arXiv subjects

Patrick Draper

Publications and source records attributed to Patrick Draper.

At least 19 recordsLinked to original sources

arXiv2026

Block Encoding Non-Abelian Lattice Gauge Theory

Gauge theories like lattice QCD present a complex problem for quantum simulation. In a basis where the electric part of the Hamiltonian is simple, the magnetic part, generally expressed as a sum over the plaquette operators of the lattice, is quite complicated, producing correlated transitions between several link and site degrees of freedom. We provide an efficient block encoding of the plaquette operator in the irrep basis, a refinement of the electric basis where the internal gauge-variant degrees of freedom are integrated out. The construction removes the plaquette matrix element scaling wall which has been a significant barrier for other approaches in this basis. The algorithm leverages a convenient factorization property of the matrix elements, cheap classical precomputation, and quantum oracles built from lookup tables and programmed rotations.

quant-ph↗

arXiv2026

Lattice Quantum Chromodynamics for Quantum Simulations

We develop a framework for quantum simulations of lattice SU($N_c$) gauge theory with quarks. Staggered and Wilson lattice fermions are considered in two and three spatial dimensions and a theta angle is included in three dimensions. The physical, gauge-invariant Hilbert space is formulated in a representation basis, where gauge and fermionic degrees of freedom are encoded by irreducible representations of SU($N_c$) that tensor at each lattice site to contain a singlet. We discuss algorithms for simulating time evolution on quantum computers and carry out noiseless simulations of lattice quantum chromodynamics ($N_c=3$) on small lattices with up to 32 qubits, showcasing theta angle effects, hadronic states, string dynamics, and a baryon chemical potential for the first time in three spatial dimensions.

quant-ph↗

arXiv2025

Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of SU(3) lattice gauge theory

We study methods for efficient preparation of approximate ground states of $SU(3)$ lattice gauge theory on quantum hardware. Working in a variant of the electric basis, we introduce a refinement of the irrep truncation based on the energy density of site singlets, which provides a finer gradation of simulation complexity. Using strong-coupling perturbation theory as a guide, we develop simple ansatz circuits for ground state preparation and test them via classical simulation on small lattices, including the $2\times 2$ plaquette lattice in $d=2$ and the cube in $d=3$. We contrast state fidelities and resource requirements of variational methods against adiabatic state preparation and introduce a method that hybridizes the two approaches. Finally, we report on the public release of \texttt{ymcirc} -- a package of tools for building $SU(3)$ circuits and processing measurements -- and \texttt{pyclebsch}, a package for efficiently computing $SU(N)$ Clebsch-Gordan coefficients.

hep-lat↗

arXiv2025

Hamiltonian truncation and quantum simulation of strong-field QED beyond tree level

Quantum electrodynamics in strong background fields provides an interesting class of problems for classical and quantum simulation. In this paper we formulate simulations of polarization (helicity) flip for a photon colliding with a high-intensity plane wave. Polarization flip is a one loop effect, which requires addressing new issues that do not arise in simulations of tree-level processes. Working in the momentum-space Fock basis, while convenient for the extraction of scattering amplitudes, requires tuning counterterms to cancel large cutoff effects. We compute analytic formulas for the counterterms at one loop. We then construct circuits for quantum simulations of the process, perform noiseless simulations on classical computers to assess discretization errors, and discuss resource estimates for future simulations on quantum hardware.

hep-ph↗

arXiv2025

Quantum Properties of Non-Dirichlet Boundary Conditions in Gravity

The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Dirichlet conditions on the boundary induced metric; microcanonical conditions, which refers to fixing some components of the Brown-York boundary stress tensor; and conformal conditions, in which the conformal structure of the induced metric and the trace of the extrinsic curvature are fixed. Boundaries also present interesting problems of consistency. The Dirichlet problem is known, under various (and generally different) conditions, to be inconsistent with perturbative quantization of graviton fluctuations; to exhibit thermodynamic instability; or to require infinite fine-tuning in the presence of matter fluctuations. We extend some of these results to other boundary conditions. We find that similarly to the Dirichlet problem, the graviton fluctuation operator is not elliptic with microcanonical boundaries, and the non-elliptic modes correspond to ``boundary-moving diffeomorphisms." However, we argue that microcanonical factorization of path integrals -- essentially, the insertion of microcanonical constraints on two-sided surfaces in the bulk -- is not affected by the same issues of ellipticity. We also show that for a variety of matter field boundary conditions, matter fluctuations renormalize the gravitational bulk and boundary terms differently, so that the classical microcanonical or conformal variational problems are not preserved unless an infinite fine-tuning is performed.

hep-th↗

arXiv2025

Three-qubit encoding in ytterbium-171 atoms for simulating 1+1D QCD

Simulating nuclear matter described by quantum chromodynamics using quantum computers is notoriously inefficient because of the assortment of quark degrees of freedom such as matter/antimatter, flavor, color, and spin. Here, we propose to address this resource efficiency challenge by encoding three qubits within individual ytterbium-171 atoms of a neutral atom quantum processor. The three qubits are encoded in three distinct sectors: an electronic "clock" transition, the spin-1/2 nucleus, and the lowest two motional states in one radial direction of the harmonic trapping potential. We develop a family of composite sideband pulses and demonstrate a universal gate set and readout protocol for this three-qubit system. We then apply it to single-flavor quantum chromodynamics in 1+1D axial gauge for which the three qubits directly represent the occupancy of quarks in the three colors. We show that two atoms are sufficient to simulate both vacuum persistence oscillations and string breaking. We consider resource requirements and connections to error detection/correction. Our work is a step towards resource-efficient digital simulation of nuclear matter and opens new opportunities for versatile qubit encoding in neutral atom quantum processors.

quant-ph↗

arXiv2025

Quantum Circuits for SU(3) Lattice Gauge Theory

Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about the quantum structure of gauge theories. In this work, we consider pure $SU(3)$ gauge theory in two and three spatial dimensions in a streamlined version of the electric basis. We use a formulation of the theory that balances locality of the Hamiltonian and size of the gauge-invariant state space, and we classically pre-compute dictionaries of plaquette operator matrix elements for use in circuit construction. We build circuits for simulating time evolution on arbitrary lattice volumes, spanning circuits suitable for NISQ era hardware to future fault-tolerant devices. Relative to spin models, time evolution in lattice gauge theories involves more complex local unitaries, and the Hilbert space of all quantum registers may have large unphysical subspaces. Based on these features, we develop general, volume-scalable tools for optimizing circuit depth, including pruning and fusion algorithms for collections of large multi-controlled unitaries. We describe scalings of quantum resources needed to simulate larger circuits and some directions for future algorithmic development.

hep-lat↗

arXiv2024

Generalized Entanglement Capacity of de Sitter Space

Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1+1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic quantities associated with the horizon, and the leading cutoff sensitivity of the heat capacity is found to equal to the leading cutoff sensitivity of the entropy. One can also compute contributions to the thermodynamic quantities from the gravitational path integral. For the cosmological horizon of the static patch of de Sitter space, a natural conjecture for the relevant heat capacity is shown to equal the Bekenstein-Hawking entropy. These observations allow us to extend the well-known notion of the generalized entropy to a generalized heat capacity for the static patch of dS. The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggests it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain.

hep-th↗

arXiv2024

Breakdown of Field Theory in Near-Horizon Regions

We discuss back-reaction in the semiclassical treatment of quantum fields near a black hole. When the state deviates significantly from Hartle-Hawking, simple energetic considerations of back-reaction give rise to a characteristic radial distance scale $\sim (r_s^{2}G_N)^{1/D}$, below which some breakdown of effective field theory may occur.

hep-th↗

arXiv2023

Quantum Simulations for Strong-Field QED

Quantum field theory in the presence of strong background fields contains interesting problems where quantum computers may someday provide a valuable computational resource. In the NISQ era it is useful to consider simpler benchmark problems in order to develop feasible approaches, identify critical limitations of current hardware, and build new simulation tools. Here we perform quantum simulations of strong-field QED (SFQED) in $3+1$ dimensions, using real-time nonlinear Breit-Wheeler pair-production as a prototypical process. The strong-field QED Hamiltonian is derived and truncated in the Furry-Volkov mode expansion, and the interactions relevant for Breit-Wheeler are transformed into a quantum circuit. Quantum simulations of a "null double slit" experiment are found to agree well with classical simulations following the application of various error mitigation strategies, including an asymmetric depolarization algorithm which we develop and adapt to the case of Trotterization with a time-dependent Hamiltonian. We also discuss longer-term goals for the quantum simulation of SFQED.

hep-ph↗

arXiv2023

Fast Partitioning of Pauli Strings into Commuting Families for Expectation Value Measurements of Dense Operators

The cost of measuring quantum expectation values of an operator can be reduced by grouping the Pauli string ($SU(2)$ tensor product) decomposition of the operator into maximally commuting sets. We detail an algorithm, presented in [1], to partition the full set of $m$-qubit Pauli strings into the minimal number of commuting families, and benchmark the performance with dense Hamiltonians on IBM hardware. Here we also compare how our method scales compared to graph-theoretic techniques for the generally commuting case.

hep-lat↗

arXiv2023

Path Integral Factorization and the Gravitational Effective Action

We discuss the factorization and continuity properties of fields in the Euclidean gravitational path integral with higher dimension operators constructed from powers of the Riemann tensor. We construct the boundary terms corresponding to the microcanonical ensemble and show that the saddle point approximation to the path integral with a quasilocal energy constraint generally yields a saddle point with discontinuous temperature. This extends a previous result for the Euclidean Schwarzschild-de Sitter geometry in Einstein gravity and shows that it is robust against at least some types of quantum corrections from heavy fields. As an application, we compute the entropy of SdS in $\text{D}=4$ using the BTZ method. Our result matches the entropy calculated using Wald's formula.

hep-th↗

arXiv2023

Vacuum Decay in Time-Dependent Backgrounds

We develop semiclassical methods for studying bubble nucleation in models with parameters that vary slowly in time. Introducing a more general rotation of the time contour allows access to a larger set of final states, and typically a non-Euclidean rotation is necessary in order to find the most relevant tunneling solution. We work primarily with effective quantum mechanical models parametrizing tunneling along restricted trajectories in field theories, which are sufficient, for example, to study thin wall bubble nucleation. We also give one example of an exact instanton solution in a particular Kaluza-Klein cosmology where the circumference of the internal circle is changing in time.

hep-th↗

arXiv2023

Neutralizing Topological Obstructions to Bubbles of Nothing

Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by $1/g^2$ effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged $R$-symmetry.

hep-th↗

arXiv2023

Fast Partitioning of Pauli Strings into Commuting Families for Optimal Expectation Value Measurements of Dense Operators

The Pauli strings appearing in the decomposition of an operator can be can be grouped into commuting families, reducing the number of quantum circuits needed to measure the expectation value of the operator. We detail an algorithm to completely partition the full set of Pauli strings acting on any number of qubits into the minimal number of sets of commuting families, and we provide python code to perform the partitioning. The partitioning method scales linearly with the size of the set of Pauli strings and it naturally provides a fast method of diagonalizing the commuting families with quantum gates. We provide a package that integrates the partitioning into Qiskit, and use this to benchmark the algorithm with dense Hamiltonians, such as those that arise in matrix quantum mechanics models, on IBM hardware. We demonstrate computational speedups close to the theoretical limit of $(3/2)^m$ relative to qubit-wise commuting groupings, for $m=2,\dotsc,6$ qubits.

quant-ph↗

arXiv2022

Simulating the Femtouniverse on a Quantum Computer

We compute the low-lying spectrum of 4D SU(2) Yang-Mills in a finite volume using quantum simulations. In contrast to small-volume lattice truncations of the Hilbert space, we employ toroidal dimensional reduction to the ``femtouniverse" matrix quantum mechanics model. In this limit the theory is equivalent to the quantum mechanics of three interacting particles moving inside a 3-ball with certain boundary conditions. We use the variational quantum eigensolver and quantum subspace expansion techniques to compute the string tension to glueball mass ratio near the small/large-volume transition point, finding qualitatively good agreement with large volume Euclidean lattice simulations.

hep-lat↗

arXiv2022

Vacuum Decay and Euclidean Lattice Monte Carlo

The decay rate of a metastable vacuum is usually calculated using a semiclassical approximation to the Euclidean path integral. The extension to a complete Euclidean lattice Monte Carlo computation, however, is hampered by analytic continuations that are ill-suited to numerical treatment, and the nonequilibrium nature of a metastable state. In this paper we develop a new methodology to compute vacuum decay rates from Monte Carlo simulations of Euclidean lattice theories. To test the new method, we consider simple quantum mechanical systems systems with metastable vacua. This work can be extended to Euclidean field theories, which we discuss in the Conclusions.

hep-lat↗

arXiv2022

TF08 Snowmass Report: BSM Model Building

We summarize the state of Beyond the Standard Model (BSM) model building in particle physics for Snowmass 2021, focusing mainly on several whitepaper contributions to BSM model building (TF08) and closely related areas.

hep-ph↗