About

Professor Patrick I. Draper is an Associate Professor at The Grainger College of Engineering, University of Illinois Urbana-Champaign. He received his Ph.D. in Physics from The University of Chicago in 2011, following his B.S. from the University of Illinois in 2005. He held postdoctoral appointments at the University of California Santa Cruz and the University of California Santa Barbara, and a faculty appointment at the University of Massachusetts Amherst before joining the University of Illinois in 2018. His research focuses on theoretical high energy physics, with recent work centered on developing applications of quantum computing to theories and phenomena in high energy physics. His projects include building circuits for Hamiltonian simulation of lattice gauge theories, exploring new applications of quantum simulations to theories such as strong-field QED and quantum mechanical matrix models, developing qudit platforms, and creating algorithms to utilize quantum resources more efficiently.

Research topics

• Political Science
• Physics
• Computer Science
• Quantum mechanics
• Particle physics
• Geometry
• Engineering
• Nuclear physics
• Mathematical physics
• Law
• Theoretical physics
• Library science
• Astrophysics
• Engineering ethics
• Public relations
• Pure mathematics
• Statistical physics
• Mathematics

Selected publications

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

  Physical review. D/Physical review. D. · 2026-02-05

  articleOpen access1st authorCorresponding

  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.

  PublisherDOI

• Three-Qubit Encoding in Ytterbium-171 Atoms for Simulating 1+1D Quantum Chromodynamics

  PRX Quantum · 2025-12-22

  articleOpen access

  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 a screened hadron-number transition. We consider resource requirements and connections to error detection/correction. Our work is a step toward resource-efficient digital simulation of nuclear matter and opens new opportunities for versatile qubit encoding in neutral atom quantum processors.

  PublisherDOI

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

  ArXiv.org · 2025-09-19

  preprintOpen access1st authorCorresponding

  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.

  PublisherOA PDFDOI

• Quantum Circuits for SU(3) Lattice Gauge Theory

  ArXiv.org · 2025-03-11

  preprintOpen access

  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.

  PublisherOA PDFDOI

• Quantum circuits for SU(3) lattice gauge theory

  Physical review. D/Physical review. D. · 2025-08-26 · 7 citations

  articleOpen access

  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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>3</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> 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 Noisy Intermediate-Scale Quantum 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 multicontrolled unitaries. We describe scalings of quantum resources needed to simulate larger circuits and some directions for future algorithmic development.

  PublisherDOI

• Quantum simulations for strong-field QED

  Physical review. D/Physical review. D. · 2024-04-08 · 11 citations

  articleOpen accessSenior author

  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 noisy intermediate-scale quantum 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>3</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math> 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. Published by the American Physical Society 2024

  PublisherOA PDFDOI

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

  2024-05-03

  articleOpen accessSenior author

  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.

  PublisherOA PDFDOI

• Generalized entanglement capacity of de Sitter space

  Physical review. D/Physical review. D. · 2024-08-26 · 6 citations

  articleOpen accessSenior author

  Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math> 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 de Sitter (dS). The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggest it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain. Published by the American Physical Society 2024

  PublisherOA PDFDOI

• A natural mechanism for approximate Higgs alignment in the 2HDM

  OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2024-11-25 · 13 citations

  articleOpen access1st authorCorresponding

  The 2HDM possesses a neutral scalar interaction eigenstate whose tree-level properties coincide with the Standard Model (SM) Higgs boson. In light of the LHC Higgs data which suggests that the observed Higgs boson is SM-like, it follows that the mixing of the SM Higgs interaction eigenstate with the other neutral scalar interaction eigenstates of the 2HDM should be suppressed, corresponding to the so-called Higgs alignment limit. The exact Higgs alignment limit can arise naturally due to a global symmetry of the scalar potential. If this symmetry is softly broken, then the Higgs alignment limit becomes approximate (although still potentially consistent with the current LHC Higgs data). In this paper, we obtain the approximate Higgs alignment suggested by the LHC Higgs data as a consequence of a softly broken global symmetry of the Higgs Lagrangian. However, this can only be accomplished if the Yukawa sector of the theory is extended. We propose an extended 2HDM with vector-like top quark partners, where explicit mass terms in the top sector provide the source of the soft symmetry breaking of a generalized CP symmetry. In this way, we can realize approximate Higgs alignment without a significant fine-tuning of the model parameters. We then explore the implications of the current LHC bounds on vector-like top quark partners for the success of our proposed scenario.

  PublisherOA PDFDOI

• Generalized Entanglement Capacity of de Sitter Space

  arXiv (Cornell University) · 2024-04-21

  preprintOpen accessSenior author

  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.

  PublisherOA PDFDOI

Recent grants

• Exploring the Scalar Sector

  NSF · $120k · 2017–2019

• Exploring the Scalar Sector

  NSF · $122k · 2018–2021

Frequent coauthors

• Carlos E. M. Wagner

  47 shared

• Nathaniel Craig

  University of California, Santa Barbara

  39 shared

• Marcela Carena

  30 shared

• Kyoungchul Kong

  University of Kansas

  29 shared

• D. Whiteson

  27 shared

• Tao Liu

  University of Hong Kong

  26 shared

• Yvonne Ng

  St. Catherine University

  26 shared

• Jonathan Kozaczuk

  University of California, San Diego

  22 shared

Education

• Ph.D., Physics

  University of Chicago

  2011

Awards & honors

• Illinois physicists develop a new technique to model particl…