arXiv subjects

Takuya Okuda

Publications and source records attributed to Takuya Okuda.

At least 19 recordsLinked to original sources

arXiv2026

Measurement-based simulation of lattice gauge theory dynamics with adaptive quantum circuits on a trapped-ion processor

Measurement-based quantum simulation (MBQS)---a recently proposed architecture for simulating lattice gauge theories---implements Hamiltonian dynamics by consuming a model-specific entangled resource state with adaptive mid-circuit measurements, rather than by a gate-based circuit. The local constraints in lattice gauge theories are mirrored by the higher-form symmetries of the resource state. Here we report, to our knowledge, the first experimental realization of MBQS of real-time dynamics in the $(2+1)$-dimensional $\mathbb{Z}_2$ gauge theory using the Quantinuum System Model H2 trapped-ion processor. We observe coherent evolution of gauge-invariant observables on $2\times2$ and $3\times3$ spatial lattices, consuming virtual three-dimensional cluster states of 200 and 288 resource-state qubits that are generated from instantaneous blocks of 48 and 54 qubits within the 56-qubit register by measurement, reset, and re-entanglement. The measurement record that drives the evolution simultaneously provides one-form-symmetry syndromes at no additional cost, enabling postselection that strongly suppresses observed Gauss-law violations and improves aggregate agreement with ideal Trotterized dynamics. Our results demonstrate that MBQS is a viable, symmetry-aware architecture for simulating lattice field theories on present-day hardware.

quant-ph↗

arXiv2025

Fermionic CFTs from topological boundaries in abelian Chern-Simons theories

A quantum field theory is referred to as bosonic (non-spin) if its physical quantities are independent of the spacetime spin structure, and as fermionic (spin) if they depend on it. We explore fermionic conformal field theories (CFTs) that emerge from bosonic abelian Chern-Simons theories, playing the role of a symmetry topological field theory, by imposing topological boundary conditions. Our construction includes the fermionic generalization of code CFTs. When the Chern-Simons theory is associated with the root lattice of a simply laced Lie algebra, this approach yields a fermionic CFT with a level-one affine Lie algebra symmetry. As an application, we consider the Chern-Simons theories corresponding to a class of supersymmetric vertex operator algebras studied by Johnson-Freyd and classify their fermionic topological boundary conditions that give rise to supersymmetric CFTs.

hep-th↗

arXiv2024

Critical behavior of the Schwinger model via gauge-invariant VUMPS

We study the lattice Schwinger model by combining the variational uniform matrix product state (VUMPS) algorithm with a gauge-invariant matrix product ansatz that locally enforces the Gauss law constraint. Both the continuum and lattice versions of the Schwinger model with $\theta=\pi$ are known to exhibit first-order phase transitions for the values of the fermion mass above a critical value, where a second-order phase transition occurs. Our algorithm enables a precise determination of the critical endpoint in the continuum theory. We further analyze the scaling in the simultaneous critical and continuum limits and confirm that the data collapse aligns with the Ising universality class to remarkable precision.

hep-lat↗

arXiv2024

Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement

Calderbank-Shor-Steane (CSS) codes are a class of quantum error correction codes that contains the toric code and fracton models. A procedure called foliation defines a cluster state for a given CSS code. We use the CSS chain complex and its tensor product with other chain complexes to describe the topological structure in the foliated cluster state, and argue that it has a symmetry-protected topological order protected by generalized global symmetries supported on cycles in the foliated CSS chain complex. We demonstrate the so-called anomaly inflow between CSS codes and corresponding foliated cluster states by explicitly showing the equality of the gauge transformations of the bulk and boundary partition functions defined as functionals of defect world-volumes. We show that the bulk and boundary defects are related via measurement of the bulk system. Further, we provide a procedure to obtain statistical models associated with general CSS codes via the foliated cluster state, and derive a generalization of the Kramers-Wannier-Wegner duality for such statistical models with insertion of twist defects. We also study the measurement-assisted gauging method with cluster-state entanglers for CSS/fracton models based on recent proposals in the literature, and demonstrate a non-invertible fusion of duality operators. Using the cluster-state entanglers, we construct the so-called strange correlator for general CSS/fracton models. Finally, we introduce a new family of subsystem-symmetric quantum models each of which is self-dual under the generalized Kramers-Wannier-Wegner duality transformation, which becomes a non-invertible symmetry.

quant-ph↗

arXiv2024

Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements

Previous work [SciPost Phys. 14, 129 (2023)] has demonstrated that quantum simulation of abelian lattice gauge theories (Wegner models including the toric code in a limit) in general dimensions can be achieved by local adaptive measurements on symmetry-protected topological (SPT) states with higher-form generalized global symmetries. The entanglement structure of the resource SPT state reflects the geometric structure of the gauge theory. In this work, we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk, by showing that the anomalous gauge variation of the boundary state obtained by bulk measurement matches that of the bulk theory. Moreover, we construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field (Fradkin-Shenker model), where a simple scheme to protect gauge invariance of the simulated state against errors is proposed. We further consider taking an overlap between the wave function of the resource state for lattice gauge theories and that of a parameterized product state, and we derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries, as well as measurement-induced phases where states induced by a partial overlap possess different (symmetry-protected) topological orders. Measurement-assisted operators to dualize quantum Hamiltonians of lattice gauge theories and their non-invertibility are also presented.

cond-mat.str-el↗

arXiv2023

Measurement-based quantum simulation of Abelian lattice gauge theories

The digital quantum simulation of lattice gauge theories is expected to become a major application of quantum computers. Measurement-based quantum computation is a widely studied competitor of the standard circuit-based approach. We formulate a measurement-based scheme to perform the quantum simulation of Abelian lattice gauge theories in general dimensions. The scheme uses an entangled resource state that is tailored for the purpose of gauge theory simulation and reflects the spacetime structure of the simulated theory. Sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary. We treat as our main example the $\mathbb{Z}_2$ lattice gauge theory in $2+1$ dimensions, simulated on a 3-dimensional cluster state. Then we generalize the simulation scheme to Wegner's lattice models that involve higher-form Abelian gauge fields. The resource state has a symmetry-protected topological order with respect to generalized global symmetries that are related to the symmetries of the simulated gauge theories. We also propose a method to simulate the imaginary-time evolution with two-qubit measurements and post-selections.

hep-lat↗

arXiv2023

Narain CFTs from quantum codes and their $\mathbb{Z}_2$ gauging

We investigate the gauging of a $\mathbb{Z}_2$ symmetry in Narain conformal field theories (CFTs) constructed from qudit stabilizer codes. Considering both orbifold and fermionization, we establish a connection between $\mathbb{Z}_2$ gauging procedures and modifications of the momentum lattice by vectors characterizing the $\mathbb{Z}_2$ symmetry. We also provide three-dimensional interpretations of $\mathbb{Z}_2$ gaugings through abelian Chern-Simons theories, which act as symmetry topological field theories.

hep-th↗

arXiv2023

Supersymmetric conformal field theories from quantum stabilizer codes

We construct fermionic conformal field theories (CFTs) whose spectra are characterized by quantum stabilizer codes. We exploit our construction to search for fermionic CFTs with supersymmetry by focusing on quantum stabilizer codes of the Calderbank-Shor-Steane type, and derive simple criteria for the theories to be supersymmetric. We provide several examples of fermionic CFTs that meet the criteria, and find quantum codes that realize $\mathcal{N} =4$ supersymmetry. Our work constitutes a new application of quantum codes and paves the way for the methodical search for supersymmetric CFTs.

hep-th↗

arXiv2023

Narain CFTs from nonbinary stabilizer codes

We generalize the construction of Narain conformal field theories (CFTs) from qudit stabilizer codes to the construction from quantum stabilizer codes over the finite field of prime power order ($\mathbb{F}_{p^m}$ with $p$ prime and $m\geq 1$) or over the ring $\mathbb{Z}_k$ with $k>1$. Our construction results in rational CFTs, which cover a larger set of points in the moduli space of Narain CFTs than the previous one. We also propose a correspondence between a quantum stabilizer code with non-zero logical qubits and a finite set of Narain CFTs. We illustrate the correspondence with well-known stabilizer codes.

hep-th↗

arXiv2022

Narain CFTs from qudit stabilizer codes

We construct a discrete subset of Narain CFTs from quantum stabilizer codes with qudit (including qubit) systems whose dimension is a prime number. Our construction exploits three important relations. The first relation is between qudit stabilizer codes and classical codes. The second is between classical codes and Lorentzian lattices. The third is between Lorentzian lattices and Narain CFTs. In particular, we study qudit Calderbank-Shor-Steane (CSS) codes as a special class of qudit stabilizer codes and the ensembles of the Narain code CFTs constructed from CSS codes. We obtain exact results for the averaged partition functions over the ensembles and discuss their implications for holographic duality.

hep-th↗

arXiv2022

Measurement-based quantum simulation of Abelian lattice gauge theories

Numerical simulation of lattice gauge theories is an indispensable tool in high energy physics, and their quantum simulation is expected to become a major application of quantum computers in the future. In this work, for an Abelian lattice gauge theory in $d$ spacetime dimensions, we define an entangled resource state (generalized cluster state) that reflects the spacetime structure of the gauge theory. We show that sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary. Our construction includes the $(2+1)$-dimensional Abelian lattice gauge theory simulated on three-dimensional cluster state as an example, and generalizes to the simulation of Wegner's lattice models $M_{(d,n)}$ that involve higher-form Abelian gauge fields. We demonstrate that the generalized cluster state has a symmetry-protected topological order with respect to generalized global symmetries that are related to the symmetries of the simulated gauge theories on the boundary. Our procedure can be generalized to the simulation of Kitaev's Majorana chain on a fermionic resource state. We also study the imaginary-time quantum simulation with two-qubit measurements and post-selections, and a classical-quantum correspondence, where the statistical partition function of the model $M_{(d,n)}$ is written as the overlap between the product of two-qubit measurement bases and the wave function of the generalized cluster state.

quant-ph↗

arXiv2022

Schwinger model on an interval: analytic results and DMRG

Quantum electrodynamics in $1+1$ dimensions (Schwinger model) on an interval admits lattice discretization with a finite-dimensional Hilbert space, and is often used as a testbed for quantum and tensor network simulations. In this work we clarify the precise mapping between the boundary conditions in the continuum and lattice theories. In particular we show that the conventional Gauss law constraint commonly used in simulations induces a strong boundary effect on the charge density, reflecting the appearance of fractionalized charges. Further, we obtain by bosonization a number of exact analytic results for local observables in the massless Schwinger model. We compare these analytic results with the simulation results obtained by the density matrix renormalization group (DMRG) method and find excellent agreements.

hep-lat↗

arXiv2022

Conserved charges in the quantum simulation of integrable spin chains

When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and of the Trotter error due to time discretization. The Trotter error in integrable spin chains can be under control if the discrete time evolution preserves integrability. In this work we implement, on a real quantum computer and on classical simulators, the integrable Trotterization of the spin-1/2 Heisenberg XXX spin chain. We study how quantum noise affects the time evolution of several conserved charges, and observe the decay of the expectation values. We in addition study the early time behaviors of the time evolution, which can potentially be used to benchmark quantum devices and algorithms in the future. We also provide an efficient method to generate the conserved charges at higher orders.

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

ABCD of 't Hooft operators

We compute by supersymmetric localization the expectation values of half-BPS 't Hooft line operators in $\mathcal{N}=2$ $U(N)$, $SO(N)$ and $USp(N)$ gauge theories on $S^1 \times \mathbb{R}^3$ with an $Ω$-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the 't Hooft operators using branes and orientifolds in type II string theories.

hep-th↗

arXiv2021

U(1) spin Chern-Simons theory and Arf invariants in two dimensions

The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd. Its dynamics is captured by the 2d CFT of a compact boson with a certain radius. Recently it was recognized that a dependence on the 2d spin structure can be given to the CFT by modifying it using the so-called Arf invariant. We demonstrate that one can reorganize the torus partition function of the modified CFT into a finite sum involving a finite number of conformal blocks. This allows us to reproduce the modular matrices of the spin theory. We use the modular matrices to calculate the partition function of the spin Chern-Simons theory on the lens space $L(a,\pm 1)$, and demonstrate the expected dependence on the 3d spin structure.

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↗

arXiv2019

Wall-crossing and operator ordering for 't Hooft operators in N=2 gauge theories

We study half-BPS 't Hooft line operators in 4d $\mathcal{N}=2$ $U(N)$ gauge theories on $S^1\times \mathbb{R}^3$ with an $Ω$-deformation. The recently proposed brane construction of 't Hooft operators shows that non-perturbative contributions to their correlator are identified with the Witten indices of quiver supersymmetric quantum mechanics. For the products of minimal 't Hooft operators, a chamber in the space of Fayet-Iliopoulos parameters in the quantum mechanics corresponds to an ordering of the operators inserted along a line. These considerations lead us to conjecture that the Witten indices can be read off from the Moyal products of the expectation values of the minimal 't Hooft operators, and also that wall-crossing occurs in the quantum mechanics only when the ordering of the operators changes. We confirm the conjectures by explicitly computing the Witten indices for the products of two and three minimal 't Hooft operators in all possible chambers.

hep-th↗