Abstract
We develop a scheme for engineering genuine thermal states in analog quantum simulation platforms by coupling local degrees of freedom to driven, dissipative ancilla pseudospins. We demonstrate the scheme in a many-body quantum spin lattice simulation setting. A Born-Markov master equation describing the dynamics of the many-body system is developed, and we show that if the ancilla energies are periodically modulated, with a carefully chosen hierarchy of timescales, one can effectively thermalize the many-body system. Through analysis of the time-dependent dynamical generator, we determine the conditions under which the true thermal state is an approximate dynamical fixed point for general system Hamiltonians. Finally, we evaluate the thermalization protocol through numerical simulation and discuss prospects for implementation on current quantum simulation hardware.
Highlights
Preparation of mixed states of many-body systems, thermal states at low temperatures, is valuable for many scientific and algorithmic tasks, e.g., calculating finitetemperature response of materials, Gibbs sampling for machine learning, and optimization [1,2,3]
As we prove in Appendix A, within this parameter regime, we can derive a time-dependent, Markovian master equation describing the dynamics of the principal spins alone: dρ(t ) dt g2m m=1 ω λtm (ω )
We have developed an alternative approach to engineered thermalization with reduced resource counts by introducing a periodically driven and dissipated ancilla degrees of freedom (DOF), such that a single ancilla is resonant with different transitions at different times
Summary
Preparation of mixed states of many-body systems, thermal states at low temperatures, is valuable for many scientific and algorithmic tasks, e.g., calculating finitetemperature response of materials, Gibbs sampling for machine learning, and optimization [1,2,3]. We develop a technique to engineer thermalization of many-body spin Hamiltonians based on coupling to driven, dissipative ancilla degrees of freedom (DOF) that effectively. The scheme we develop can be viewed as a protocol for filtering and transforming the structureless electromagnetic vacuum reservoir to a structured reservoir suitable for thermalizing the many-body quantum system at hand This enables thermalization using a finite number of controlled ancilla DOF. We set out to demonstrate that thermalization is possible with a reservoir composed of a small number of ancilla qudits (finitedimensional systems) when coupled with time-dependent driving and local dissipation. This significantly increases the practicality of the engineered thermalization scheme.
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