Variational quantum Gibbs state preparation with a truncated Taylor series

A Generalized Circuit for the Hamiltonian Dynamics Through the Truncated Series

In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we present a fixed-quantum circuit design for the simulation of the Hamiltonian dynamics, $H(t)$, through the truncated Taylor series method described by Berry et al. \cite{berry2015simulating}. The circuit is general and can be used to simulate any given matrix in the phase estimation algorithm by only changing the angle values of the quantum gates implementing t…

Eigenstate Gibbs Ensemble in Integrable Quantum Systems

The Eigenstate Thermalization Hypothesis implies that for a thermodynamically large system in one of its eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of {\it relevant} conserved quantities. In a generic system, only the energy plays that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and hence the reduced density matrix requires specification of an infinite number of parameters (Generalized Gibbs Ensemble). However, here we show by unbiase…

从纠缠态熵密度矩阵出发的广义吉布斯 Ensemble

Generalized Gibbs Ensemble from Eigenstate Entanglement Hamiltonian

本文提出通过纠缠哈密顿量超密度矩阵框架，从本征态缩减密度矩阵中自然获得GGE的守恒量，从而更准确地描述自由费米子和硬核玻色子的弛豫行为。

Gibbs phenomenon and the emergence of the steady-state in quantum transport

Simulations are increasingly employing explicit reservoirs - internal, finite regions - to drive electronic or particle transport. This naturally occurs in simulations of transport via ultracold atomic gases. Whether the simulation is numerical or physical, these approaches rely on the rapid development of the steady state. We demonstrate that steady state formation is a manifestation of the Gibbs phenomenon well-known in signal processing and in truncated discrete Fourier expansions. Each particle separately develops into an individual steady state due to the spreading of its wave packet in e…

Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization

We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision, an exponential improvement over all prior methods. The two algorithms developed in this work rely on a second quantized encoding of the wavefunction in which the state of an $N$ spin-orbital system is encoded in ${\cal …

Newton series expansion of bosonic operator functions

We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in cases where the Taylor expansion fails. For a function of number operators, such an expansion is automatically normal ordered. Applied to the Holstein-Primakoff representation of spins, the scheme yields an exact series expansion with a finite number of terms and, in addition, allows for a systematic expansion of the spin operators that respects the spin commut…

Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries

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 approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative pr…

Bounding the costs of quantum simulation of many-body physics in real space

We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system and using a high-order finite difference approximation to the kinetic energy operator. We find that our algorithm can simulate $η$ interacting particles using a number of calculations of the pairwise interactions that scales, for a fixed spatial grid spacing, as $\tilde{O}(η^2)$, versus the $\tilde{O}(η^5)$ time required by previous methods (assuming the numbe…

使用TEPID-ADAPT-VQE算法的分子激发态势能面和能量的量子模拟

Quantum simulation of molecular excited-state manifolds and energies using the TEPID-ADAPT-VQE algorithm

本文利用TEPID-ADAPT-VQE算法，通过变分对角化截断低温吉布斯态，同时制备多个激发态，在H2、LiH和线性H4分子上实现了化学精度内的激发态谱和势能曲线，并展示了其相比MORE-ADAPT仅需单一超参数的优势。