Related papers: Optimal simulation of nonlocal Hamiltonians using …
A nonlocal circulator protocol is proposed in hybrid optomechanical system. By analogy with quantum communication, using the input-output relationship, we establish the quantum channel between two optical modes with long-range. The three…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
Recent advances in model predictive control (MPC) leverage local communication constraints to produce localized MPC algorithms whose complexities scale independently of total network size. However, no characterization is available regarding…
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…
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…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
We study when a non--local unitary operation acting on two $d$--level systems can probabilistically simulate another one when arbitrary local operations and classical communication are allowed. We provide necessary and sufficient conditions…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
Since quantum feedback is based on classically accessible measurement results, it can provide fundamental insights into the dynamics of quantum systems by making available classical information on the evolution of system properties and on…
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…
We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
Evolutions of local Hamiltonians in short times are expected to remain local and thus limited. In this paper, we validate this intuition by proving some limitations on short-time evolutions of local time-dependent Hamiltonians. We show that…
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are independent of the eigenvalues and based on the algebraic-geometric invariants introduced in [1-2]. Our results indicate…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
Given a protocol ${\cal P}$ that implements multipartite quantum channel ${\cal E}$ by repeated rounds of local operations and classical communication (LOCC), we construct an alternate LOCC protocol for ${\cal E}$ in no more rounds than…