arXiv subjects

Jacob Bringewatt

Publications and source records attributed to Jacob Bringewatt.

At least 19 recordsLinked to original sources

arXiv2026

Multiparameter function estimation for general Hamiltonians

Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cram\'er-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems.

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arXiv2026

Butterfly Echo Protocol for Axis-Agnostic Heisenberg-Limited Metrology

The extreme sensitivity of chaotic systems to external perturbations makes them natural candidates for sensing applications. We propose a single-shot echo-based protocol for estimating small rotations about an unknown axis that leverages random symmetric probe states prepared via chaotic dynamics. In contrast to previous protocols for this axis-agnostic rotation sensing problem that depend on difficult-to-prepare anticoherent states, the random probe states used in our protocol can be prepared via constant-depth chaotic circuits composed of random one-axis twisting pulses. Further, the signal of interest can be extracted simply by measuring the total spin polarization. We demonstrate analytically that our protocol achieves Heisenberg scaling relative to an arbitrary rotation axis that need not be a priori known. We also investigate the effects of collective and single-particle dephasing in our protocol using analytical and numerical tools. While the requirements on dephasing rates to maintain Heisenberg sensitivity are strict, they are achievable in near-term experiments, for instance, in magnetometric rotosensing with high-spin lanthanide atoms such as dysprosium-164.

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arXiv2026

A New Angle on Quantum Subspace Diagonalization for Quantum Chemistry

Quantum subspace diagonalization and quantum Krylov algorithms offer a feasible, pre- or early-fault tolerant alternative to quantum phase estimation for using quantum computers to estimate the low-lying spectra of quantum systems. However, despite promising proof-of-principle results, such methods suffer from high sensitivity to noise (including intrinsic sources such as sampling noise), making their utility for realistic industry-relevant problems an open question. To improve the potential applicability of such methods, we introduce a new variant of thresholding for noisy generalized eigenvalue problems that arise in quantum subspace diagonalization that has the potential to better control sensitivity to noise. Our approach leverages eigenvector-preserving transformations (rotations) of the generalized eigenvalue problem prior to thresholding. We study this effect in practical settings by applying this rotation thresholding scheme to an iterative quantum Krylov algorithm for several chemical systems, including the industry-relevant Fe(III)-NTA chelate complex. We develop a particular heuristic to select the rotation angle from noisy data and find for certain systems and noise regimes that the samples required to reach a target error for ground state estimation can be reduced by a factor of up to 100. Furthermore, with oracle access to the optimal transformation, more dramatic improvements are possible and we observe reductions in sample requirements by up to $10^4$, motivating the continued development of methods that can realize these improvements in practice. While we develop our approach in the context of quantum subspace diagonalization, the improved thresholding scheme we develop could be advantageous in any context where one must solve noisy, ill-conditioned generalized eigenvalue problems.

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arXiv2025

Classical shadows for sample-efficient measurements of gauge-invariant observables

Classical shadows provide a versatile framework for estimating many properties of quantum states from repeated, randomly chosen measurements without requiring full quantum state tomography. When prior information is available, such as knowledge of symmetries of states and operators, this knowledge can be exploited to significantly improve sample efficiency. In this work, we develop three classical shadow protocols for $\mathbb{Z}_2$ lattice gauge theory, where a dual formulation enables a rigorous analysis of resource requirements, including both circuit depth and sample complexity. Our approaches can offer exponential improvements in sample complexity over symmetry-agnostic methods, albeit at the cost of increased circuit complexity. While our analysis is restricted to $\mathbb{Z}_2$ lattice gauge theory, our approach offers a blueprint for similar protocols for more general lattice gauge theory models which are currently at the forefront of quantum simulation efforts.

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arXiv2025

Optimally learning functions in interacting quantum sensor networks

Estimating extensive combinations of local parameters in distributed quantum systems is a central problem in quantum sensing, with applications ranging from magnetometry to timekeeping. While optimal strategies are known for sensing non-interacting Hamiltonians in quantum sensor networks, fundamental limits in the presence of uncontrolled interactions remain unclear. Here, we establish optimal bounds and protocols for estimating a linear combination of local parameters of Hamiltonians with arbitrary, unknown interactions. In the process, we more generally establish bounds for learning any linear combination of Hamiltonian coefficients for arbitrary, commuting terms. Our results unify and extend existing bounds for non-interacting qubits and multimode interferometers, providing a general framework for distributed sensing and Hamiltonian learning in realistic many-body systems.

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arXiv2025

Lieb-Mattis states for robust entangled differential phase sensing

We explore a two-node, entanglement-enhanced sensor network for differential phase sensing that exploits decoherence-free subspaces to suppress common-mode noise, a primary limitation of many state-of-the-art quantum sensors. We identify a class of entangled states that, while not strictly optimal, achieve the same asymptotic sensitivity scaling as optimal states and can be prepared efficiently from initially unentangled atomic ensembles. Importantly, the preparation time decreases with increasing system size. This makes the states compatible with realistic noise processes in present-day quantum sensors that operate with large particle numbers but lack full error correction. We illustrate these ideas using two cavity-mediated preparation protocols: (i) coherent, unitary entanglement generation analogous to bosonic two-mode squeezing, yielding Heisenberg scaling; and (ii) dissipative preparation via collective emission into a shared cavity mode, providing a square-root improvement beyond the standard quantum limit. Numerical simulations show that both approaches remain effective at experimentally realistic cavity cooperativities, establishing a practical path toward scalable, quantum-enhanced differential phase sensing.

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arXiv2024

Exponential entanglement advantage in sensing correlated noise

In this work, we propose a new form of exponential quantum advantage in the context of sensing correlated noise. Specifically, we focus on the problem of estimating parameters associated with Lindblad dephasing dynamics, and show that entanglement can lead to an exponential enhancement in the sensitivity (as quantified via quantum Fisher information of the sensor state) for estimating a small parameter characterizing the deviation of system Lindbladians from a class of maximally correlated dephasing dynamics. This result stands in stark contrast with previously studied scenarios of sensing uncorrelated dephasing noise, where one can prove that entanglement does not lead to an advantage in the signal-to-noise ratio. Our work thus opens a novel pathway towards achieving entanglement-based sensing advantage, which may find applications in characterizing decoherence dynamics of near-term quantum devices. Further, our approach provides a potential quantum-enhanced probe of many-body correlated phases by measuring noise generated by a sensing target. We also discuss realization of our protocol using near-term quantum hardware.

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arXiv2024

Generalized geometric speed limits for quantum observables

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension $\geq 3$, tighten existing bounds -- in some cases by an arbitrarily large multiplicative constant. The generalized bounds can be used to design "fast" Hamiltonians that enable the rapid driving of the expectation values of observables with potential applications e.g.~to quantum annealing, optimal control, variational quantum algorithms, and quantum sensing. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. Possibly of independent interest, along the way to one of our bounds we derive a novel upper bound on the generalized quantum Fisher information with respect to time (including the standard symmetric logarithmic derivative quantum Fisher information) for unitary dynamics in terms of the variance of the associated Hamiltonian and the condition number of the density matrix.

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arXiv2024

Resilience-Runtime Tradeoff Relations for Quantum Algorithms

A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer's potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize the resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm's number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.

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arXiv2024

Optimal function estimation with photonic quantum sensor networks

The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here, we resolve a number of open questions that arise when extending this framework to Mach-Zehnder interferometers and quadrature displacement sensing. In particular, we derive lower bounds on the achievable mean square error in estimating a linear function of either local phase shifts or quadrature displacements. In the case of local phase shifts, these results prove, and somewhat generalize, a conjecture by Proctor et al. [arXiv:1702.04271 (2017)]. For quadrature displacements, we extend proofs of lower bounds to the case of arbitrary linear functions. We provide optimal protocols achieving these bounds up to small (multiplicative) constants and describe an algebraic approach to deriving new optimal protocols, possibly subject to additional constraints. Using this approach, we prove necessary conditions for the amount of entanglement needed for any optimal protocol for both local phase and displacement sensing.

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arXiv2024

Estimation of Hamiltonian parameters from thermal states

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 $1/\sqrt{n}$, 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.

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arXiv2023

Quantum Algorithms for Simulating Nuclear Effective Field Theories

Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources to realize this potential, 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. Within the framework of nuclear lattice EFT, we obtain simulation costs for the leading-order pionless and pionful EFTs. For the latter, 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. Within these models, 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. We find that the pionless EFT is the least costly to simulate, followed by the one-pion-exchange theory, then the dynamical-pion theory. We demonstrate how symmetries of the low-energy nuclear Hamiltonians can be utilized to obtain tighter error bounds. By retaining the locality of nucleonic interactions when mapped to qubits, we achieve reduced circuit depth and substantial parallelization. In the process, we develop new methods to bound the algorithmic error for classes of fermionic number-preserving Hamiltonians, and obtain tighter Trotter error bounds by explicitly computing nested commutators of Hamiltonian terms. Compared to previous estimates for the pionless EFT, our results represent an improvement by several orders of magnitude.

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arXiv2023

Quantum Sensing with Erasure Qubits

The 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

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arXiv2023

Randomized measurement protocols for lattice gauge theories

Randomized 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. Crucially, unlike symmetry-blind randomized measurement protocols, these latter tasks can be performed without relearning symmetries via full reconstruction of the density matrix.

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arXiv2023

On the stability of solutions to Schr\"{o}dinger's equation short of the adiabatic limit

We prove an adiabatic theorem that applies at timescales short of the typical 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 subspace, (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 is close to that of the unperturbed Hamiltonian, and (4) bound leakage effects in terms of the global spectral gap when the Hamiltonian is ``stoquastic'' (a $Z$-matrix). Our results can help explain quantum annealing protocols that exhibit faster convergence than is 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, when our results apply, convergence to particular global target states can be understood as the result of local dynamics.

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arXiv2022

Lower Bounds on Quantum Annealing Times

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.

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arXiv2022

Parallelization techniques for quantum simulation of fermionic systems

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.

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arXiv2022

Simultaneous Stoquasticity

Stoquastic 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.

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