems that are currently intractable on classical computers. VQE trains parameterized quantum circuits using a classical optimizer to approximate the eigenvalues and eigenstates of a given Hamiltonian. However, VQE faces challenges in task-specific design and machine-specific architecture, particularly when running on noisy quantum devices. This can have a negative impact on its trainability, accuracy, and efficiency, resulting in noisy quantum data. We propose variational denoising, an unsupervised learning method that employs a parameterized quantum neural network to improve the solution of VQE by learning from noisy VQE outputs. Our approach can significantly decrease energy estimation errors and increase fidelities with ground states compared to noisy input data for the $\text{H}_2$, LiH, and $\text{BeH}_2$ molecular Hamiltonians, and the transverse field Ising model. Surprisingly, it only requires noisy data for training. Variational denoising can be integrated into quantum hardware, increasing its versatility as an end-to-end quantum processing for quantum data.

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arXiv2023

Quantum error correction with an Ising machine under circuit-level noise

Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of actual quantum computing devices. In this work, we develop a decoder for circuit-level noise that solves the error estimation problems as Ising-type optimization problems. We confirm that the threshold theorem in the surface code under the circuitlevel noise is reproduced with an error threshold of approximately 0.4%. We also demonstrate the advantage of the decoder through which the Y error detection rate can be improved compared with other matching-based decoders. Our results reveal that a lower logical error rate can be obtained using our algorithm compared with that of the minimum-weight perfect matching algorithm.

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arXiv2023

Computation of Green's function by local variational quantum compilation

Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on classical computers, the development of quantum computers may enable us to compute the Green's function with high accuracy even for classically-intractable large-scale systems. Here, we propose an efficient method to compute the real-time Green's function based on the local variational quantum compilation (LVQC) algorithm, which simulates the time evolution of a large-scale quantum system using a low-depth quantum circuit constructed through optimization on a smaller-size subsystem. Our method requires shallow quantum circuits to calculate the Green's function and can be utilized on both near-term noisy intermediate-scale and long-term fault-tolerant quantum computers depending on the computational resources we have. We perform a numerical simulation of the Green's function for the one- and two-dimensional Fermi-Hubbard model up to $4\times4$ sites lattice (32 qubits) and demonstrate the validity of our protocol compared to a standard method based on the Trotter decomposition. We finally present a detailed estimation of the gate count for the large-scale Fermi-Hubbard model, which also illustrates the advantage of our method over the Trotter decomposition.

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arXiv2023

Partially Fault-tolerant Quantum Computing Architecture with Error-corrected Clifford Gates and Space-time Efficient Analog Rotations

Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually becoming available, but it is still challenging to achieve useful quantum advantages in meaningful tasks at this moment. On the other hand, the full fault-tolerant quantum computing (FTQC) based on the quantum error correction (QEC) code remains far beyond realization due to its extremely large requirement of high-precision physical qubits. In this study, we propose a quantum computing architecture to close the gap between NISQ and FTQC. Our architecture is based on erroneous arbitrary rotation gates and error-corrected Clifford gates implemented by lattice surgery. We omit the typical distillation protocol to achieve direct analog rotations and small qubit requirements, and minimize the remnant errors of the rotations by a carefully-designed state injection protocol. Our estimation based on numerical simulations shows that, for early-FTQC devices that consist of $10^4$ physical qubits with physical error probability $p = 10^{-4}$, we can perform roughly $1.72 \times 10^7$ Clifford operations and $3.75 \times 10^4$ arbitrary rotations on 64 logical qubits. Such computations cannot be realized by the existing NISQ and FTQC architectures on the same device, as well as classical computers. We hope that our proposal and the corresponding development of quantum algorithms based on it bring new insights on realization of practical quantum computers in future.

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arXiv2022

A Practical and Scalable Decoder for Topological Quantum Error Correction with Digital Annealer

Quantum error correction is one of the most important milestones for realization of large-scale quantum computation. To achieve this, it is essential not only to integrate a large number of qubits with high fidelity, but also to build a scalable classical system that can perform error correction. Here, we propose an efficient and scalable decoder for quantum error correction using Fujitsu Digital Annealer (DA). Specifically, the error correction problem of stabilizer codes is mapped into an Ising-type optimization problem, so-called quadratic unconstrained binary optimization (QUBO) problem, which is solved by DA. In particular, we implement the proposed DA decoder for the surface code and perform detailed numerical experiments for various code distances to see its performance and scalability. We observe that computational scaling for the DA decoder has a lower order of polynomial than the decoding methods using simulated annealing (SA) and minimum-weight perfect matching (MWPM) algorithm under all tested conditions. It is also shown that the DA decoder has advantages over the Union-Find (UF) decoder from a variety of perspectives including hardware implementation. Furthermore, the threshold behavior of the logical error probability for the DA decoder is analyzed and the resultant threshold lies between 9.4% and 9.8%, which is very close to that obtained by the MWPM decoder. This result clearly shows the high potential of the DA decoder for quantum error correction.

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arXiv2022

Pauli String Partitioning Algorithm with the Ising Model for Simultaneous Measurement

We propose an efficient algorithm for partitioning Pauli strings into subgroups, which can be simultaneously measured in a single quantum circuit. Our partitioning algorithm drastically reduces the total number of measurements in a variational quantum eigensolver for a quantum chemistry, one of the most promising applications of quantum computing. The algorithm is based on the Ising model optimization problem, which can be quickly solved using an Ising machine. We develop an algorithm that is applicable to problems with sizes larger than the maximum number of variables that an Ising machine can handle ($n_\text{bit}$) through its iterative use. The algorithm has much better time complexity and solution optimality than other algorithms such as Boppana--Halldórsson algorithm and Bron--Kerbosch algorithm, making it useful for the quick and effective reduction of the number of quantum circuits required for measuring the expectation values of multiple Pauli strings. We investigate the performance of the algorithm using the second-generation Digital Annealer, a high-performance Ising hardware, for up to $65,535$ Pauli strings using Hamiltonians of molecules and the full tomography of quantum states. We demonstrate that partitioning problems for quantum chemical calculations can be solved with a time complexity of $O(N)$ for $N\leq n_\text{bit}$ and $O(N^2)$ for $N>n_\text{bit}$ for the worst case, where $N$ denotes the number of candidate Pauli strings and $n_\text{bit}=8,192$ for the second-generation Digital Annealer used in this study. The reduction factor, which is the number of Pauli strings divided by the number of obtained partitions, can be $200$ at maximum.

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