arXiv subjects

Jumpei Kato

Publications and source records attributed to Jumpei Kato.

6 recordsLinked to original sources

arXiv2026

Circuit Design based on Feature Similarity for Quantum Generative Modeling

Quantum generative models are among the most promising candidates for a practical application of near-term quantum devices. However, current approaches mostly rely on general-purpose circuits, such as the hardware efficient ansatz paired with a random initialization strategy, which are known to suffer from trainability issues such as barren plateaus. To address these issues, a tensor network pretraining framework that initializes a quantum circuit ansatz with a classically computed high-quality solution for a linear entanglement structure has been proposed in literature. In order to improve the classical solution, the quantum circuit needs to be extended, while it is still an open question how the extension affects trainability. In this work, we propose the metric-based extension heuristic to design an extended circuit based on a similarity metric measured between the dataset features. We evaluate this method on the bars and stripes dataset and carry out simulations on financial data. Our results provide an experimental basis for problem-informed circuit design and show that the metric-based extension heuristic offers the means to introduce inductive bias while designing a circuit under limited resources.

quant-ph↗

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{é}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.

quant-ph↗

arXiv2026

Explicit block-encoding for partial differential equation-constrained optimization

Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally demanding because it requires repeatedly solving a PDE and using its solution within an optimization process. In this paper, we first propose a fully coherent quantum algorithm for solving PDE-constrained optimization problems. The proposed method combines a quantum PDE solver that prepares the solution vector as a quantum state, and a quantum optimizer that assumes oracle access to a quantized objective function. The central idea is the explicit construction of the oracle in a form of block-encoding for the objective function, which coherently uses the output of a quantum PDE solver. This enables us to avoid classical access to the full solution that requires quantum state tomography canceling out the potential quantum speedups. We also derive the overall computational complexity of the proposed method with respect to parameters for optimization and PDE simulation, where quantum speedup is inherited from the underlying quantum PDE solver. We numerically demonstrate the validity of the proposed method by applications, including a parameter calibration problem in the Black-Scholes equation and a material parameter design problem in the wave equation. This work presents the concept of composing quantum subroutines so that the weakness of one (i.e., prohibitive readout overhead) is neutralized by the strength of another (i.e., coherent oracle access), toward a bottleneck-free quantum algorithm.

quant-ph↗

arXiv2026

Tensor-based phase difference estimation on time series analysis

We propose a phase-difference estimation algorithm based on the tensor-network circuit compression, leveraging time-evolution data to pursue scalability and higher accuracy on a quantum phase estimation (QPE)-type algorithm. Using tensor networks, we construct circuits composed solely of nearest-neighbor gates and extract time-evolution data by four-type circuit measurements. In addition, to enhance the accuracy of time-evolution and state-preparation circuits, we propose techniques based on algorithmic error mitigation and on iterative circuit optimization combined with merging into matrix product states, respectively. Verifications using a noiseless simulator for the 8-qubit one-dimensional Hubbard model using an ancilla qubit show that the proposed algorithm achieves accuracies with 0.4--4.7\% error from a true energy gap on an appropriate time-step size, and that accuracy improvements due to the algorithmic error mitigation are observed. We also confirm the enhancement of the overlap with matrix product states through iterative optimization. Finally, the proposed algorithm is demonstrated on IBM Heron devices with Q-CTRL error suppression for 8-, 36-, and 52-qubit models using more than 4,000 2-qubit gates. These largest-scale demonstrations for the QPE-type algorithm represent significant progress not only toward practical applications of near-term quantum computing but also toward preparation for the era of error-corrected quantum devices.

quant-ph↗

arXiv2026

Exponentially accurate open quantum simulation via randomized dissipation with minimal ancilla

Simulating open quantum systems is an essential technique for understanding complex physical phenomena and advancing quantum technologies. Some quantum algorithms simulate Lindblad dynamics exponentially accurately, i.e., they achieve logarithmically short circuit depth in terms of accuracy, but they need to coherently encode all possible jump operators with a large ancilla consumption. Minimizing the gate and ancilla counts while achieving such a logarithmic scaling in accuracy remains an important challenge. In this work, we present two randomized quantum algorithms for simulating general Lindblad dynamics with multiple jump operators aimed at an observable estimation that achieve a circuit depth with not only logarithmic scaling in accuracy but also either partial or complete independence from the parameters specifying the Lindbladian. This is based on a novel random circuit compilation method that leverages dissipative processes with only a single jump operator, leading to the proposed methods using minimal ancilla qubits -- $4+\lceil\log_2 M\rceil$ in the first case and $7$ in the other, where each single jump operator has at most $M$ Pauli strings. In addition, we numerically demonstrate the practical advantage over existing approaches by providing a detailed analysis of the required gate and ancilla counts. This work represents a significant step towards making open quantum system simulations more feasible on early fault-tolerant quantum computing devices.

quant-ph↗

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 $Θ(1/\varepsilon)$ 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.

quant-ph↗