arXiv subjects

Kazunori Maruyama

Publications and source records attributed to Kazunori Maruyama.

12 recordsLinked to original sources

arXiv2026

Mirror subspace diagonalization: A real-time quantum Krylov algorithm with near-optimal sampling cost

Quantum Krylov algorithms are a promising approach for ground-state energy estimation on near-term quantum computers. However, their sampling cost is inherently high because each Hamiltonian term is measured individually. Despite various mitigation techniques, this overhead remains a bottleneck for large-scale electronic structure problems. We introduce mirror subspace diagonalization (MSD), which approaches the theoretical lower bound on the sampling cost for quantum Krylov algorithms built upon real-time evolution. MSD uses a finite-difference formula to express the Hamiltonian as a linear combination of time-evolution unitaries with symmetrically shifted timesteps, enabling efficient estimation of the Hamiltonian matrix within the Krylov subspace. By optimizing the timestep and shifting the energy spectrum, finite-difference and statistical errors are minimized simultaneously, allowing MSD to attain the sampling-cost lower bound up to a logarithmic factor. We further apply classical post-processing to infer Hamiltonian moments, which mitigate the ground-state energy error via the Lanczos scheme. Our analysis shows MSD is particularly effective when the Hamiltonian's spectral norm is much smaller than its 1-norm, as in high-accuracy molecular simulations with large basis sets and strong electronic correlations. Numerical results for various molecular models show sampling-cost reductions of roughly 10 to 10,000 times over the conventional quantum Krylov algorithm.

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arXiv2026

Circuit growth and subspace read-out in quantum-selected configuration interaction: Separating the Hartree-Fock determinant

Predicting many molecular properties requires accurate ground-state energies of molecular Hamiltonians. Quantum-selected configuration interaction (QSCI) obtains such energies by measuring an input state to select important electronic configurations and classically diagonalizing the Hamiltonian in the subspace they span. ADAPT-QSCI, an adaptive extension of QSCI, improves the input state through iterative circuit growth. For single-reference molecules, the sampling distribution is dominated by the Hartree-Fock (HF) configuration, so most measurements reproduce a configuration already known. We reduce this redundancy by placing the HF configuration in the diagonalization subspace classically, before any measurement. This invalidates the operator-selection criterion of ADAPT-QSCI, and we derive a consistent replacement with energy and gradient in closed form, adding no query to the quantum device. At the per-iteration shot budgets previously used for ADAPT-QSCI, the proposed scheme reaches chemical accuracy with approximately $63\%$ and $43\%$ of the CNOT gates for $\mathrm{H}_4$ and $\mathrm{H}_6$, and $44\%$ and $40\%$ of the total shots. The advantage depends on the budget, however: in the infinite-shot limit the $\mathrm{H}_4$ CNOT count increases to $125\%$ of that of ADAPT-QSCI. These results identify the per-iteration shot budget as a key design variable governing resource savings in QSCI-based algorithms.

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arXiv2026

Implementation and verification of coherent error suppression using randomized compiling for Grover's algorithm on a trapped-ion device

In near-term quantum computations that do not employ fault tolerant error correction, noise can proliferate rapidly, corrupting the quantum state and making results unreliable. These errors originate from both decoherence and control imprecision and the latter can manifest as coherent error that is especially detrimental. In the pre-fault tolerant setting, previous work has shown that different error suppression methods have shown promising complementary advantages but highly variable performance under different algorithmic and error model conditions. Here, we evaluate the effectiveness of several error suppression methods under varying algorithmic settings, both theoretically with numerical simulations and experimentally on a trapped-ion quantum computer. For our case study, we explore a range of output states under Grover's algorithm quantum circuits containing up to 10 qubits and 28 two-qubit gates with varying output state features. We explore the complementary effectiveness of randomized compiling and algorithm error detection, where the latter is realized via post-selection on ancillary qubits that ideally return to the ground state at the end of each circuit. In all settings, combining randomized compiling and error detection yields the largest suppression of error, indicating that these methods are most effective when combined to extend the capabilities of near-term devices for moderately deep circuits. We demonstrate for the first time significant suppression of coherent error on a trapped-ion platform, and moreover achieve this outcome via cloud access. However our results highlight that the degree of error suppression depends sensitively on the nature of the error model and the algorithm instance.

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arXiv2026

Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition

We study the Hamiltonian algebra of qubit-mapped interacting fermion models and their fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such a model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that, under fermion-qubit mappings that map Majorana operators to single-term Pauli strings, the qubit models obtained from these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method.

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arXiv2026

Idling error suppression through gate scheduling

Achieving high-precision quantum computation requires effective suppression of idling errors that occur when qubits remain inactive during waiting periods within a quantum circuit. Conventional mitigation techniques, such as dynamical decoupling, suppress decoherence by periodically refreshing quantum states through the insertion of additional control gates. In this paper, we propose an alternative approach that suppresses idling errors through quantum circuit scheduling without introducing any additional gate operations. By appropriately adjusting the execution timing of quantum gates with scheduling flexibility, we demonstrate through both numerical simulations and hardware experiments that the overall computational accuracy can be significantly influenced and, in many cases, improved. In addition, we analytically derive the density-matrix evolution under idling noise and provide a theoretical framework that explains the observed behavior.

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arXiv2026

Enabling Chemically Accurate Quantum Phase Estimation in the Early Fault-Tolerant Regime

Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE) on fault-tolerant quantum computing (FTQC) devices. Existing resource estimates for typical FTQC architectures suggest that such calculations demand millions of physical qubits, thereby placing them beyond the reach of near-term devices. Here, we investigate the feasibility of performing QPE for chemically relevant molecular systems in an early-FTQC regime, characterized by partial fault tolerance, constrained qubit budgets, and limited circuit depth. Our framework is based on single-ancilla, Trotter-based QPE implementations combined with partially randomized time evolution. Within this framework, we develop a novel Hamiltonian optimization strategy, termed unitary weight concentration, that reduces algorithmic cost by reshaping linear-combination-of-unitaries representations. Applying this framework to active-space models of iron-sulfur clusters, cytochrome P450 active sites, and CO$_2$-utilization catalysts, we perform end-to-end resource estimation using the latest version of the space-time efficient analog rotation (STAR) architecture. Our results indicate that ground-state energy estimation for active spaces of approximately 20 to 50 spatial orbitals, well beyond the reach of classical full configuration interaction, is achievable using $\sim 10^5$ physical qubits, with runtimes on the order of days to weeks. These findings demonstrate that while full-fledged fault-tolerant quantum computers will be required for even larger molecular simulations, chemically meaningful quantum chemistry problems are already within reach in an experimentally relevant, early-FTQC regime.

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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

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

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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