Related papers: Locality optimization for parent Hamiltonians of T…

We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are…

We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in…

A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only…

An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum…

We construct a family of rotationally invariant, local, S=1/2 Klein Hamiltonians on various lattices that exhibit ground state manifolds spanned by nearest-neighbor valence bond states. We show that with selected perturbations such models…

The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions…

Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a…

We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states…

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…

Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be…

We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual…

This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling…

An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an \it unbiased \rm numerical optimization scheme to systematically…

We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.…

In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an…

Lattice quantum field theory calculations may potentially combine the advantages of Hamiltonian formulations with the scalability and control of conventional Lagrangian frameworks. However, such hybrid approaches need to consider (1) the…

We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of…

Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior.…

Fault tolerant quantum simulation via the phase estimation algorithm and qubitization has a T-gate count that scales proportionally to the 1-norm of the Hamiltonian, the cost of block encoding the Hamiltonian, and inversely proportionally…

Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…