arXiv subjects

Masanori Hanada

Publications and source records attributed to Masanori Hanada.

At least 19 recordsLinked to original sources

arXiv2026

Comments on "Ether of Orbifolds"

We comment on a recent manuscript "Ether of Orbifolds" by Henry Lamm. In the first version, it was mistakenly claimed that the orbifold lattice Hamiltonian is not gauge invariant, and a quantity $ε_g$, which has nothing to do with a non-existent "gauge violation", was introduced. The scaling of this $ε_g$ was used to claim a huge simulation cost. In fact, $ε_g$ characterizes the shift of the effective lattice spacing -- because, in the orbifold lattice formulation, the lattice is generated dynamically from the vacuum expectation value of the complex matrices. In the second version, the claim about the gauge symmetry was partially corrected, based on our comments. However, $ε_g$ is still mistakenly interpreted as a measure of "departure from SU($N$)", inconsistently with the foundational results by Kaplan, Katz, and Ünsal, and also by Arkani-Hamed, Cohen, and Georgi. This interpretation plays a central role in sustaining the argument introduced in the first version.

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arXiv2026

A minimal implementation of Yang-Mills theory on a digital quantum computer

We present a minimal implementation of SU($N$) pure Yang-Mills theory in $3+1$ dimensions for digital quantum simulation, designed to enable quantum advantage. Building on the orbifold lattice simulation protocol with logarithmic scaling in the local Hilbert-space truncation, we introduce further simplified Hamiltonians. Furthermore, we test simple methods that improve the convergence to the infinite mass limit, thereby removing the requirement of a large scalar mass to obtain the Kogut-Susskind Hamiltonian. For the SU(2) theory, we can cut the resource requirement further by utilizing the embedding of $\mathrm{SU}(2)\cong\mathrm{S}^3$ into $\mathbb{R}^4$. Monte Carlo simulations of the Euclidean path integral were used to benchmark the accuracy of these new analytical improvements to the theory. These results provide further support for the noncompact-variable-based approach as a practical framework for quantum simulation of non-Abelian gauge theories.

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arXiv2026

Toward Quantum Simulation of SU(2) Gauge Theory using Non-Compact Variables

Simulating lattice gauge theories on quantum computers presents unique challenges that drive the development of novel theoretical frameworks. The orbifold lattice approach offers a scalable method for simulating SU($N$) gauge theories in arbitrary dimensions. In this work, we present three improvements: (i) two new simplified Hamiltonians, (ii) an encoding of the SU(2) theory with smaller number of qubits, and (iii) a reduction in the requirement for large scalar masses to reach the Kogut-Susskind limit, achieved via the inclusion of an additional term in the Hamiltonian. These advancements significantly reduce circuit depth and qubit requirements for quantum simulations. We benchmarked these improvements using Monte Carlo simulations of SU(2) in (2+1) dimensions. Preliminary results demonstrate the effectiveness of these developments and further validate the use of noncompact variables as a promising framework for scalable quantum simulations of gauge theories.

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arXiv2026

Gauge Symmetry in Quantum Simulation

Quantum simulation of non-Abelian gauge theories requires careful handling of gauge redundancy. We address this challenge by presenting universal principles for treating gauge symmetry that apply to any quantum simulation approach, clarifying that physical states need not be represented solely by gauge singlets. Both singlet and non-singlet representations are valid, with distinct practical trade-offs, which we elucidate using analogies to BRST quantization. We demonstrate these principles within a complete quantum simulation framework based on the orbifold lattice, which enables explicit and efficient circuit constructions relevant to real-world QCD. For singlet-based approaches, we introduce a Haar-averaging projection implemented via linear combinations of unitaries, and analyze its cost and truncation errors. We also introduce an efficient simulation protocol with an additional term to the Hamiltonian that eliminates non-singlet states from the low-energy spectrum. Beyond the singlet-approach, we show how non-singlet approaches can yield gauge-invariant observables through wave packets and string excitations. This non-singlet approach is proven to be both universal and efficient. Working in temporal gauge, we provide explicit mappings of lattice Yang-Mills dynamics to Pauli-string Hamiltonians suitable for Trotterization. Classical simulations of small systems validate convergence criteria and quantify truncation and Trotter errors, showing concrete resource estimates and scalable circuit recipes for SU$(N)$ gauge theories. Our framework provides both conceptual clarity and practical tools toward quantum advantage in simulating non-Abelian gauge theories.

quant-ph↗

arXiv2026

Two-local modifications of SYK model with quantum chaos

The Sachdev--Ye--Kitaev (SYK) model may provide us with a good starting point for the experimental study of quantum chaos and holography in the laboratory. Still, the four-local interaction of fermions makes quantum simulation challenging, and it would be good to search for simpler models that keep the essence. In this paper, we argue that the four-local interaction may not be important by introducing a few models that have two-local interactions. The first model is a generalization of the spin-SYK model, which is obtained by replacing the spin variables with SU($d$) generators. Simulations of this class of models might be straightforward on qudit-based quantum devices. We study the case of $d=3, 4, 5, 6$ numerically and observe quantum chaos already for two-local interactions in a wide energy range. We also introduce modifications of spin-SYK and SYK models that have similar structures to the SU($d$) model (e.g., $H=\sum_{p,q}J_{pq}χ_pχ_{p+1}χ_qχ_{q+1}$ instead of the original SYK Hamiltonian $H=\sum_{p,q,r,s}J_{pqrs}χ_pχ_qχ_rχ_{s}$), which shows strongly chaotic features although the interaction is essentially two-local. These models may be a good starting point for the quantum simulation of the original SYK model.

quant-ph↗

arXiv2025

A universal framework for the quantum simulation of Yang-Mills theory

We provide a universal framework for the quantum simulation of SU(N) Yang--Mills theories on fault-tolerant digital quantum computers adopting the orbifold lattice formulation. As warm-up examples, we also consider simple models, including scalar field theory and the Yang--Mills matrix model, to illustrate the universality of our formulation, which shows up in the fact that the truncated Hamiltonian can be expressed in the same simple form for any N, any dimension, and any lattice size, in stark contrast to the popular approach based on the Kogut--Susskind formulation. In all these cases, the truncated Hamiltonian can be programmed on a quantum computer using only standard tools well-established in the field of quantum computation. As a concrete application of this universal framework, we consider Hamiltonian time evolution by Suzuki--Trotter decomposition. This turns out to be a straightforward task due to the simplicity of the truncated Hamiltonian. We also provide a simple circuit structure that contains only CNOT and one-qubit gates, independent of the details of the theory investigated.

quant-ph↗

arXiv2025

Exponential improvement in quantum simulations of bosons

Hamiltonian quantum simulation of bosons on digital quantum computers requires truncating the Hilbert space to finite dimensions. The method of truncation and the choice of basis states can significantly impact the complexity of the quantum circuit required to simulate the system. For example, a truncation in the Fock basis where each boson is encoded with a register of $Q$ qubits, can result in an exponentially large number of Pauli strings required to decompose the truncated Hamiltonian. This, in turn, can lead to an exponential increase in $Q$ in the complexity of the quantum circuit. For lattice quantum field theories such as Yang-Mills theory and QCD, several Hamiltonian formulations and corresponding truncations have been put forward in recent years. There is no exponential increase in $Q$ when resorting to the orbifold lattice Hamiltonian, while we do not know how to remove the exponential complexity in $Q$ in the commonly used Kogut-Susskind Hamiltonian. Specifically, when using the orbifold lattice Hamiltonian, the continuum limit, or, in other words, the removal of the ultraviolet energy cutoff, is obtained with circuits whose resources scale like $Q$, while they scale like $\mathcal{O}(\exp(Q))$ for the Kogut-Susskind Hamiltonian: this can be seen as an exponential speed up in approaching the physical continuum limit for the orbifold lattice Hamiltonian formulation. We show that the universal framework, advocated by three of the authors (M.~H., S.~M., and E.~R.) and collaborators, provides a natural avenue to solve the exponential scaling of circuit complexity with $Q$, and it is the reason why using the orbifold lattice Hamiltonian is advantageous.

quant-ph↗

arXiv2025

New phases in QCD at finite temperature and chemical potential

Understanding the phases of quantum chromodynamics (QCD) at finite temperature and baryon density is crucial for describing matter in heavy-ion collisions and the interior of neutron stars. While the transition from the confined phase to the deconfined phase has been extensively studied at vanishing chemical potential, recent theoretical work suggests the existence of intermediate phases with partial deconfinement, where only a subset of the color degrees of freedom is deconfined. In this paper, we study the generalization of partial deconfinement in QCD in the Veneziano large-$N_{\rm c}$ limit ($N_{\rm f}/N_{\rm c}$ fixed) to finite baryon chemical potential. We find that the partially deconfined phase has finer structure, and hence that there are four phases in QCD at finite temperature and moderately large chemical potential: complete confinement, complete deconfinement, and two kinds of partial deconfinement. A key ingredient is the refined understanding of the meaning of the 'Gross-Witten-Wadia point', i.e., the opening of a gap in the distribution of Polyakov line phases: either string condensation or baryon condensation causes the GWW transition. As a by-product, we observe the emergence of the QCD critical point from the interplay between baryon condensation and partial deconfinement. While our approach is necessarily qualitative due to the fermion sign problem, it provides a unified theoretical framework for understanding the rich phase structure of dense QCD matter and offers new perspectives on the location and nature of the QCD critical point.

hep-th↗

arXiv2025

Variational Monte Carlo with Neural Network Quantum States for Yang-Mills Matrix Model

We apply the variational Monte Carlo method based on neural network quantum states, using a neural autoregressive flow architecture as our ansatz, to determine the ground state wave function of the bosonic SU($N$) Yang-Mills-type two-matrix model at strong coupling. Previous literature hinted at the inaccuracy of such an approach at strong coupling. In this work, the accuracy of the results is tested using lattice Monte Carlo simulations: we benchmark the expectation value of the energy of the ground state for system sizes $N$ that are beyond brute-force exact diagonalization methods. We observe that the variational method with neural network states reproduces the right ground state energy when the width of the network employed in this work is sufficiently large. We confirm that the correct result is obtained for $N=2$ and $3$, while obtaining a precise value for $N=4$ requires more resources than the amount available for this work.

hep-th↗

arXiv2025

Universal framework with exponential speedup for the quantum simulation of quantum field theories including QCD

We present a quantum simulation framework universally applicable to a wide class of quantum systems, including quantum field theories such as quantum chromodynamics (QCD). Specifically, we generalize an efficient quantum simulation protocol developed for bosonic theories in [Halimeh et al., arXiv:2411.13161] which, when applied to Yang-Mills theory, demonstrated an exponential resource advantage with respect to the truncation level of the bosonic modes, to systems with both bosons and fermions using the Jordan-Wigner transform and also the Verstraete-Cirac transform. We apply this framework to QCD using the orbifold lattice formulation and achieve an exponential speedup compared to previous proposals. As a by-product, exponential speedup is achieved in the quantum simulation of the Kogut-Susskind Hamiltonian, the latter being a special limit of the orbifold lattice Hamiltonian. In the case of Hamiltonian time evolution of a theory on an $L^d$ spatial lattice via Trotterization, one Trotter step can be realized using $\mathcal{O}(L^d)$ numbers of CNOT gates, Hadamard gates, phase gates, and one-qubit rotations. We show this analytically for any matter content and $\mathrm{SU}(N)$ gauge group with any $N$. Even when we use the Jordan-Wigner transform, we can utilize the cancellation of quantum gates to significantly simplify the quantum circuit. We also discuss a block encoding of the Hamiltonian as a linear combination of unitaries using the Verstraete-Cirac transform. Our protocols do not assume oracles, but rather present explicit constructions with rigorous resource estimations without a hidden cost, and are thus readily implementable on a quantum computer.

quant-ph↗

arXiv2025

Exponential speedup in quantum simulation of Kogut-Susskind Hamiltonian via orbifold lattice

We demonstrate that the orbifold lattice Hamiltonian -- an approach known for its efficiency in simulating SU($N$) Yang-Mills theory and QCD on digital quantum computers -- can reproduce the Kogut-Susskind Hamiltonian in a controlled limit. We show that it emerges naturally as the infinite scalar mass limit of the orbifold lattice formulation, even at finite lattice spacing. Our analysis provides both a general analytical framework applicable to SU($N$) gauge theories in arbitrary dimensions and specific numerical evidence for $(2+1)$-dimensional SU($N$) Yang-Mills theories ($N=2,3$). Using Euclidean path integral methods, we quantify the approach to this limit by comparing the standard Wilson action with the orbifold lattice action, matching lattice parameters, and systematically extrapolating results as the bare scalar mass approaches infinity. This reformulation resolves longstanding technical obstacles and offers a straightforward implementation protocol for digital quantum simulation of the Kogut-Susskind Hamiltonian with exponential speedup compared to classical methods and previously known quantum methods, modulo standard assumptions made also for the original Kogut-Susskind approach. We emphasize that the present work establishes this equivalence using classical Euclidean Monte Carlo; the exponential speedup itself is a property of quantum simulation of the orbifold Hamiltonian established in earlier work, which the equivalence shown here lets one inherit for the Kogut-Susskind Hamiltonian.

quant-ph↗

arXiv2025

Toward QCD on Quantum Computer: Orbifold Lattice Approach

We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in the coordinate basis. We show that SU(3) gauge group variables and quarks in the fundamental representation can be implemented straightforwardly on qubits, for arbitrary truncation of the gauge manifold.

hep-th↗

arXiv2024

Operator algebra, quantum entanglement, and emergent geometry from matrix degrees of freedom

For matrix model and QFT, we discuss how dual gravitational geometry emerges from matrix degrees of freedom (specifically, adjoint scalars in super Yang-Mills theory) and how operator algebra that describes an arbitrary region of the bulk geometry can be constructed. We pay attention to the subtle difference between the notions of wave packets that describe low-energy excitations: QFT wave packet associated with the spatial dimensions of QFT, matrix wave packet associated with the emergent dimensions from matrix degrees of freedom, and bulk wave packet which is a combination of QFT and matrix wave packets. In QFT, there is an intriguing interplay between QFT wave packet and matrix wave packet that connects quantum entanglement and emergent geometry. We propose that the bulk wave packet is the physical object in QFT that describes the emergent geometry from entanglement. This proposal sets a unified view on two seemingly different mechanisms of holographic emergent geometry: one based on matrix eigenvalues and the other based on quantum entanglement. Further intuition comes from the similarity to a traversable wormhole discussed as the dual description of the coupled SYK model by Maldacena and Qi: the bulk can be seen as an eternal traversable wormhole connecting boundary regions.

hep-th↗

arXiv2024

Wilson Loops and Random Matrices

Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories.

hep-th↗

arXiv2024

A new perspective on thermal transition in QCD

Motivated by the picture of partial deconfinement developed in recent years for large-$N$ gauge theories, we propose a new way of analyzing and understanding thermal phase transition in QCD. We find nontrivial support for our proposal by analyzing the WHOT-QCD collaboration's lattice configurations for SU(3) QCD in $3+1$ spacetime dimensions with up, down, and strange quarks. We find that the Polyakov line (the holonomy matrix around a thermal time circle) is governed by the Haar-random distribution at low temperatures. The deviation from the Haar-random distribution at higher temperatures can be measured via the character expansion, or equivalently, via the expectation values of the Polyakov loop defined by the various nontrivial representations of SU(3). We find that the Polyakov loop corresponding to the fundamental representation and loops in the higher representation condense at different temperatures. This suggests that there are (at least) three phases, one intermediate phase existing in between the completely-confined and the completely-deconfined phases. Our identification of the intermediate phase is supported also by the condensation of instantons: by studying the instanton numbers of the WHOT-QCD configurations, we find that the instanton condensation occurs for temperature regimes corresponding to what we identify as the completely-confined and intermediate phases, whereas the instantons do not condense in the completely-deconfined phase. Our characterization of confinement based on the Haar-randomness explains why the Polyakov loop is a good observable to distinguish the confinement and the deconfinement phases in QCD despite the absence of the $\mathbb{Z}_3$ center symmetry.

hep-th↗

arXiv2024

A model of randomly-coupled Pauli spins

We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.

hep-th↗

arXiv2024

Estimating truncation effects of quantum bosonic systems using sampling algorithms

To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.

quant-ph↗

arXiv2024

On thermal transition in QCD

We describe how the general mechanism of partial deconfinement applies to large-$N$ QCD and the partially-deconfined phase inevitably appears between completely-confined and completely-deconfined phases. Furthermore, we propose how the partial deconfinement can be observed in the real-world QCD with the SU(3) gauge group. For this purpose, we employ lattice configurations obtained by the WHOT-QCD collaboration and examine our proposal numerically. In the discussion, the Polyakov loop plays a crucial role in characterizing the phases, without relying on center symmetry, and hence, we clarify the meaning of the Polyakov loop in QCD at large $N$ and finite $N$. Both at large $N$ and finite $N$, the complete confinement is characterized by the Haar-random distribution of the Polyakov line phases. Haar-randomness, which is stronger than unbroken center symmetry, indicates that Polyakov loops in any nontrivial representations have vanishing expectation values and deviation from the Haar-random distribution at higher temperatures is quantified with the loops. We discuss that the transitions separating the partially-deconfined phase are characterized by the behaviors of Polyakov loops in various representations. The lattice QCD data provide us with the signals exhibiting two different characteristic temperatures: deconfinement of the fundamental representation and deconfinement of higher representations. As a nontrivial test for our proposal, we also investigate the relation between partial deconfinement and instanton condensation and confirm the consistency with the lattice data. To make the presentation more easily accessible, we provide a detailed review of the previously known aspects of partial deconfinement.

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