Related papers: Hamiltonian Complexity in the Thermodynamic Limit
Finding the ground state energy of electrons subject to an external electric field is a fundamental problem in computational chemistry. We prove that this electronic-structure problem, when restricted to a fixed single-particle basis and…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
We consider the geometry of quantum states associated with different classes of random matrix Hamiltonians, in particular ensembles that show integrability to chaotic transition in terms of the nearest neighbour energy level spacing…
The efficient validation of quantum devices is critical for emerging technological applications. In a wide class of use-cases the precise engineering of a Hamiltonian is required both for the implementation of gate-based quantum information…
All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition…
We consider the problem of finding the energy minimum of a complex quantum Hamiltonian by employing a non-Markovian bath prepared in a low energy state. The energy minimization problem is thus turned into a thermodynamic cooling protocol in…
The separation of internal energy into heat and work in quantum thermodynamics is a controversial issue for a long time, and we revisit and solve this problem in this work. It is shown that the Hamiltonian plays dual roles for a quantum…
We present a quantum algorithm for simulating rovibrational Hamiltonians on fault-tolerant quantum computers. The method integrates exact curvilinear kinetic energy operators and general-form potential energy surfaces expressed in a hybrid…
Free energy fixes the maximum work of a thermodynamic process once the state and Hamiltonian are specified. A work-extraction task asks a different question: how much average work can a single device realize across several preparations and…
We study the mean-field approximation of Quantum Electrodynamics, by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal-ordering or choice of bare electron/positron subspaces.…
The phase diagram of a material is of central importance to describe the properties and behaviour of a condensed matter system. We prove that the general task of determining the quantum phase diagram of a many-body Hamiltonian is…
We address the question whether the super-Heisenberg scaling for quantum estimation is realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter dependent…
Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…
We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared…
Quantum chromodynamics (QCD) describes the structure of hadrons such as the proton at a fundamental level. The precision of calculations in QCD limits the precision of the values of many physical parameters extracted from collider data. For…
The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more…
A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we demonstrate that the ground state of a topological phase itself encodes critical properties of its transition to a…
We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor XY spin chain through control of a…
Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it -- one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions.…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…