Fast Quantum Many Body State Synthesis

TL;DR

This work introduces a fast, analog approach to prepare entangled ground states of quantum many-body systems by evolving an initial fiducial state for a fixed short time under a solver Hamiltonian $H_s$ whose parameters are optimized to minimize the energy with respect to a target problem Hamiltonian $H_p$. By restricting to anisotropic XYZ Heisenberg models on graphs and using a shallow $L\le 2$ layer evolution, the authors demonstrate that a carefully chosen $H_s$ can drive the system close to the ground state in far less time than adiabatic methods. They develop a variational framework with a cost function $C(oldsymbol{J_s})=ra{oldsymbol\psi(oldsymbol{J_s})}H_p(oldsymbol{J_p})ig|oldsymbol\psi(oldsymbol{J_s}) angle$, gradients via JAX, and fidelity/gradient-based diagnostics, plus four warm-start strategies. The combination ramp (warm-start plus incremental coupling) yields the best fidelity, achieving $F\approx 0.999$ for a 10-qubit chain and $F\approx 0.99$ for a 6-qubit complete graph, indicating a viable path toward fast, scalable ground-state synthesis on analog quantum simulators. This approach complements traditional variational algorithms and could enable rapid preparation of resource states for nonequilibrium dynamics and quantum information tasks.

Abstract

Quantum Mechanical ground states of many-body systems can be important resources for various investigations: for quantum sensing, as the initial state for nonequilibrium quantum dynamics following quenches, and the simulation of quantum processes that start by coupling systems in ground states, eg, could be a process in quantum chemistry. However, to prepare ground states can be challenging; for example, requires adiabatic switching of Hamiltonian terms slower than an inverse gap, which can be time consuming and bring in decoherence. Here we investigate the possibility of preparing a many-body entangled ground state of a certain Hamiltonian, which can be called a quantum ``problem'' Hamiltonian, using the time evolution of an initial fiducial state by another ``solver'' Hamiltonian/s for a very short fixed (unit) time. The parameters of the solver Hamiltonian are optimised classically using energy minimisation as the cost function. We present a study of up to n=10 qubit many-body states prepared using this methodology.

Figures (4)

• Figure 1: An illustration of the different proposed methods for the 10 qubit chain: (1) Warm start by size expansion, (2) Incremental coupling ramp, (3) Combination Ramp, (4) Cold Start.
• Figure 2: Analog variational optimisation circuits used in this work.
• Figure 3: The data gathered for the for a 10 qubit system, arranged in chain, at the coupling stage, $J_{max}$ for the different methods, cold start, warm start, warm start with incremental coupling increase, warm start combination (a) The energy difference between the observed and known ground state energy as the number of optimisation steps (b) The beta parameter $\beta = \frac{\Delta E}{||\nabla C||}$ which the difference in the cost function over the gradient of the cost function (c) The final fidelity of the different methods, Sample size = 100
• Figure 4: The data gathered for the for a 6 qubit system, complete graph at the coupling stage, $J_{max}$ for the different methods, cold start, warm start, warm start with incremental coupling increase, warm start combination (a) The energy difference between the observed and known ground state energy as the number of optimisation steps (b) The beta parameter $\beta = \frac{\Delta E}{||\nabla C||}$ which the difference in the cost function over the gradient of the cost function (c) The final fidelity of the different methods, Sample size = 100