01817nas a2200181 4500008004100000245006100041210006100102260001400163520125300177100003201430700001901462700002201481700002201503700002001525700002801545700002501573856003701598 2024 eng d00aEstimation of Hamiltonian parameters from thermal states0 aEstimation of Hamiltonian parameters from thermal states c1/18/20243 a
We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term's degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/n−−√, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g. a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.
1 aGarcía-Pintos, Luis, Pedro1 aBharti, Kishor1 aBringewatt, Jacob1 aDehghani, Hossein1 aEhrenberg, Adam1 aHalpern, Nicole, Yunger1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2401.1034301434nas a2200145 4500008004100000245005900041210005800100260001400158490000600172520100600178100002001184700002201204700002501226856003701251 2023 eng d00aMinimum-entanglement protocols for function estimation0 aMinimumentanglement protocols for function estimation c9/29/20230 v53 aWe 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 network applications. We demonstrate how to select different protocols from this family under various constraints. Focusing primarily 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 entanglement. We prove that the protocols which satisfy these conditions use the minimum amount of entanglement possible, even when given access to arbitrary controls and ancilla. Our protocols require some amount of time-dependent control, and we show that a related class of time-independent protocols fail to achieve optimal scaling for generic functions.
1 aEhrenberg, Adam1 aBringewatt, Jacob1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2110.0761301544nas a2200133 4500008004100000024001800041245007500059210006900134260001400203520111400217100002201331700002001353856003701373 2023 eng d aUMD-PP-022-0600aParallelization techniques for quantum simulation of fermionic systems0 aParallelization techniques for quantum simulation of fermionic s c3/30/20233 aMapping 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.
1 aBringewatt, Jacob1 aDavoudi, Zohreh uhttps://arxiv.org/abs/2207.1247002470nas a2200169 4500008004100000245007100041210006900112260001400181520193200195100002202127700002202149700002402171700002302195700002502218700002002243856003702263 2023 eng d00aQuantum Algorithms for Simulating Nuclear Effective Field Theories0 aQuantum Algorithms for Simulating Nuclear Effective Field Theori c12/8/20233 aQuantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources, we employ state-of-the-art Hamiltonian-simulation methods, and conduct a thorough algorithmic analysis, to estimate the qubit and gate costs to simulate low-energy effective field theories (EFTs) of nuclear physics. In particular, within the framework of nuclear lattice EFT, we obtain simulation costs for the leading-order pionless and pionful EFTs. We consider both static pions represented by a one-pion-exchange potential between the nucleons, and dynamical pions represented by relativistic bosonic fields coupled to non-relativistic nucleons. We examine the resource costs for the tasks of time evolution and energy estimation for physically relevant scales. We account for model errors associated with truncating either long-range interactions in the one-pion-exchange EFT or the pionic Hilbert space in the dynamical-pion EFT, and for algorithmic errors associated with product-formula approximations and quantum phase estimation. Our results show that the pionless EFT is the least costly to simulate and the dynamical-pion theory is the costliest. We demonstrate how symmetries of the low-energy nuclear Hamiltonians can be utilized to obtain tighter error bounds on the simulation algorithm. By retaining the locality of nucleonic interactions when mapped to qubits, we achieve reduced circuit depth and substantial parallelization. We further develop new methods to bound the algorithmic error for classes of fermionic Hamiltonians that preserve the number of fermions, and demonstrate that reasonably tight Trotter error bounds can be achieved by explicitly computing nested commutators of Hamiltonian terms. This work highlights the importance of combining physics insights and algorithmic advancement in reducing quantum-simulation costs.
1 aWatson, James, D.1 aBringewatt, Jacob1 aShaw, Alexander, F.1 aChilds, Andrew, M.1 aGorshkov, Alexey, V.1 aDavoudi, Zohreh uhttps://arxiv.org/abs/2312.0534401594nas a2200217 4500008004100000245004000041210004000081260001400121520100000135100002101135700001601156700001501172700002201187700002001209700001901229700001901248700002501267700002201292700002501314856003701339 2023 eng d00aQuantum Sensing with Erasure Qubits0 aQuantum Sensing with Erasure Qubits c10/2/20233 aThe dominant noise in an "erasure qubit" is an erasure -- a type of error whose occurrence and location can be detected. Erasure qubits have potential to reduce the overhead associated with fault tolerance. To date, research on erasure qubits has primarily focused on quantum computing and quantum networking applications. Here, we consider the applicability of erasure qubits to quantum sensing and metrology. We show theoretically that, for the same level of noise, an erasure qubit acts as a more precise sensor or clock compared to its non-erasure counterpart. We experimentally demonstrate this by artificially injecting either erasure errors (in the form of atom loss) or dephasing errors into a differential optical lattice clock comparison, and observe enhanced precision in the case of erasure errors for the same injected error rate. Similar benefits of erasure qubits to sensing can be realized in other quantum platforms like Rydberg atoms and superconducting qubits
1 aNiroula, Pradeep1 aDolde, Jack1 aZheng, Xin1 aBringewatt, Jacob1 aEhrenberg, Adam1 aCox, Kevin, C.1 aThompson, Jeff1 aGullans, Michael, J.1 aKolkowitz, Shimon1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2310.0151201324nas a2200145 4500008004100000024001900041245006400060210006400124260001400188520087300202100002201075700002401097700002001121856003701141 2023 eng d aIQuS@UW-21-04800aRandomized measurement protocols for lattice gauge theories0 aRandomized measurement protocols for lattice gauge theories c3/27/20233 aRandomized 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.
1 aBringewatt, Jacob1 aKunjummen, Jonathan1 aMueller, Niklas uhttps://arxiv.org/abs/2303.1551901752nas a2200133 4500008004100000245009000041210007000131260001400201520130500215100002201520700002001542700001901562856003701581 2023 eng d00aOn the stability of solutions to Schrödinger's equation short of the adiabatic limit0 astability of solutions to Schrödingers equation short of the adi c3/23/20233 aWe 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.
1 aBringewatt, Jacob1 aJarret, Michael1 aMooney, T., C. uhttps://arxiv.org/abs/2303.1347801457nas a2200157 4500008004100000245003100041210003100072260001500103490000800118520103500126653002701161653003101188100002201219700002101241856003701262 2022 eng d00aSimultaneous Stoquasticity0 aSimultaneous Stoquasticity c06/09/20220 v1053 aStoquastic 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.
10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aBringewatt, Jacob1 aBrady, Lucas, T. uhttps://arxiv.org/abs/2202.0886301652nas a2200133 4500008004100000245005900041210005900100260001500159520124500174100001901419700002201438700002101460856003701481 2021 eng d00aLefschetz Thimble Quantum Monte Carlo for Spin Systems0 aLefschetz Thimble Quantum Monte Carlo for Spin Systems c10/20/20213 aMonte 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.
1 aMooney, T., C.1 aBringewatt, Jacob1 aBrady, Lucas, T. uhttps://arxiv.org/abs/2110.1069901637nas a2200181 4500008004100000022001400041245010300055210006900158260001300227490000600240520106000246100002201306700002001328700002101348700002401369700002501393856003701418 2021 eng d a2643-156400aProtocols for estimating multiple functions with quantum sensor networks: Geometry and performance0 aProtocols for estimating multiple functions with quantum sensor c5/3/20210 v33 aWe 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.
1 aBringewatt, Jacob1 aBoettcher, Igor1 aNiroula, Pradeep1 aBienias, Przemyslaw1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2104.0954001342nas a2200169 4500008004100000245007000041210006900111260001400180520083000194100002201024700001301046700002001059700001801079700001701097700002101114856003701135 2020 eng d00aConfronting lattice parton distributions with global QCD analysis0 aConfronting lattice parton distributions with global QCD analysi c10/1/20203 aWe 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
1 aBringewatt, Jacob1 aSato, N.1 aMelnitchouk, W.1 aQiu, Jian-Wei1 aSteffens, F.1 aConstantinou, M. uhttps://arxiv.org/abs/2010.0054801710nas a2200121 4500008004100000245011300041210006900154260001400223520127200237100002201509700002001531856003701551 2020 eng d00aEffective gaps are not effective: quasipolynomial classical simulation of obstructed stoquastic Hamiltonians0 aEffective gaps are not effective quasipolynomial classical simul c4/21/20203 aAll 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.
1 aBringewatt, Jacob1 aJarret, Michael uhttps://arxiv.org/abs/2004.0868101302nas a2200157 4500008004100000245007300041210006900114260001400183520080100197100001800998700002201016700002001038700002401058700002501082856003701107 2020 eng d00aOptimal Measurement of Field Properties with Quantum Sensor Networks0 aOptimal Measurement of Field Properties with Quantum Sensor Netw c11/2/20203 aWe 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.
1 aQian, Timothy1 aBringewatt, Jacob1 aBoettcher, Igor1 aBienias, Przemyslaw1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2011.0125901973nas a2200145 4500008004100000245008000041210006900121260001400190490000800204520151100212100002201723700002101745700002401766856003701790 2019 eng d00aPolynomial Time Algorithms for Estimating Spectra of Adiabatic Hamiltonians0 aPolynomial Time Algorithms for Estimating Spectra of Adiabatic H c10/1/20200 v1003 aMuch 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.
1 aBringewatt, Jacob1 aDorland, William1 aJordan, Stephen, P. uhttps://arxiv.org/abs/1905.0746101752nas a2200169 4500008004100000245007800041210006900119260001500188300001100203490000700214520121000221100002201431700002101453700002401474700001501498856006901513 2018 eng d00aDiffusion Monte Carlo Versus Adiabatic Computation for Local Hamiltonians0 aDiffusion Monte Carlo Versus Adiabatic Computation for Local Ham c2018/02/15 a0223230 v973 aMost 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.
1 aBringewatt, Jacob1 aDorland, William1 aJordan, Stephen, P.1 aMink, Alan uhttps://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.02232310586nas a2200301 4500008004100000245007200041210006900113520978200182100001609964700001609980700001909996700001810015700001610033700002210049700001510071700001310086700001210099700001610111700001210127700001410139700001510153700001710168700001610185700001610201700001310217700001710230856003710247 2018 eng d00aStudy of radon reduction in gases for rare event search experiments0 aStudy of radon reduction in gases for rare event search experime3 aThe 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 (