Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.

%8 3/30/2023 %G eng %U https://arxiv.org/abs/2207.12470 %0 Journal Article %D 2023 %T Randomized measurement protocols for lattice gauge theories %A Jacob Bringewatt %A Jonathan Kunjummen %A Niklas Mueller %XRandomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments.

%8 3/27/2023 %G eng %U https://arxiv.org/abs/2303.15519 %0 Journal Article %D 2023 %T On the stability of solutions to Schrödinger's equation short of the adiabatic limit %A Jacob Bringewatt %A Michael Jarret %A T. C. Mooney %XWe prove an adiabatic theorem that applies at timescales short of the adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger's equation under perturbation. We directly characterize cross-subspace effects of perturbation, which are typically significantly less than suggested by the perturbation's operator norm. This stability has numerous consequences: we can (1) find timescales where the solution of Schrodinger's equation converges to the ground state of a block, (2) lower bound the convergence to the global ground state by demonstrating convergence to some other known quantum state, (3) guarantee faster convergence than the standard adiabatic theorem when the ground state of the perturbed Hamiltonian (H) is close to that of the unperturbed H, and (4) bound tunneling effects in terms of the global spectral gap when H is ``stoquastic'' (a Z-matrix). Our results apply to quantum annealing protocols with faster convergence than usually guaranteed by a standard adiabatic theorem. Our upper and lower bounds demonstrate that at timescales short of the adiabatic limit, subspace dynamics can dominate over global dynamics. Thus, we see that convergence to particular target states can be understood as the result of otherwise local dynamics.

%8 3/23/2023 %G eng %U https://arxiv.org/abs/2303.13478 %0 Journal Article %J Phys. Rev. A %D 2022 %T Simultaneous Stoquasticity %A Jacob Bringewatt %A Brady, Lucas T. %K FOS: Physical sciences %K Quantum Physics (quant-ph) %XStoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

%B Phys. Rev. A %V 105 %8 06/09/2022 %G eng %U https://arxiv.org/abs/2202.08863 %N 062601 %R https://doi.org/10.1103/PhysRevA.105.062601 %0 Journal Article %D 2021 %T Lefschetz Thimble Quantum Monte Carlo for Spin Systems %A T. C. Mooney %A Jacob Bringewatt %A Lucas T. Brady %XMonte Carlo simulations are often useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, which manifests as an oscillating phase attached to the probabilities being sampled. This sign problem generally leads to an exponential slow down in the time taken by a Monte Carlo algorithm to reach any given level of accuracy, and it has been shown that completely solving the sign problem for an arbitrary quantum system is NP-hard. However, a variety of techniques exist for mitigating the sign problem in specific cases; in particular, the technique of deforming the Monte Carlo simulation's plane of integration onto Lefschetz thimbles (that is, complex hypersurfaces of stationary phase) has seen success for many problems of interest in the context of quantum field theories. We extend this methodology to discrete spin systems by utilizing spin coherent state path integrals to re-express the spin system's partition function in terms of continuous variables. This translation to continuous variables introduces additional challenges into the Lefschetz thimble method, which we address. We show that these techniques do indeed work to lessen the sign problem on some simple spin systems.

%8 10/20/2021 %G eng %U https://arxiv.org/abs/2110.10699 %0 Journal Article %D 2021 %T Minimum Entanglement Protocols for Function Estimation %A Adam Ehrenberg %A Jacob Bringewatt %A Alexey V. Gorshkov %XWe derive a family of optimal protocols, in the sense of saturating the quantum Cramér-Rao bound, for measuring a linear combination of d field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor networks applications. We demonstrate how to select different protocols from this family under various constraints via linear programming. Focusing on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality in many cases. Specifically, we prove necessary and sufficient conditions for the existence of optimal protocols using at most k-partite entangled cat-like states.

%8 10/14/2021 %G eng %U https://arxiv.org/abs/2110.07613 %0 Journal Article %J Physical Review Research %D 2021 %T Protocols for estimating multiple functions with quantum sensor networks: Geometry and performance %A Jacob Bringewatt %A Boettcher, Igor %A Niroula, Pradeep %A Bienias, Przemyslaw %A Alexey V. Gorshkov %XWe consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds of Rubio et. al. [J. Phys. A: Math. Theor. 53 344001 (2020)] and develop a new optimized sequential protocol for measuring such functions. We compare the performance of both approaches to one another and to local protocols that do not utilize quantum entanglement, emphasizing the geometric significance of the coefficient vectors of the measured functions in determining the best choice of measurement protocol. We show that, in many cases, especially for a large number of sensors, the optimized sequential protocol results in more accurate measurements than the other strategies. In addition, in contrast to the the sensor symmetric approach, the sequential protocol is known to always be explicitly implementable. The sequential protocol is very general and has a wide range of metrological applications.

%B Physical Review Research %V 3 %8 5/3/2021 %G eng %U https://arxiv.org/abs/2104.09540 %R 10.1103/physrevresearch.3.033011 %0 Journal Article %D 2020 %T Confronting lattice parton distributions with global QCD analysis %A Jacob Bringewatt %A N. Sato %A W. Melnitchouk %A Jian-Wei Qiu %A F. Steffens %A M. Constantinou %XWe present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions

%8 10/1/2020 %G eng %U https://arxiv.org/abs/2010.00548 %0 Journal Article %D 2020 %T Effective gaps are not effective: quasipolynomial classical simulation of obstructed stoquastic Hamiltonians %A Jacob Bringewatt %A Michael Jarret %XAll known examples confirming the possibility of an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (AQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric subspaces. The symmetries produce large effective eigenvalue gaps, which in turn make adiabatic computation efficient. We present a classical algorithm to efficiently sample from the effective subspace of a k-local stoquastic Hamiltonian H, without a priori knowledge of its symmetries (or near-symmetries). Our algorithm maps any k-local Hamiltonian to a graph G=(V,E) with |V|=O(poly(n)) where n is the number of qubits. Given the well-known result of Babai, we exploit graph isomorphism to study the automorphisms of G and arrive at an algorithm quasi-polynomial in |V| for producing samples from the effective subspace eigenstates of H. Our results rule out exponential separations between stoquastic AQC and classical computation that arise from hidden symmetries in k-local Hamiltonians. Furthermore, our graph representation of H is not limited to stoquastic Hamiltonians and may rule out corresponding obstructions in non-stoquastic cases, or be useful in studying additional properties of k-local Hamiltonians.

%8 4/21/2020 %G eng %U https://arxiv.org/abs/2004.08681 %0 Journal Article %D 2020 %T Optimal Measurement of Field Properties with Quantum Sensor Networks %A Timothy Qian %A Jacob Bringewatt %A Igor Boettcher %A Przemyslaw Bienias %A Alexey V. Gorshkov %XWe consider a quantum sensor network of qubit sensors coupled to a field f(x⃗ ;θ⃗ ) analytically parameterized by the vector of parameters θ⃗ . The qubit sensors are fixed at positions x⃗ 1,…,x⃗ d. While the functional form of f(x⃗ ;θ⃗ ) is known, the parameters θ⃗ are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function q(θ⃗ ) of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.

%8 11/2/2020 %G eng %U https://arxiv.org/abs/2011.01259 %0 Journal Article %J Phys. Rev. A %D 2019 %T Polynomial Time Algorithms for Estimating Spectra of Adiabatic Hamiltonians %A Jacob Bringewatt %A William Dorland %A Stephen P. Jordan %XMuch research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians with Hamming symmetric potentials, such as the well studied "spike" example. Due to the large amount of symmetry in these potentials such problems are readily open to analysis both analytically and computationally. However, more realistic potentials do not have such a high degree of symmetry and may have many local minima. Here we present a somewhat more realistic class of problems consisting of many individually Hamming symmetric potential wells. For two or three such wells we demonstrate that such a problem can be solved exactly in time polynomial in the number of qubits and wells. For greater than three wells, we present a tight binding approach with which to efficiently analyze the performance of such Hamiltonians in an adiabatic computation. We provide several basic examples designed to highlight the usefulness of this toy model and to give insight into using the tight binding approach to examining it, including: (1) adiabatic unstructured search with a transverse field driver and a prior guess to the marked item and (2) a scheme for adiabatically simulating the ground states of small collections of strongly interacting spins, with an explicit demonstration for an Ising model Hamiltonian.

%B Phys. Rev. A %V 100 %8 10/1/2020 %G eng %U https://arxiv.org/abs/1905.07461 %N 032336 %R https://doi.org/10.1103/PhysRevA.100.032336 %0 Journal Article %J Physical Review A %D 2018 %T Diffusion Monte Carlo Versus Adiabatic Computation for Local Hamiltonians %A Jacob Bringewatt %A William Dorland %A Stephen P. Jordan %A Alan Mink %XMost research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real, nonnegative amplitudes. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k-SAT problems, use k-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n-body interactions. Here we present a new 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

%B Physical Review A %V 97 %P 022323 %8 2018/02/15 %G eng %U https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022323 %N 2 %R 10.1103/PhysRevA.97.022323 %0 Journal Article %D 2018 %T Study of radon reduction in gases for rare event search experiments %A K. Pushkin %A C. Akerlof %A D. Anbajagane %A J. Armstrong %A M. Arthurs %A Jacob Bringewatt %A T. Edberg %A C. Hall %A M. Lei %A R. Raymond %A M. Reh %A D. Saini %A A. Sander %A J. Schaefer %A D. Seymour %A N. Swanson %A Y. Wang %A W. Lorenzon %XThe noble elements, argon and xenon, are frequently employed as the target and event detector for weakly interacting particles such as neutrinos and Dark Matter. For such rare processes, background radiation must be carefully minimized. Radon provides one of the most significant contaminants since it is an inevitable product of trace amounts of natural uranium. To design a purification system for reducing such contamination, the adsorption characteristics of radon in nitrogen, argon, and xenon carrier gases on various types of charcoals with different adsorbing properties and intrinsic radioactive purities have been studied in the temperature range of 190-295 K at flow rates of 0.5 and 2 standard liters per minute. Essential performance parameters for the various charcoals include the average breakthrough times (