arXiv subjects

Naoki Yamamoto

Publications and source records attributed to Naoki Yamamoto.

At least 19 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.

quant-ph↗

arXiv2026

Efficient Quantum Circuit Construction of Controlled Time-Evolution for Arbitrary Pauli-Sum Hamiltonians

Controlled time-evolution circuits select forward or backward Hamiltonian time evolution according to the state of an ancilla qubit. They are fundamental building blocks in quantum eigenvalue transformation of unitaries, Hamiltonian filtering, and related quantum algorithms. A direct realization adds ancilla control to the elementary gates of the time-evolution circuit and therefore increases the two-qubit gate count, compiled T depth and CX depth. We develop an efficient recursive algorithm that, for an arbitrary Pauli-sum Hamiltonian, partitions the input Pauli terms into groups and assigns to each group a sign-flip Pauli string that anti-commutes with the in-group terms, thereby removing ancilla control from the grouped time-evolution blocks. Numerical benchmarks on random Hamiltonians and structured spin Hamiltonians show reductions in compiled T depth and compiled CX depth. For a Kagome Hamiltonian with 24 spins under full connectivity, the proposed construction reduces the compiled T depth by 85.2% and the compiled CX depth by 68.9%, compared with a conventional implementation that decomposes the Hamiltonian into individual Pauli terms and implements the controlled time evolution of each term by directly adding the ancilla qubit to the corresponding Pauli-rotation circuit.

quant-ph↗

arXiv2026

Spin Hall effect and Berry curvature of gravitons from quantum field theory

Based on quantum field theory of linearized gravity, we formulate the Wigner function for right- and left-handed gravitons. By applying the Wigner transformation to the second-order metric perturbations in the graviton energy-momentum tensor obtained from the Einstein-Hilbert action, we demonstrate the emergence of the spin Hall effect of gravitons in curved spacetime. This effect originates from the Berry curvature of gravitons, which has opposite signs for right- and left-handed helicities, and leads to a helicity-dependent splitting of the graviton energy Hall current. The magnitude of this splitting is found to be exactly twice that of the corresponding spin Hall current for photons.

hep-th↗

arXiv2026

Quantum Metric and Nonlinear Hall Effect of Photons

Using the path-integral formalism, we show that photons possess a nontrivial quantum metric in momentum space. We derive the semiclassical action and equations of motion by taking into account the quantum metric. In media with a spatially varying refractive index $n(\mathbf{x})$, the quantum metric induces a shift in the trajectory of light at second order in derivatives of $n$, which may be regarded as a nonlinear Hall effect of light. The quantum metric also gives rise to corrections to gravitational lensing in curved spacetime at the nonlinear order in wavelength. This gravitational nonlinear Hall effect results from the interplay between the geometry of position space and that of momentum space.

hep-th↗

arXiv2026

Random Access Codes: Explicit Constructions, Optimality, and Classical-Quantum Gaps

A random access code (RAC) encodes an $L$-bit string into a $k$-bit message, $L>k$, so that any requested bit can be recovered with high probability; a quantum RAC (QRAC) uses $k$ qubits instead. We give a geometric characterization of optimal classical $(L,k)$-RACs under average and worst-case decoding criteria. The average criterion is reduced to choosing $2^k$ representatives in $\{0,1\}^L$, while the worst-case criterion is reduced to a minimax problem over $2^k$ points in $[0,1]^L$ with a distance-like objective. This framework proves optimality for several parameter families, with many optimal constructions arising from standard infinite families of binary linear codes. It also yields two explicit classical--quantum separations. First, for every $L>1$, we construct a $(L,1)$-QRAC whose average decoding success probability strictly exceeds the optimal classical value. Second, for the family $(2^k-1,k)$, we prove worst-case optimality of a classical RAC and construct a QRAC with strictly larger worst-case success probability. For the family $(L,L-1)$, the framework identifies a classical RAC that is average-case optimal and, under a stated conjecture, also worst-case optimal. The same viewpoint further recovers explicit $(L,L-1)$-QRACs attaining a previously conjectured upper-bound value.

quant-ph↗

arXiv2026

Generative Circuit Design for Quantum-Selected Configuration Interaction

Quantum-selected configuration interaction (QSCI) has emerged as a feasible approach for approximating electronic ground states on noisy quantum devices toward large-system demonstrations. In QSCI, Slater determinants are sampled from a quantum-prepared state, and the Hamiltonian is then diagonalized in the sampled subspace. To create a high-quality subspace under hardware constraints, the design of the state-preparation circuit is crucial. Here, we present a Generative Quantum Eigensolver (GQE)-based framework that optimizes ansatz structures using a Transformer policy trained on the QSCI subspace energy. We validate the framework on N2 in active spaces of up to 32 qubits. We found that the optimized circuits reach chemical precision with substantially lower gate counts than time-evolved circuits. Quantitatively, this corresponds to an average reduction of 98% in the required two-qubit gate count relative to the single-step first-order Trotterized approximation and 83% relative to the qDRIFT approximation. Furthermore, the resulting wavefunctions are competitive with heat-bath configuration interaction (HCI) in terms of compactness. In stretched-bond, strongly correlated regimes, they achieve chemical precision with subspaces that are 50% smaller than those required by HCI.

quant-ph↗

arXiv2026

Learning from imperfect quantum data via unsupervised domain adaptation with classical shadows

Learning from quantum data using classical machine learning models has emerged as a promising paradigm toward realizing quantum advantages. Despite extensive analyses on their performance, clean and fully labeled quantum data from the target domain are often unavailable in practical scenarios, forcing models to be trained on data collected under conditions that differ from those encountered at deployment. This mismatch highlights the need for new approaches beyond the common assumptions of prior work. In this work, we address this issue by employing an unsupervised domain adaptation framework for learning from imperfect quantum data. Specifically, by leveraging classical representations of quantum states obtained via classical shadows, we perform unsupervised domain adaptation entirely within a classical computational pipeline once measurements on the quantum states are executed. We numerically evaluate the framework on quantum phases of matter and entanglement classification tasks under realistic domain shifts. Across both tasks, our method outperforms source-only non-adaptive baselines and target-only unsupervised learning approaches, demonstrating the practical applicability of domain adaptation to realistic quantum data learning.

quant-ph↗

arXiv2026

Auger Spectroscopy via Generative Quantum Eigensolver: A Quantum Approach to Molecular Excitations

Auger electron spectroscopy, a way of characterizing electronic structure through core-level decay processes, is widely used in materials characterization; however direct calculation from molecular geometry requires accurate treatment of many excited states, posing a challenge for classical methods. We present a hybrid quantum-classical workflow for calculating Auger spectra that combines the generative quantum eigensolver (GQE) for ground-state preparation, the quantum self-consistent equation-of-motion method for excited-state calculations, and the one-centre approximation for Auger transition rates. GQE uses a GPT-2 model to generate quantum circuits for ground-state optimization, allowing our workflow to benefit from HPC parallelization and GPU-acceleration for favourable scaling with system size. We demonstrate the validity of our workflow by calculating the Auger spectrum of water with the STO-3G basis set and demonstrating qualitative and quantitative agreement with spectra obtained using completely classical full configuration interaction calculations, from the computational literature, and from the experimental literature. We also find that for water, substituting the variational quantum eigensolver (VQE) for GQE results in near-identical spectra, but that the ground state estimator generated by GQE contains about half the total gate count as that generated by VQE.

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↗

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.

quant-ph↗

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.

quant-ph↗

arXiv2025

Quantum spectroscopy of topological dynamics via a supersymmetric Hamiltonian

Topological data analysis (TDA) characterizes complex dynamics through global invariants, but classical computation becomes prohibitive for high-dimensional data. We reinterpret time-domain dynamics as the eigenvalue spectrum of a supersymmetric (SUSY) Hamiltonian and thereby estimate topological descriptors through quantum spectroscopy. While zero modes correspond to Betti numbers, we show that low-lying excited states quantify the stability of topological features. Using a Takens embedding of the Lorenz system together with a resource-efficient quantum phase estimation implemented on IBM quantum hardware, we observe that the spectral gap of the SUSY Laplacian tracks the persistence of homological structures. Notably, the minimum of this spectral gap coincides with the onset of chaos, whereas its reopening reflects the geometric maturation of the attractor. Validated on small complexes yet offering an exponential advantage over classical diagonalization (from $O(N^3)$ to $\mathrm{poly}(\log N)$), this framework suggests that quantum hardware can function as a spectrometer for data topologies beyond classical reach.

quant-ph↗

arXiv2025

Graph Rewriting Language as a Platform for Quantum Diagrammatic Calculi

Systematic discovery of optimization paths in quantum circuit simplification remains a challenge. Today, ZX-calculus, a computing model for quantum circuit transformation, is attracting attention for its highly abstract graph-based approach. Whereas existing tools such as PyZX and Quantomatic offer domain-specific support for quantum circuit optimization, visualization and theorem-proving, we present a complementary approach using LMNtal, a general-purpose hierarchical graph rewriting language, to establish a diagrammatic transformation and verification platform with model checking. Our methodology shows three advantages: (1) manipulation of ZX-diagrams through native graph transformation rules, enabling direct implementation of basic rules; (2) quantified pattern matching via QLMNtal extensions, greatly simplifying rule specification; and (3) interactive visualization and validation of optimization paths through state space exploration. Through case studies, we demonstrate how our framework helps understand optimization paths and design new algorithms and strategies. This suggests that the declarative language LMNtal and its toolchain could serve as a new platform to investigate quantum circuit transformation from a different perspective.

cs.PL↗

arXiv2025

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↗

arXiv2025

Vorticity-induced effects from Wess-Zumino-Witten terms

We study vorticity-induced effects arising from the Wess-Zumino-Witten terms for Nambu-Goldstone modes in chiral perturbation theory. We first provide an alternative derivation of the Wess-Zumino-Witten terms in the presence of external vector, axial-vector, and pseudoscalar fields using a derivative expansion of the fermion determinant. We then employ the previously found correspondence in which vorticity is treated as an axial-vector field coupled to Dirac fermions in flat spacetime. Using this, we derive vorticity-induced contributions for Nambu-Goldstone modes in the presence of electromagnetic fields at finite baryon and isospin chemical potentials, including a vorticity-induced current, a magnetic-field-induced angular momentum, and a vorticity-modified photon-pion coupling. We also briefly discuss the phenomenological implications of these vorticity-induced effects.

hep-ph↗

arXiv2025

Introducing Linear Implication Types to $\lambda_{GT}$ for Computing With Incomplete Graphs

Designing programming languages that enable intuitive and safe manipulation of data structures is a critical research challenge. Conventional destructive memory operations using pointers are complex and prone to errors. Existing type systems, such as affine types and shape types, address this problem towards safe manipulation of heaps and pointers, but design of high-level declarative languages that allow us to manipulate complex pointer data structures at a higher level of abstraction is largely an open problem. The $\lambda_{GT}$ language, a purely functional programming language that treats hypergraphs (hereafter referred to as graphs) as primary data structures, addresses some of these challenges. By abstracting data with shared references and cycles as graphs, it enables declarative operations through pattern matching and leverages its type system to guarantee safety of these operations. Nevertheless, the previously proposed type system of $\lambda_{GT}$ leaves two significant open challenges. First, the type system does not support \emph{incomplete graphs}, that is, graphs in which some elements are missing from the graphs of user-defined types. Second, the type system relies on dynamic type checking during pattern matching. This study addresses these two challenges by incorporating linear implication into the $\lambda_{GT}$ type system, while introducing new constraints to ensure its soundness.

cs.PL↗

arXiv2025

Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer

Quantum-selected configuration interaction (QSCI) is an approach for quantum chemical calculations using current quantum computers. In conventional QSCI, Slater determinants used for the wave function expansion are sampled by iteratively performing approximate wave function preparation and subsequent measurement in the computational basis, and then the subspace Hamiltonian matrix is diagonalized on a classical computer. In this approach, preparation of a high-quality approximate wave function is necessary to accurately compute total energies. Here we propose a Hamiltonian simulation-based QSCI (HSB-QSCI) to avoid this difficulty, by sampling the Slater determinants from quantum states generated by the real-time evolution of approximate wave functions. We provide numerical simulations for the lowest spin-singlet and triplet states of oligoacenes (benzene, naphthalene, and anthracene), phenylene-1,4-dinitrene, and hexa-1,2,3,4,5-pentaene. We found that the HSB-QSCI is applicable not only to molecules where the Hartree--Fock provides a good approximation of the ground state, but also to strongly correlated systems where preparing a high-quality approximate wave function is hard. Hardware demonstrations of the HSB-QSCI are also reported for carbyne molecules expressed by up to 36 qubits, using an IBM Quantum processor. The HSB-QSCI captures more than 99.18\% of the correlation energies in the active space by considering about 1\% of all the Slater determinants in 36 qubit systems, illustrating the ability of the proposed method to efficiently consider important electronic configurations.

quant-ph↗

arXiv2025

The generative quantum eigensolver (GQE) and its application for ground state search

We introduce the generative quantum eigensolver (GQE), a new quantum computational framework that operates outside the variational quantum algorithm paradigm by applying classical generative models to quantum simulation. The GQE algorithm optimizes a classical generative model to produce quantum circuits with desired properties. Here, we develop a transformer-based implementation, which we name the generative pre-trained transformer-based (GPT) quantum eigensolver (GPT-QE). We show a proof-of-concept of training and pretraining of GPT-QE applied to electronic structure Hamiltonians, and demonstrate its ability illustrated by surpassing coupled cluster singles and doubles (CCSD) for the strong bond dissociation of the nitrogen molecule and approaching chemical accuracy. We also demonstrate the method on real quantum hardware.

quant-ph↗