arXiv subjects

Kosuke Mitarai

Publications and source records attributed to Kosuke Mitarai.

At least 19 recordsLinked to original sources

arXiv2026

QSCI-CMP: Quantum-Selected Configuration Interaction with Chemically Motivated Preselection

We present QSCI-CMP, a quantum-classical hybrid algorithm for molecular ground-state calculations that reduces both the query count and the gate count of sample-based quantum diagonalization with amplitude amplification (SQD-AA). SQD-AA mitigates the measurement bottleneck of quantum-selected configuration interaction (QSCI) by amplifying the basis states that have not yet been measured. Its oracle, however, specifies the measured states by listing them one by one, so its gate count grows with the number of collected states. Moreover, the quantum resources are spent even on states whose importance is evident from chemical knowledge, such as low-order excitations from the Hartree-Fock reference, which could be collected classically at the outset. We therefore propose to fix such chemically trivial states in advance, include them in the diagonalization subspace from the start, and exclude them from the amplification target, using a low-cost oracle that recognizes them through the excitation level and the seniority number of each basis state. We numerically demonstrate that QSCI-CMP reduces the query count and the gate count required to reach chemical accuracy by up to approximately 68% and 72% relative to SQD-AA for 24-qubit systems. The chemically trivial subspace is freely tunable within the classical computational budget. A larger subspace shifts more work onto the classical solver and increases the reduction in quantum cost, and when it captures the ground state sufficiently well, no quantum sampling is needed at all. We also point out that a query-optimal iteration count known from the analysis of quantum search further reduces the query count of both methods by approximately 12%.

quant-ph↗

arXiv2026

Quantum machine learning interatomic potential: Application of variational quantum algorithm

This study applied quantum circuit learning, a commonly used hybrid quantum-classical machine learning algorithm, to a machine learning interatomic potential (MLIP) for predicting the energies of molecules in molecular datasets. We retrained the ANI model using the quantum transfer learning architecture [Mari et al., Quantum, 4:340, 2020] and evaluated numerical accuracy with a quantum circuit simulator. The evaluation confirmed that inserting a quantum circuit into the classical neural network of the MLIP yielded slightly higher accuracy than the fully classical neural network under certain conditions. In particular, the model incorporating a quantum circuit was more effective when the pretraining model had room for improvement in accuracy. These findings may contribute to advancing the application of quantum machine learning for MLIPs.

quant-ph↗

arXiv2026

An LLM System for Autonomous Variational Quantum Circuit Design

The design of high performing quantum circuits remains largely dependent on human expertise. We introduce an autonomous agentic framework that employs large language models (LLMs) to conduct iterative quantum circuit designs under explicit design constraints. Our system integrates seven components: Exploration, Generation, Discussion, Validation, Storage, Evaluation, and Review. These components form a closed-loop workflow that combines web-based knowledge acquisition, literature-grounded critique, executable code generation, and experimental feedback. We evaluate the framework on two tasks: quantum feature map construction for quantum machine learning and ansatz generation for variational quantum eigensolver applications in quantum chemistry. In image classification benchmarks, the best generated feature map outperforms representative quantum feature maps and, when scaled to larger qubit counts, surpasses the classical radial basis function kernel. In molecular ground state estimation across seven molecules, the generated ansatz attains competitive accuracy with widely used chemically inspired and hardware-efficient constructions while satisfying the imposed scaling constraints. These results establish LLM driven agentic system as a viable paradigm for automated quantum circuit design and illustrate how AI systems can participate in iterative scientific optimization workflows across scientific domains.

quant-ph↗

arXiv2026

Evaluating higher-order product formulae for molecular ground-state energy estimation

We evaluate deterministic higher-order product formulae for molecular ground-state energy estimation. Motivated by recent fault-tolerant architectures in which non-Clifford operations may be generated more locally and cheaply than in conventional assumptions, we re-examine such formulae as practical candidates for quantum chemistry. Using one-dimensional hydrogen chains from $\mathrm{H}_2$ to $\mathrm{H}_{15}$ as benchmarks, we estimate both the total gate count and the depth of $R_Z$-rotation layers required to reach a target energy error. To make this comparison feasible at larger system sizes, we use a perturbative method to estimate the eigenvalue error induced by each product formula and thereby evaluate the cost of the corresponding phase-estimation procedure. Among the previously considered formulae, the eighth-order construction introduced by Morales et al. [M. E. S. Morales et al., "Greatly improved higher-order product formulae for quantum simulation," arXiv:2210.15817v2 (2024)] minimizes both cost metrics in the benchmark at a chemically relevant target error. We also find that increasing the formal order does not automatically reduce the total cost: near chemical accuracy, the tenth-order formula introduced in the same work can be less efficient than the eighth-order one. Motivated by this observation, we construct a new fourth-order formula; it achieves the lowest total gate count among the formulae considered for all H-chain instances near chemical accuracy and over much of the 0.1-10 mHa target-error window for most instances, while also reducing the $R_Z$-layer depth. These results clarify how deterministic higher-order product formulae should be selected for molecular ground-state energy estimation.

quant-ph↗

arXiv2026

Efficient equivalence checking of Clifford-U circuits with shared single-qubit unitaries

Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit depth, or are restricted to specific circuit structures. In this work, we present an equivalence-checking method for circuits formed by arbitrary single-qubit layers interleaved with Clifford layers. This pattern is common in variational quantum algorithms and Hamiltonian simulation via Trotter decomposition. It can also represent any unitary with sufficient depth. We prove the existence of an efficient classical algorithm that determines whether a pair of circuits with shared single-qubit layers are equivalent for every possible choice of the shared single-qubit unitaries. The same algorithm can also certify their non-equivalence for fixed assignments of single-qubit unitaries. Our framework supports the validation of emerging quantum compilers and facilitate the discovery of novel circuit optimization passes.

quant-ph↗

arXiv2026

Fisher information based lower bounds on the cost of quantum phase estimation

Quantum phase estimation (QPE) is a cornerstone of quantum algorithms designed to estimate the eigenvalues of a unitary operator. QPE is typically implemented through two paradigms with distinct circuit structures: quantum Fourier transform-based QPE (QFT-QPE) and Hadamard test-based QPE (HT-QPE). Existing performance assessments fail to separate the statistical information inherent in the quantum circuit from the efficiency of classical post-processing, thereby obscuring the limits intrinsic to the circuit structure itself. In this study, we employ Fisher information and the Cramer-Rao lower bound to formulate the performance limits of circuit designs independent of the efficiency of classical post-processing. Defining the circuit depth as $T$ and the total runtime as $t_{\rm total}$, our results demonstrate that the achievable scaling is constrained by a non-trivial lower bound on their product $T\,t_{\rm total}$, although previous studies have typically treated the circuit depth $T$ and the total runtime $t_{\rm total}$ as separate resources. Notably, QFT-QPE possesses a more favorable scaling with respect to the overlap between the input state and the target eigenstate corresponding to the desired eigenvalue than HT-QPE. Numerical simulations confirm these theoretical findings, demonstrating a clear performance crossover between the two paradigms depending on the overlap. Furthermore, we verify that practical algorithms, specifically the quantum multiple eigenvalue Gaussian filtered search (QMEGS) and curve-fitted QPE, achieve performance levels closely approaching our derived limits. By elucidating the performance limits inherent in quantum circuit structures, this work concludes that the optimal choice of circuit configuration depends significantly on the overlap.

quant-ph↗

arXiv2026

Low-Resource Quantum Energy Gap Estimation via Randomization

Estimating the energy spectra of quantum many-body systems is a fundamental task in quantum physics, with applications ranging from chemistry to condensed matter. Algorithmic shadow spectroscopy is a recent method that leverages randomized measurements on time-evolved quantum states to extract spectral information. However, implementing accurate time evolution with low-depth circuits remains a key challenge for near-term quantum hardware. In this work, we propose a hybrid quantum-classical protocol that integrates Time Evolution via Probabilistic Angle Interpolation (TE-PAI) into the shadow spectroscopy framework. TE-PAI enables the simulation of time evolution using shallow stochastic circuits while preserving unbiased estimates through quasiprobability sampling. We construct the combined estimator and derive its theoretical properties. Through numerical simulations, we demonstrate that our method accurately resolves energy gaps and exhibits enhanced robustness to gate noise compared to standard Trotter-based shadow spectroscopy. We further validate the protocol experimentally on up to 20 qubits using IBM quantum hardware. This makes TE-PAI shadow spectroscopy a promising tool for spectral analysis on noisy intermediate-scale quantum (NISQ) devices.

quant-ph↗

arXiv2025

Quasi-Monte Carlo Method for Linear Combination Unitaries via Classical Post-Processing

We propose the quasi-Monte Carlo method for linear combination of unitaries via classical post-processing (LCU-CPP) on quantum applications. The LCU-CPP framework has been proposed as an approach to reduce hardware resources, expressing a general target operator $F(A)$ as $F(A) = \int_V f(t) G(A, t)dt$, where each $G(A, t)$ is proportional to a unitary operator. On a quantum device, $Re[Tr(G(A, t)\rho)]$ can be estimated using the Hadamard test and then combined through classical integration, allowing for the realization of nonunitary functions with reduced circuit depth. While previous studies have employed the Monte Carlo method or the trapezoid rule to evaluate the integral in LCU-CPP, we show that the quasi-Monte Carlo method can achieve even lower errors. In two numerical experiments, ground state property estimation and Green's function estimation, the quasi-Monte Carlo method achieves the lowest errors with a number of Hadamard test shots per unitary that is practical for real hardware implementations. These results indicate that quasi-Monte Carlo is an effective integration strategy within the LCU-CPP framework.

quant-ph↗

arXiv2025

Learning functions of Hamiltonians with Hamiltonian Fourier features

We propose a quantum machine learning task that is provably easy for quantum computers and arguably hard for classical ones. The task involves predicting quantities of the form $\mathrm{Tr}[f(H)\rho]$, where $f$ is an unknown function, given descriptions of $H$ and $\rho$. Using a Fourier-based feature map of Hamiltonians and linear regression, we theoretically establish the learnability of the task and implement it on a superconducting device using up to 40 qubits. This work provides a machine learning task with practical relevance, provable quantum easiness, and near-term feasibility.

quant-ph↗

arXiv2025

Automating quantum feature map design via large language models

Quantum feature maps are a key component of quantum machine learning, encoding classical data into quantum states to exploit the expressive power of high-dimensional Hilbert spaces. Despite their theoretical promise, designing quantum feature maps that offer practical advantages over classical methods remains an open challenge. In this work, we propose an agentic system that autonomously generates, evaluates, and refines quantum feature maps using large language models. The system consists of five components: Generation, Storage, Validation, Evaluation, and Review. Using these components, it iteratively improves quantum feature maps. Through numerical evaluations on widely used benchmark datasets, the system discovers and improves quantum feature maps without human intervention. On MNIST, the best generated feature map achieves 97.3% classification accuracy, outperforming existing quantum feature maps and achieving competitive performance with classical kernels, remaining within 0.3 percentage points of the radial basis function kernel. Similar improvements are observed on Fashion-MNIST and CIFAR-10. These results demonstrate that LLM-driven closed-loop discovery can autonomously explore dataset-adaptive quantum features. More broadly, our approach provides a practical methodology for automated discovery in quantum circuit design, helping bridge the gap between theoretical QML models and their empirical performance on real-world machine learning tasks.

quant-ph↗

arXiv2024

Quantum expectation value estimation by doubling the number of qubits

Expectation value estimation is ubiquitous in quantum algorithms. The expectation value of a Hamiltonian, which is essential in various practical applications, is often estimated by measuring a large number of Pauli strings on quantum computers and performing classical post-processing. In the case of $n$-qubit molecular Hamiltonians in quantum chemistry calculations, it is necessary to evaluate $O(n^4)$ Pauli strings, requiring a large number of measurements for accurate estimation. To reduce the measurement cost, we assess an existing idea that uses two copies of an $n$-qubit quantum state of interest and coherently measures them in the Bell basis, which enables the simultaneous estimation of the absolute values of expectation values of all the $n$-qubit Pauli strings. We numerically investigate the efficiency of energy estimation for molecular Hamiltonians of up to 12 qubits. The results show that, when the target precision is no smaller than tens of milli-Hartree, this method requires fewer measurements than conventional sampling methods. This suggests that the method may be useful for many applications that rely on expectation value estimation of Hamiltonians and other observables as well when moderate precision is sufficient.

quant-ph↗

arXiv2024

Efficient state preparation for multivariate Monte Carlo simulation

Quantum state preparation is a task to prepare a state with a specific function encoded in the amplitude, which is an essential subroutine in many quantum algorithms. In this paper, we focus on multivariate state preparation, as it is an important extension for many application areas. Specifically in finance, multivariate state preparation is required for multivariate Monte Carlo simulation, which is used for important numerical tasks such as risk aggregation and multi-asset derivative pricing. Using existing methods, multivariate quantum state preparation requires the number of gates exponential in the number of variables $D$. For this task, we propose a quantum algorithm that only requires the number of gates linear in $D$. Our algorithm utilizes multivariable quantum signal processing (M-QSP), a technique to perform the multivariate polynomial transformation of matrix elements. Using easily prepared block-encodings corresponding to each variable, we apply the M-QSP to construct the target function. In this way, our algorithm prepares the target state efficiently for functions achievable with M-QSP.

quant-ph↗

arXiv2024

Explicit quantum surrogates for quantum kernel models

Quantum machine learning (QML) leverages quantum states for data encoding, with key approaches being explicit models that use parameterized quantum circuits and implicit models that use quantum kernels. Implicit models often have lower training errors but face issues such as overfitting and high prediction costs, while explicit models can struggle with complex training and barren plateaus. We propose a quantum-classical hybrid algorithm to create an explicit quantum surrogate (EQS) for trained implicit models. This involves diagonalizing an observable from the implicit model and constructing a corresponding quantum circuit using an extended automatic quantum circuit encoding algorithm. The EQS framework reduces prediction costs, provides a powerful strategy to mitigate barren plateau issues, and combines the strengths of both QML approaches.

quant-ph↗

arXiv2024

Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation

Combinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently a novel feedback-based quantum optimization algorithm has been proposed by Magann \textit{et al}. The method explicitly determines quantum circuit parameters by feeding back measurement results thus avoids classical parameter optimization that is known to cause significant trouble in quantum approximate optimization algorithm, the well-studied near-term algorithm. Meanwhile, a significant drawback of the feedback-based quantum optimization is that it requires deep circuits, rendering the method unsuitable to noisy quantum devices. In this study we propose a new feedback law for parameter determination by introducing the second-order approximation with respect to time interval, a hyperparameter in the feedback-based quantum optimization. This allows one to take larger time interval, leading to acceleration of convergence to solutions. In numerical simulations on the maximum cut problem we demonstrate that our proposal significantly reduces circuit depth, with its linear scaling with the problem size smaller by more than an order of magnitude. We expect that the new feedback law proposed in this work may pave the way for feedback-based quantum optimization with near-term noisy quantum computers.

quant-ph↗

arXiv2023

Quantum Kernel t-Distributed Stochastic Neighbor Embedding

Data visualization is important in understanding the characteristics of data that are difficult to see directly. It is used to visualize loss landscapes and optimization trajectories to analyze optimization performance. Popular optimization analysis is performed by visualizing a loss landscape around the reached local or global minimum using principal component analysis. However, this visualization depends on the variational parameters of a quantum circuit rather than quantum states, which makes it difficult to understand the mechanism of optimization process through the property of quantum states. Here, we propose a quantum data visualization method using quantum kernels, which enables us to offer fast and highly accurate visualization of quantum states. In our numerical experiments, we visualize hand-written digits dataset and apply $k$-nearest neighbor algorithm to the low-dimensional data to quantitatively evaluate our proposed method compared with a classical kernel method. As a result, our proposed method achieves comparable accuracy to the state-of-the-art classical kernel method, meaning that the proposed visualization method based on quantum machine learning does not degrade the separability of the input higher dimensional data. Furthermore, we visualize the optimization trajectories of finding the ground states of transverse field Ising model and successfully find the trajectory characteristics. Since quantum states are higher dimensional objects that can only be seen via observables, our visualization method, which inherits the similarity of quantum data, would be useful in understanding the behavior of quantum circuits and algorithms.

quant-ph↗

arXiv2023

Continuous optimization by quantum adaptive distribution search

In this paper, we introduce the quantum adaptive distribution search (QuADS), a quantum continuous optimization algorithm that integrates Grover adaptive search (GAS) with the covariance matrix adaptation - evolution strategy (CMA-ES), a classical technique for continuous optimization. QuADS utilizes the quantum-based search capabilities of GAS and enhances them with the principles of CMA-ES for more efficient optimization. It employs a multivariate normal distribution for the initial state of the quantum search and repeatedly updates it throughout the optimization process. Our numerical experiments show that QuADS outperforms both GAS and CMA-ES. This is achieved through adaptive refinement of the initial state distribution rather than consistently using a uniform state, resulting in fewer oracle calls. This study presents an important step toward exploiting the potential of quantum computing for continuous optimization.

quant-ph↗

arXiv2023

End-to-end complexity for simulating the Schwinger model on quantum computers

The Schwinger model is one of the simplest gauge theories. It is known that a topological term of the model leads to the infamous sign problem in the classical Monte Carlo method. In contrast to this, recently, quantum computing in Hamiltonian formalism has gained attention. In this work, we estimate the resources needed for quantum computers to compute physical quantities that are challenging to compute on classical computers. Specifically, we propose an efficient implementation of block-encoding of the Schwinger model Hamiltonian. Considering the structure of the Hamiltonian, this block-encoding with a normalization factor of $\mathcal{O}(N^3)$ can be implemented using $\mathcal{O}(N+\log^2(N/\varepsilon))$ T gates. As an end-to-end application, we compute the vacuum persistence amplitude. As a result, we found that for a system size $N=128$ and an additive error $\varepsilon=0.01$, with an evolution time $t$ and a lattice spacing a satisfying $t/2a=10$, the vacuum persistence amplitude can be calculated using about $10^{13}$ T gates. Our results provide insights into predictions about the performance of quantum computers in the FTQC and early FTQC era, clarifying the challenges in solving meaningful problems within a realistic timeframe.

quant-ph↗

arXiv2023

Quantum Circuit Unoptimization

Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so far. In this study, we define and construct a quantum algorithmic primitive called quantum circuit unoptimization, which makes a given quantum circuit complex by introducing some redundancies while preserving circuit equivalence, i.e., the inverse operation of circuit optimization. Using quantum circuit unoptimization, we propose the quantum circuit equivalence test, a decision problem contained both in the NP and BQP classes but is not trivially included in the P class. Furthermore, as a practical application, we construct concrete unoptimization recipes to generate compiler benchmarks and evaluate circuit optimization performance using Qiskit and Pytket. Our numerical simulations demonstrate that quantum circuit unoptimizer systematically generates redundant circuits that are challenging for compilers to optimize, which can be used to compare the performance of different compilers and improve them. We also offer potential applications of quantum circuit unoptimization, such as generating quantum advantageous machine learning datasets and quantum computer fidelity benchmarks.

quant-ph↗