arXiv subjects

Jesse R. Stryker

Publications and source records attributed to Jesse R. Stryker.

14 recordsLinked to original sources

arXiv2026

Exponential-in-$N_c^2$ cost reduction of product-formula-based quantum simulations of quantum chromodynamics

Quantum algorithms for simulating quantum chromodynamics (QCD) have matured steadily since the pioneering work of Byrnes and Yamamoto [PRA 73, 022328 (2006)]. The most popular strategies for Hamiltonian simulation involve product-formula decompositions. However, the application of product-formula methods to SU($N_c$) lattice gauge theories by Byrnes and Yamamoto leads to $O(Λ^{8(N_c^2-1)})$ gate complexity per Trotter step, where $Λ$ is the bosonic cutoff in the electric (i.e., irreducible-representation) basis. A seminal work by Kan and Nam [arXiv:2107.12769 (2021)] significantly improves over such an undesirable cost and reports an $O\big(Λ\text{polylog}(Λ)\big)$ scaling, yet it still calls for an unrealistically large number of quantum gates. Here, we illuminate one of the reasons behind this high cost estimate and show that a factor of size $O(2^{4(N_c^2-1)})$ can be removed from the per-Trotter-step cost estimate by Kan and Nam. We specifically show that, by using methods developed in our past works [PRD 112, 014508 (2025); Quantum 7, 1213 (2023)], exponentiated-Hamiltonian decomposition---a necessary step in the application of product-formula algorithms---can be performed far more efficiently than previously thought. Our method reduces the T-gate cost estimate of QCD simulations using a second-order product formula by a factor of nearly $10^{14}$, independent of simulation parameters and sizes. Focusing on simulations in the electric basis, we further contrast our results with other methods: the local-multiplet basis approach of Ciavarella, Klco, and Savage [PRD 103, 094501 (2021)] and the near-optimal algorithm of Rhodes, Kreshchuk, and Pathak [PRX Quantum 5, 040347 (2024)]. This work highlights the importance of continued algorithmic improvement to bringing the quantum-simulation cost of QCD within reach of realistic quantum computers.

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arXiv2026

String-breaking statics and dynamics in a (1+1)D SU(2) lattice gauge theory

String breaking is at the core of hadronization models of relevance to particle colliders. Yet, studies of string-breaking dynamics rooted in quantum chromodynamics remain fundamentally challenging. Tensor networks enable sign-problem-free studies of static and dynamical properties of lattice gauge theories. In this work, we develop and apply a tensor-network toolkit based on the loop-string-hadron formulation of an SU(2) lattice gauge theory in 1+1 dimensions with dynamical fermions. We apply this toolkit to study static and dynamical aspects of strings and their breaking in this theory. The simple, gauge-invariant, and local structure of the loop-string-hadron states and constraints removes the need to impose non-Abelian constraints in the algorithm, and allows for a systematic computation of observables at increasingly large bosonic cutoffs, and toward the infinite-volume and continuum limits. Our study of static strings yields a determination of the string tension in the continuum and thermodynamic limits. Our study of dynamical string breaking, performed at a fixed lattice spacing and system size, illuminates underlying processes at play during the quench dynamics of a string. The loop, string, and hadron description offers a systematic and intuitive way to diagnose these processes, including string expansion and contraction, endpoint splitting and particle shower, chain scattering events, and inelastic processes resulting from string dissociation and recombination, and particle production. We relate these processes to several features of the dynamics, such as energy transport, entanglement-entropy production, and correlation spreading. This work opens the way to future tensor-network studies of string breaking and particle production in increasingly complex lattice gauge theories.

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arXiv2026

Loop-string-hadron approach to SU(3) lattice Yang-Mills theory, II: Operator representation for the trivalent vertex

This work is the second installment of a series on the loop-string-hadron (LSH) approach to SU(3) lattice Yang-Mills theory. Here, we present the infinite-dimensional matrix representation for arbitrary gauge-invariant operators at a trivalent vertex, which results in a standalone framework for computations that supersedes the underlying Schwinger-boson framework. To that end, we present a partial summary of the commutation relations and use it to evaluate the result of applying any gauge-invariant operator on the LSH basis states introduced in Part I (arXiv:2407.19181). Classical calculations in the LSH basis run significantly faster than equivalent calculations performed using Schwinger bosons. A companion code script is provided, which implements the derived formulas and aims to facilitate rapid progress towards Hamiltonian-based calculations of quantum chromodynamics.

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arXiv2025

Shearing approach to gauge-invariant Trotterization

Universal quantum simulations of gauge field theories are exposed to the risk of gauge symmetry violations when it is not known how to compile the desired operations exactly using the available gate set. In this article, we show how time evolution can be compiled in an Abelian gauge theory -- if only approximately -- without compromising gauge invariance, by graphically motivating a block-diagonalization procedure. When gauge-invariant interactions are associated with a "spatial network" in the space of discrete quantum numbers, it is seen that cyclically shearing the spatial network converts simultaneous updates to many quantum numbers into conditional updates of a single quantum number; ultimately, this eliminates any need to pass through (and acquire overlap onto) unphysical intermediate configurations. Shearing is explicitly applied to gauge-matter and magnetic interactions of lattice quantum electrodynamics. The features that make shearing successful at preserving Abelian gauge symmetry may also be found in non-Abelian theories, bringing one closer to gauge-invariant simulations of quantum chromodynamics.

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arXiv2025

Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex

The construction of gauge invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but implementing them is complicated by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH) approach to lattice gauge theories, the elementary excitations are strictly gauge invariant, and constructing the basis requires no knowledge of Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH formulation was recently generalized to SU(3), but limited to one spatial dimension. In this work, we generalize the LSH approach to constructing the basis of SU(3) gauge invariant states at a trivalent vertex -- the essential building block to multidimensional space. A direct generalization from the SU(2) vertex yields a legitimate basis; however, in certain sectors of the Hilbert space, the naive LSH basis vectors so defined suffer from being nonorthogonal. The issues with orthogonality are directly related to the "missing label" or "outer multiplicity" problem associated with SU(3) tensor products, and may also be phrased in terms of Littlewood-Richardson coefficients or the need for a "seventh Casimir" operator. The states that are unaffected by the problem are orthonormalized in closed form. For the sectors that are afflicted, we discuss the nonorthogonal bases and their orthogonalization. A few candidates for seventh Casimir operators are readily constructed from the suite of LSH gauge-singlet operators. The diagonalization of a seventh Casimir represents one prescriptive solution toward obtaining a complete orthonormal basis, but a closed-form general solution remains to be found.

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arXiv2023

General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple (bosonic and fermionic) quantum numbers with non-trivial functional coefficients. In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.

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arXiv2023

Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks

Towards the goal of quantum computing for lattice quantum chromodynamics, we present a loop-string-hadron (LSH) framework in 1+1 dimensions for describing the dynamics of SU(3) gauge fields coupled to staggered fermions. This novel framework was previously developed for an SU(2) lattice gauge theory in $d\leq3$ spatial dimensions and its advantages for classical and quantum algorithms have thus far been demonstrated in $d=1$. The LSH approach uses gauge invariant degrees of freedoms such as loop segments, string ends, and on-site hadrons, it is free of all nonabelian gauge redundancy, and it is described by a Hamiltonian containing only local interactions. In this work, the SU(3) LSH framework is systematically derived from the reformulation of Hamiltonian lattice gauge theory in terms of irreducible Schwinger bosons, including the addition of staggered quarks. Furthermore, the superselection rules governing the LSH dynamics are identified directly from the form of the Hamiltonian. The SU(3) LSH Hamiltonian with open boundary conditions has been numerically confirmed to agree with the completely gauge-fixed Hamiltonian, which contains long-range interactions and does not generalize to either periodic boundary conditions or to $d>1$.

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arXiv2021

Gauss's Law, Duality, and the Hamiltonian Formulation of U(1) Lattice Gauge Theory

Quantum computers have the potential to explore the vast Hilbert space of entangled states that play an important role in the behavior of strongly interacting matter. This opportunity motivates reconsidering the Hamiltonian formulation of gauge theories, with a suitable truncation scheme to render the Hilbert space finite-dimensional. Conventional formulations lead to a Hilbert space largely spanned by unphysical states; given the current inability to perform large scale quantum computations, we examine here how one might restrict wave function evolution entirely or mostly to the physical subspace. We consider such constructions for the simplest of these theories containing dynamical gauge bosons -- U(1) lattice gauge theory without matter in $d=2,3$ spatial dimensions -- and find that electric-magnetic duality naturally plays an important role. We conclude that this approach is likely to significantly reduce computational overhead in $d=2$ by a reduction of variables and by allowing one to regulate magnetic fluctuations instead of electric. The former advantage does not exist in $d=3$, but the latter might be important for asymptotically-free gauge theories.

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arXiv2020

Quantum Algorithms for Simulating the Lattice Schwinger Model

The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x^{-1/2}$ and electric field cutoff $x^{-1/2}Λ$ can be simulated on a quantum computer for time $2xT$ using a number of $T$-gates or CNOTs in $\widetilde{O}( N^{3/2} T^{3/2} \sqrt{x} Λ)$ for fixed operator error. This scaling with the truncation $Λ$ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.

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arXiv2020

Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization

We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,'"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how the bases are digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.

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arXiv2020

Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories

The question of how to efficiently formulate Hamiltonian gauge theories is experiencing renewed interest due to advances in building quantum simulation platforms. We introduce a reformulation of an SU(2) Hamiltonian lattice gauge theory---a loop-string-hadron (LSH) formulation---that describes dynamics directly in terms of its loop, string, and hadron degrees of freedom, while alleviating several disadvantages of quantumly simulating the Kogut-Susskind formulation. This LSH formulation transcends the local loop formulation of $d+1$-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and being used to reconstruct dynamics between states that have Gauss's law built in to them. LSH operators are then factored into products of "normalized" ladder operators and diagonal matrices, priming them for classical or quantum information processing. Self-contained expressions of the Hamiltonian are given up to $d=3$. The LSH formalism makes little use of structures specific to SU(2) and its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU(3).

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arXiv2019

SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers

An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto qubit degrees of freedom is presented. This new mapping allows for a reduced unphysical Hilbert space. Insensitivity to interactions within this unphysical space is exploited to design more efficient quantum circuits. Local gauge symmetry is used to analytically incorporate the angular momentum alignment, leading to qubit registers encoding the total angular momentum on each link. The results of a multi-plaquette calculation on IBM's quantum hardware are presented.

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arXiv2019

Oracles for Gauss's law on digital quantum computers

Formulating a lattice gauge theory using only physical degrees of freedom generically leads to non-local interactions. A local Hamiltonian is desirable for quantum simulation, and this is possible by treating the Hilbert space as a subspace of a much larger Hilbert space in which Gauss's law is not automatic. Digital quantum simulations of this local formulation will wander into unphysical sectors due to errors from Trotterization or from quantum noise. In this work, oracles are constructed that use local Gauss law constraints to projectively distinguish physical and unphysical wave functions in Abelian lattice gauge theories. Such oracles can be used to detect errors that break Gauss's law.

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arXiv2016

On the proton charge extensions

We examine how corrections to $S$-state energy levels, $ E_{nS}$, in hydrogenic atoms due to the finite proton size are affected by moments of the proton charge distribution. The corrections to $E_{nS}$ are computed moment by moment. The results demonstrate that the next-to-leading order term in the expansion is of order $r_p / a_B $ times the size of the leading order $ \langle r_p^2 \rangle $ term. Our analysis thus dispels any concern that the larger relative size of this term for muonic hydrogen versus electronic hydrogen might account for the current discrepancy of proton radius measurements extracted from the two systems. Furthermore, the next-to-leading order term in powers of $r_p / a_B $ that we derive from a dipole proton form factor is proportional to $\langle r_p^3 \rangle $, rather than $\langle r_p^4 \rangle$ as would be expected from the scalar nature of the form factor. The dependence of the finite-size correction on $\langle r_p^3 \rangle $ and higher odd-power moments is shown to be a general result for any spherically symmetric proton charge distribution. A method for computing the moment expansion of the finite-size correction to arbitrary order is introduced and the results are tabulated for principal quantum numbers up to $n=7$.

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