Related papers: Finite-dimensional approximations of generalized s…
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…
The limits of direct unitary transformation of many-fermion Hamiltonians are explored. Practical application of such transformations requires that effective many-body interactions be discarded over the course of a calculation. The…
The dynamical evolution of squeezing correlations in an ultracold Bose-Einstein distributed across two modes is investigated theoretically in the framework of the Bose-Hubbard model. It is shown that the eigenstates of the Hamiltonian do…
When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations…
We develop a truncated Hamiltonian method to investigate the dynamics of the $(1+1)d~\phi^4$ theory following quantum quenches. The results are compared to two different semi-classical approaches, the self-consistent Gaussian approximation…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
We study a variation of the Trotter-Suzuki decomposition, in which a Hamiltonian exponential is approximated by an ordered product of two-qubit operator exponentials such that the Trotter step size is enhanced for a small number of terms.…
We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a ``small subsystem'' and an infinite dimensional one -- a ``reservoir''. The operator, which we call a…
Starting from a general, microscopic fermion-to-boson mapping that preserves Hermitian conjugation, we discuss truncations of the boson Fock space basis. We give conditions under which the exact boson images of finite fermion operators are…
In the preceding Comment [1] it was claimed that the third-order Hamiltonian obtained in our original paper [2] is not Hermitian for general situations when considering time-dependence and the way of deriving the effective third-order…
We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality)…
We study the unitary dynamics and the thermalization properties of free-fermion-like Hamiltonians after a sudden quantum quench, extending the results of S. Ziraldo et al. [Phys. Rev. Lett. 109, 247205 (2012)]. With analytical and numerical…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et…
Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to…
The study of real-time dynamics of fermions remains one of the last frontiers beyond the reach of classical simulations and is key to our understanding of quantum behavior in chemistry and materials, with implications for quantum…
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…
We show how discrete squeezed states in an $N^{2}$-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum…