Related papers: When a local Hamiltonian must be frustration-free
The goal of our work is to characterize the landscape of the frustration-free quantum spin models over the Cayley graph of a finitely generated group $G$. This is achieved by establishing $G$-equivariant morphisms from the partially ordered…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
Our current understanding of quantum chaos in many-body quantum systems hinges on the random matrix theory(RMT) behavior of eigenstates and their energy level statistics. Although RMT has been remarkably successful in describing `coarse'…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
We consider simulating an $n$-qubit Hamiltonian with nearest-neighbor interactions evolving for time $t$ on a quantum computer. We show that this simulation has gate complexity $(nt)^{1+o(1)}$ using product formulas, a straightforward…
We point out that for a large class of parametrized theories, there is a constant in the constrained Hamiltonian which drops out of the classical equations of motion in configuration space. Examples include the mass of a relativistic…
Unspeakable coherence is a key feature separating quantum and classical physics. Modelled as asymmetry with respect to a continuous transformation generated by a physically relevant observable, such as the Hamiltonian or angular moment,…
Recent work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
Symmetry is a guiding principle in physics that allows to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role because it protects topological…
A book about turning high-degree optimization problems into quadratic optimization problems that maintain the same global minimum (ground state). This book explores quadratizations for pseudo-Boolean optimization, perturbative gadgets used…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian $H$. This is a central problem in physics with vast applications in many-body systems and…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians,…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its ground-state coincides with an excited-state of the…