arXiv subjects

Hiroyuki Harada

Publications and source records attributed to Hiroyuki Harada.

7 recordsLinked to original sources

arXiv2026

Adaptive identification of low-degree polynomials in quantum singular value transformation: application to nonlinear quantum properties estimation

Estimating properties of unknown quantum states via quantum singular value transformation (QSVT) often requires high-degree polynomials to handle small eigenvalues of density matrices. Specifically, the existing approaches determine the polynomial degree by relying on overly conservative worst-case bounds based on the minimum non-zero eigenvalue or the rank of the density matrices. In this work, we propose a spectral cutoff method that truncates the negligible eigenvalue tail depending on the task, the target accuracy, and the state, which enables the use of significantly lower-degree polynomials. To implement this, we develop a two-stage algorithm to estimate nonlinear properties, particularly von Neumann entropy and R{\'e}nyi entropy. In the first stage, we execute a search algorithm to identify the spectral cutoff directly from the unknown quantum state. In the second stage, we estimate the nonlinear properties utilizing QSVT with the degree of polynomial adaptively determined by the cutoff. This two-stage algorithm significantly improves the overall estimation cost compared to known bounds, even without knowing the minimum eigenvalue or the rank.

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arXiv2025

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits

Quantum circuit cutting and knitting are divide-and-conquer methods that enable large-scale quantum computations on hardware with limited qubit resources and connectivity by decomposing a target computation into smaller local experiments. Existing methods, however, typically incur a sampling overhead that grows exponentially with the number of cut locations, leaving open the question of whether this barrier is intrinsic. Here we show that this barrier is not universal by introducing a learning-based cutting protocol tailored to the target observable. At each cut, the protocol locally learns a Heisenberg-picture effective observable that captures the downstream information relevant to the final measurement and uses it to construct an observable-adaptive cut. This replaces the multiplicative variance amplification of conventional cutting with additive bias accumulation controlled by local learning accuracy. We apply this framework to finite tree-structured circuits. For any finite rooted tree with $K$ cut wires and cut-system dimension at most $d$, the protocol estimates the target expectation value within additive error $\epsilon$ with high probability using $\widetilde{O}(d^3K^3/\epsilon^2)$ measurements, including the local learning cost. Moreover, for two-layer trees with $R$ cut wires, we prove an information-theoretic exponential separation between our learning-based protocol and learning-free wire-cutting protocols based on pre-specified randomized cutting rules: even with arbitrary classical post-processing, any such learning-free protocol requires $\Omega((d+1)^R/\epsilon^2)$ measurements, whereas our protocol uses $\widetilde{O}(d^3R^3/\epsilon^2)$. These results identify local learning, rather than the tree structure alone, as the key mechanism driving the exponential-to-polynomial reduction in sampling overhead.

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arXiv2025

Trade-offs between Quantum and Classical Resources in the Linear Combination of Unitaries

The randomized linear combination of unitaries (LCU) method with many applications to early fault-tolerant quantum computing algorithms has been proposed. This quantum algorithm computes the same expectation values as the original, fully coherent LCU algorithm using a shallower quantum circuit with a single ancilla qubit, at the cost of a quadratically larger sampling overhead. In this work, we propose a quantum algorithm intermediate between the original and randomized LCU that manages the trade-off between the sampling overhead and circuit complexity. Our algorithm divides the set of unitary operators into several groups and then randomly samples LCU circuits from these groups to evaluate the target expectation value. Notably, we reveal that across all grouping strategies, the mechanism of the sampling overhead reduction can be solely characterized by a metric we call the reduction factor. Moreover, we analytically prove an underlying monotonicity of the reduction factor in the group size: larger group sizes entail smaller sampling overhead. Finally, our framework enables a more flexible algorithmic design by systematically yielding intermediate implementations of LCU-based algorithms; we provide intermediate implementations of non-Hermitian dynamics simulation, ground-state property estimation, and quantum error detection. Besides, we demonstrate this principle by deriving intermediate trade-off scaling in sample complexity and ancillary space for quantum linear system solver.

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arXiv2025

State-to-Hamiltonian conversion with a few copies

Density matrix exponentiation (DME) is a general procedure that converts an unknown quantum state into the Hamiltonian evolution. This enables state-dependent operations and can reveal nontrivial properties of the state, among other applications, without full tomography. However, it has been proven that for any physical process, the DME requires $\Theta(1/\varepsilon)$ state copies in error $\varepsilon$. In this work, we go beyond the lower bound and propose a procedure called the virtual DME that achieves $\mathcal{O}(\log(1/\varepsilon))$ or $\mathcal{O}(1)$ state copies, by using non-physical processes. Using the virtual DME in place of its conventional counterpart realizes a general-purpose quantum algorithm for property estimation, that achieves exponential circuit-depth reductions over existing protocols across tasks including quantum principal component analysis, quantum emulator, calculation of nonlinear functions such as entropy, and linear system solver with quantum precomputation. In such quantum algorithms, the non-physical process for virtual DME can be effectively simulated via simple classical post-processing while retaining a near-unity measurement overhead. We numerically verify this small constant overhead together with the exponential reduction of copy count in the quantum principal component analysis task. The number of state copies used in our algorithm essentially saturates the theoretical lower bound we proved.

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arXiv2023

Density matrix representation of hybrid tensor networks for noisy quantum devices

The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states.

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arXiv2023

Resource-efficient Generalized Quantum Subspace Expansion

Realizing practical quantum computing requires overcoming a number of computation errors and the limitation of device size, which have intensively been tackled by quantum error mitigation (QEM) these days. As a unified approach of noise-agnostic QEM, generalized quantum subspace expansion (GSE) has lately been proposed to be remarkably robust against stochastic and coherent errors, integrating quantum subspace expansion and virtual state purification. However, the requirement in GSE to perform entangled measurements between copies of the quantum states remains a significant drawback under the current situation of quantum devices with a restricted number of qubits and their connectivity. In this work, we propose ``Dual-GSE'', a resource-efficient implementation of GSE to circumvent this overhead by constructing an ansatz of error-mitigated quantum states via dual-state purification without state copies. Remarkably, the proposed method can further simulate larger quantum systems beyond the size of available quantum hardware, achieved by a suitable ansatz construction inspired by the divide-and-conquer strategy that classically reintroduces the effect of entanglement. While classically forging the entanglement comes with additional cost, the total sampling overhead can be notably reduced by reusing the same Pauli expectation values among divided-and-conquered subsystems. We comprehensively analyze the advantages and overhead of Dual-GSE and perform numerical simulations of the eight-qubit transverse-field Ising model under various setups. Our results demonstrate that Dual-GSE estimates the ground state energy with high accuracy under gate noise with low mitigation overhead and practical sampling cost.

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arXiv2023

Doubly optimal parallel wire cutting without ancilla qubits

A restriction in the quality and quantity of available qubits presents a substantial obstacle to the application of near-term and early fault-tolerant quantum computers in practical tasks. To confront this challenge, some techniques for effectively augmenting the system size through classical processing have been proposed; one promising approach is quantum circuit cutting. The main idea of quantum circuit cutting is to decompose an original circuit into smaller sub-circuits and combine outputs from these sub-circuits to recover the original output. Although this approach enables us to simulate larger quantum circuits beyond physically available circuits, it needs classical overheads quantified by the two metrics: the sampling overhead in the number of measurements to reconstruct the original output, and the number of channels in the decomposition. Thus, it is crucial to devise a decomposition method that minimizes both of these metrics, thereby reducing the overall execution time. This paper studies the problem of decomposing the parallel $n$-qubit identity channel, i.e., $n$-parallel wire cutting, into a set of local operations and classical communication; then we give an optimal wire-cutting method comprised of channels based on mutually unbiased bases, that achieves minimal overheads in both the sampling overhead and the number of channels, without ancilla qubits. This is in stark contrast to the existing method that achieves the optimal sampling overhead yet with ancilla qubits. Moreover, we derive a tight lower bound of the number of channels in parallel wire cutting without ancilla systems and show that only our method achieves this lower bound among the existing methods. Notably, our method shows an exponential improvement in the number of channels, compared to the aforementioned ancilla-assisted method that achieves optimal sampling overhead.

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