Related papers: Hamiltonian Locality Testing via Trotterized Posts…
The nature of randomness and complexity growth in systems governed by unitary dynamics is a fundamental question in quantum many-body physics. This problem has motivated the study of models such as local random circuits and their…
This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve…
We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…
We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial state, i.e., making a round trip along the great circle over S^2, must have a lower bound in quantum mechanics, if…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…
The quantum k-Local Hamiltonian problem is a natural generalization of classical constraint satisfaction problems (k-CSP) and is complete for QMA, a quantum analog of NP. Although the complexity of k-Local Hamiltonian problems has been well…
Local non-Hermitian (NH) quantum systems generically exhibit breakdown of Lieb-Robinson (LR) bounds, motivating study of whether new locality measures might shed light not seen by existing measures. In this paper we extend the standard…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…
Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
A quantum-mechanical Hamiltonian with a gravitational potential is derived in the framework of local times. This Hamiltonian is the one used by E. H. Lieb (Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and…
The nonrelativistic limit of nonlocal modifications to the Klein Gordon operator is studied, and the experimental possibilities of casting stringent constraints on the nonlocality scale via planned and/or current optomechanical experiments…
A central result in the study of Quantum Hamiltonian Complexity is that the k-Local hamiltonian problem is QMA-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above…
The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent…
For any pair of quantum states, an initial state |I> and a final quantum state |F>, in a Hilbert space, there are many Hamiltonians H under which |I> evolves into |F>. Let us impose the constraint that the difference between the largest and…
Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols…
Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for…