arXiv subjects

Lento Nagano

Publications and source records attributed to Lento Nagano.

14 recordsLinked to original sources

arXiv2026

Arbitrary-Distance Quantum Error Correction with Gauss's Law for $\mathbb Z_2$ Lattice Gauge Theory

It has previously been shown by Rajput, Roggero, and Wiebe that $\mathbb Z_2$ Gauss's law constraints can be used to build efficient quantum error-correcting codes (QECCs) that are robust against arbitrary single-qubit errors. In this work, we generalize the construction to be robust against arbitrary $t$-qubit errors, where $t$ is any positive integer. This includes a derivation of the optimal Gauss's law code within the considered family by minimizing the number of physical qubits required for a given code distance. Finally, we compare our codes against other efficient QECCs on metrics such as the number of physical qubits, the locality of the encoded Hamiltonian, and the logical error rate in the code capacity setting. Compared to using a domain-agnostic code for every lattice degree of freedom, we find that the Gauss's law code primarily excels at reducing the locality of the encoded Hamiltonian. Moreover, the physical qubit overhead is also reduced for $t \le 3$ (distance $d \le 7$).

hep-lat↗

arXiv2026

Symmetries and overparametrization properties of Hamiltonian variational ansatzes for the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory

We perform detailed studies of five Hamiltonian variational ansatzes (HVA) based on the Hamiltonian of the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory. The ansatzes are designed to respect local and global symmetries of the original Hamiltonian and therefore act on a finely segmented state Hilbert space. Following Larocca et al. (2023), we numerically study the dimension of the dynamical Lie algebra (DLA) and the rank of the quantum Fisher information matrix (QFIM) of the ansatzes within specific invariant subspaces. The ansatzes all involve sums of weight-three Paulis in their generators, which is a feature that have so far been underexplored in this context. We also perform numerical experiments to determine the ground state energy of the original Hamiltonian via variational quantum eigensolver (VQE), and observe that overparametrization of the ansatzes coincides with the apparent disappearance of local minima in the loss function, in line with the finding in the reference. Finally, the decay rate of the VQE loss function under gradient descent optimization is revealed to scale linearly with the number of parameters in the ansatz. These results help to enrich the theory of overparameterization of quantum circuits and inform the design of scalable variational ansatzes.

quant-ph↗

arXiv2026

Ground state preparation in $(2+1)$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory via deterministic quantum imaginary time evolution

In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a $2+1$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. We first construct the set of Pauli operators commuting with Gauss's law constraints, generalizing a previous result. This makes the deterministic QITE gauge-invariant and reduces both the measurement and gate costs significantly without adding extra algorithm errors in the QITE. Then, the classical numerical simulation of the deterministic QITE using tensor networks is performed, and the results are compared with the density matrix renormalization group (DMRG) to evaluate the accuracy of the algorithm. Specifically, we investigate the coupling and system size dependence, and find that the deterministic QITE can achieve a relative error of less than $0.1\%$ up to a twelve-plaquette system and coupling values in a regime that we study. Furthermore, the error dependence on the number of time steps is studied and discussed.

hep-lat↗

arXiv2026

Double Descent in Quantum Kernel Ridge Regression

Various classical machine learning models, including linear regression, kernel methods, and deep neural networks, exhibit double descent, in which the test risk peaks near the interpolation threshold and then decreases in the overparameterized regime. However, this phenomenon has received less attention in the quantum setting. In this work, we investigate the double descent phenomenon in quantum kernel ridge regression (QKRR). By applying deterministic equivalents from random matrix theory (RMT), we derive an asymptotic expression for the test risk of QKRR in the high-dimensional limit. Our analysis rigorously characterizes the interpolation peak and reveals how explicit regularization can effectively suppress it. We corroborate our theoretical results with numerical simulations, demonstrating close agreement even for finite-size quantum systems.

quant-ph↗

arXiv2026

Comprehensive Numerical Studies of Barren Plateau and Overparametrization in Variational Quantum Algorithm

The variational quantum algorithm (VQA) with a parametrized quantum circuit is widely applicable to near-term quantum computing, but its fundamental issues that limit optimization performance have been reported in the literature. For example, VQA optimization often suffers from vanishing gradients called barren plateau (BP) and the presence of local minima in the landscape of the cost function. Numerical studies have shown that the trap in local minima is significantly reduced when the circuit is overparametrized (OP), where the number of parameters exceeds a certain threshold. Theoretical understanding of the BP and OP phenomena has advanced over the past years, however, comprehensive studies of both effects in the same setting are not fully covered in the literature. In this paper, we perform a comprehensive numerical study in VQA, quantitatively evaluating the impacts of BP and OP and their interplay on the optimization of a variational quantum circuit, using concrete implementations of one-dimensional transverse and longitudinal field quantum Ising model. The numerical results are compared with the theoretical diagnostics of BP and OP phenomena. The framework presented in this paper will provide a guiding principle for designing VQA algorithms and ansatzes with theoretical support for behaviors of parameter optimization in practical settings.

quant-ph↗

arXiv2024

Quantum convolutional neural networks for jet images classification

Recently, interest in quantum computing has significantly increased, driven by its potential advantages over classical techniques. Quantum machine learning (QML) exemplifies one of the important quantum computing applications that are expected to surpass classical machine learning in a wide range of instances. This paper addresses the performance of QML in the context of high-energy physics (HEP). As an example, we focus on the top-quark tagging, for which classical convolutional neural networks (CNNs) have been effective but fall short in accuracy when dealing with highly energetic jet images. In this paper, we use a quantum convolutional neural network (QCNN) for this task and compare its performance with CNN using a classical noiseless simulator. We compare various setups for the QCNN, varying the convolutional circuit, type of encoding, loss function, and batch sizes. For every quantum setup, we design a similar setup to the corresponding classical model for a fair comparison. Our results indicate that QCNN with proper setups tend to perform better than their CNN counterparts, particularly when the convolution block has a lower number of parameters. For the higher parameter regime, the QCNN circuit was adjusted according to the dimensional expressivity analysis (DEA) to lower the parameter count while preserving its optimal structure. The DEA circuit demonstrated improved results over the comparable classical CNN model.

quant-ph↗

arXiv2024

Enforcing exact permutation and rotational symmetries in the application of quantum neural network on point cloud datasets

Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits. A crucial milestone in this area is the realization of $S_{n}$-permutation equivariant quantum neural networks (QNN) that are equivariant under permutations of input objects. In this work, we focus on encoding the rotational symmetry of point cloud datasets into the QNN. The key insight of the approach is that all rotationally invariant functions with vector inputs are equivalent to a function with inputs of vector inner products. We provide a novel structure of QNN that is exactly invariant to both rotations and permutations, with its efficacy demonstrated numerically in the problems of two-dimensional image classifications and identifying high-energy particle decays, produced by proton-proton collisions, with the $SO(1,3)$ Lorentz symmetry.

quant-ph↗

arXiv2023

Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group

Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage, namely a significant (in some cases exponential) speed-up of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models which are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this roadmap paper, led by CERN, DESY and IBM, we provide the status of high-energy physics quantum computations and give examples for theoretical and experimental target benchmark applications, which can be addressed in the near future. Having the IBM 100 x 100 challenge in mind, where possible, we also provide resource estimates for the examples given using error mitigated quantum computing.

quant-ph↗

arXiv2023

Quantum data learning for quantum simulations in high-energy physics

Quantum machine learning with parametrised quantum circuits has attracted significant attention over the past years as an early application for the era of noisy quantum processors. However, the possibility of achieving concrete advantages over classical counterparts in practical learning tasks is yet to be demonstrated. A promising avenue to explore potential advantages is the learning of data generated by quantum mechanical systems and presented in an inherently quantum mechanical form. In this article, we explore the applicability of quantum-data learning to practical problems in high-energy physics, aiming to identify domain specific use-cases where quantum models can be employed. We consider quantum states governed by one-dimensional lattice gauge theories and a phenomenological quantum field theory in particle physics, generated by digital quantum simulations or variational methods to approximate target states. We make use of an ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states in the Schwinger model, (de)confinement phases from time-evolved states in the $\mathbb{Z}_2$ gauge theory, and that it can extract fermion flavor/coupling constants in a quantum simulation of parton shower. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.

quant-ph↗

arXiv2023

Quench dynamics of the Schwinger model via variational quantum algorithms

We investigate the real-time dynamics of the $(1+1)$-dimensional U(1) gauge theory known as the Schwinger model via variational quantum algorithms. Specifically, we simulate quench dynamics in the presence of an external electric field. First, we use a variational quantum eigensolver to obtain the ground state of the system in the absence of an external field. With this as the initial state, we perform real-time evolution under an external field via a fixed-depth, parameterized circuit whose parameters are updated using McLachlan's variational principle. We use the same Ansatz for initial state preparation and time evolution, by which we are able to reduce the overall circuit depth. We test our method with a classical simulator and confirm that the results agree well with exact diagonalization.

hep-ph↗

arXiv2022

Resolution enhancement of one-dimensional molecular wavefunctions in plane-wave basis via quantum machine learning

Super-resolution is a machine-learning technique in image processing which generates high-resolution images from low-resolution images. Inspired by this approach, we perform a numerical experiment of quantum machine learning, which takes low-resolution (low plane-wave energy cutoff) one-particle molecular wavefunctions in plane-wave basis as input and generates high-resolution (high plane-wave energy cutoff) wavefunctions in fictitious one-dimensional systems, and study the performance of different learning models. We show that the trained models can generate wavefunctions having higher fidelity values with respect to the ground-truth wavefunctions than a simple linear interpolation, and the results can be improved both qualitatively and quantitatively by including data-dependent information in the ansatz. On the other hand, the accuracy of the current approach deteriorates for wavefunctions calculated in electronic configurations not included in the training dataset. We also discuss the generalization of this approach to many-body electron wavefunctions.

quant-ph↗

arXiv2022

Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term

We perform digital quantum simulation, using a classical simulator, to study screening and confinement in a gauge theory with a topological term, focusing on ($1+1$)-dimensional quantum electrodynamics (Schwinger model) with a theta term. We compute the ground state energy in the presence of probe charges to estimate the potential between them, via adiabatic state preparation. We compare our simulation results and analytical predictions for a finite volume, finding good agreements. In particular our result in the massive case shows a linear behavior for non-integer charges and a non-linear behavior for integer charges, consistently with the expected confinement (screening) behavior for non-integer (integer) charges.

hep-lat↗

arXiv2021

A Note on Commutation Relation in Conformal Field Theory

In this note, we explicitly compute the vacuum expectation value of the commutator of scalar fields in a d-dimensional conformal field theory on the cylinder. We find from explicit calculations that we need smearing not only in space but also in time to have finite commutators except for those of free scalar operators. Thus the equal time commutators of the scalar fields are not well-defined for a non-free conformal field theory, even if which is defined from the Lagrangian. We also have the commutator for a conformal field theory on Minkowski space, instead of the cylinder, by taking the small distance limit. For the conformal field theory on Minkowski space, the above statements are also applied.

hep-th↗

arXiv2020

Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories

We study the entropy associated with the Janus interface in a 4$d$ $\mathcal{N}=2$ superconformal field theory. With the entropy defined as the interface contribution to an entanglement entropy we show, under mild assumptions, that the Janus interface entropy is proportional to the geometric quantity called Calabi's diastasis on the space of $\mathcal{N}=2$ marginal couplings, confirming an earlier conjecture by two of the authors and generalizing a similar result in two dimensions. Our method is based on a CFT consideration that makes use of the Casini-Huerta-Myers conformal map from the flat space to the round sphere.

hep-th↗