We 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. investigate degree universality extracted PDFs when experimental data are treated under same conditions within Bayesian likelihood analysis. For unpolarized sector, we find rather weak constraints current on phenomenological PDFs, difficulties describing at large spatial...

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible state much faster with more general quantum annealing protocols, rigorous results beyond regime are rare. Here, we provide such result, deriving lower bounds on successfully perform annealing. asymptotically saturated by three toy models where fast schedules known: Roland and Cerf unstructured search model, Hamming spike problem, ferromagnetic p-spin model. Our...

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state or extract the properties of quantum states. While unraveling intricate structure states is generally difficult resource-intensive, systems in nature often tightly constrained by symmetries. This can be leveraged symmetry-conscious schemes we propose, yielding clear advantages over symmetry-blind randomization such...

We upper bound and lower the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states a known temperature. The bounds depend on uncertainty in term that contains term's degree noncommutativity full Hamiltonian: higher commuting operators lead to better precision. apply show there exist entangled such be estimated error decreases faster than 1/sqrt[n], beating standard quantum limit. This result governs Hamiltonians where scalar...

The dominant noise in an ``erasure qubit'' is 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 has primarily focused quantum computing networking applications. Here, we consider applicability sensing metrology. We show theoretically that, for same level noise, qubit acts as a more precise sensor or clock compared its nonerasure counterpart. experimentally...

We consider a quantum sensor network of qubit sensors coupled to field f ( x ; θ ) analytically parameterized by the vector parameters . The are fixed at positions x1, …, xd While functional form is known, not. derive saturable bounds on precision measuring an arbitrary analytic function q( these and construct optimal protocols that achieve bounds. Our results obtained from combination techniques information theory duality theorems for linear programming. They can be applied many problems,...

A leading approach to algorithm design aims minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing may decrease chance errors. This paradigm is particularly prevalent quantum computing, where gates are hard implement and noise rapidly decreases a computer's potential outperform classical computers. Here, we find minimizing can be counterproductive, sensitivity induces errors when running non-ideal conditions. To show this, develop framework...

We consider the problem of estimating multiple analytic functions a set local parameters via qubit sensors in quantum sensor network. To address this problem, we highlight generalization symmetric performance bounds Rubio et al., [J. Phys. A 53, 344001 (2020)] and develop an optimized sequential protocol for measuring such functions. compare both approaches to one another protocols that do not utilize entanglement, emphasizing geometric significance coefficient vectors measured determining...

We derive a family of optimal protocols, in the sense saturating quantum Cram\'er-Rao bound, for measuring linear combination $d$ field amplitudes with sensor networks, key subprotocol general network applications. demonstrate how to select different protocols from this under various constraints. Focusing primarily on entanglement-based constraints, we prove surprising result that highly entangled states are not necessary achieve optimality many cases. Specifically, and sufficient conditions...

Most 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 efficiently simulate Hamiltonians. Recent results have given counterexamples in which path integral and diffusion fail to do so. However, most algorithms, such as for solving MAX-k-SAT problems, use k-local whereas our previous counterexample involved...

The problem of optimally measuring an analytic function unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation noise characterization. Here, we resolve number open questions that arise when extending this framework Mach-Zehnder interferometers and quadrature displacement sensing. In particular, derive lower bounds on the achievable mean square error in estimating linear either phase shifts or displacements. case...

Leveraging quantum information geometry, we derive generalized speed limits on the rate of change expectation values observables. These bounds subsume and, for Hilbert space dimension $\geq 3$, tighten existing -- in some cases by an arbitrarily large multiplicative constant. The can be used to design "fast" Hamiltonians that enable rapid driving observables with potential applications e.g.~to annealing, optimal control, variational algorithms, and sensing. Our theoretical results are...

Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down their convergence value. While solving the problem is generically NP hard, many techniques exist mitigating specific cases; particular, technique of deforming simulation's plane integration onto Lefschetz thimbles (complex hypersurfaces stationary phase) has seen significant success context field theories. We extend this methodology...

All known examples suggesting an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (StoqAQC) exploit symmetries that constrain dynamics to effective, symmetric subspaces. The produce large effective eigenvalue gaps, which in turn make computation efficient. We present a algorithm subexponentially sample from subspace of any k-local Hamiltonian H, without priori knowledge its (or near symmetries). Our maps graph G=(V,E) with...

Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With goal of understanding necessary quantum resources, we employ state-of-the-art Hamiltonian-simulation methods, and conduct a thorough algorithmic analysis, estimate qubit gate costs low-energy effective field theories (EFTs) physics. In particular, within framework lattice EFT, obtain simulation for leading-order pionless pionful EFTs. We consider both static pions represented by...

Addressing the computational power of adiabatic quantum algorithms is a big challenge and simplified symmetric systems are often used to advance in this arena. Here, more realistic less symmetrical system analyzed using tight-binding approach, toy model constructed provide insight into two traditional problems: search an unstructured environment simulation ground states.

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state or extract the properties of quantum states. While unraveling intricate structure states is generally difficult resource-intensive, systems in nature often tightly constrained by symmetries. This can be leveraged symmetry-conscious schemes we propose, yielding clear advantages over symmetry-blind randomization such...

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states a known temperature. The bounds depend on uncertainty in term that contains term's degree noncommutativity full Hamiltonian: higher commuting operators lead to better precision. apply show there exist entangled such be estimated error decreases faster than $1/\sqrt{n}$, beating standard quantum limit. This result governs Hamiltonians where...

The problem of optimally measuring an analytic function unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation noise characterization. Here we resolve number open questions that arise when extending this framework Mach-Zehnder interferometers and quadrature displacement sensing. In particular, derive lower bounds on the achievable mean square error in estimating linear either phase shifts or displacements. case...

In this work, we propose a new form of exponential quantum advantage in the context sensing correlated noise. Specifically, focus on problem estimating parameters associated with Lindblad dephasing dynamics, and show that entanglement can lead to an enhancement sensitivity (as quantified via Fisher information sensor state) for small parameter characterizing deviation system Lindbladians from class maximally dynamics. This result stands stark contrast previously studied scenarios...

A leading approach to algorithm design aims minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing may decrease chance errors. This paradigm is particularly prevalent quantum computing, where gates are hard implement and noise rapidly decreases a computer's potential outperform classical computers. Here, we find minimizing can be counterproductive, sensitivity induces errors when running non-ideal conditions. To show this, develop framework...