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arXiv:2409.06012 · Physical Review Letters

Accelerating Dissipative State Preparation with Adaptive Open Quantum Dynamics

Andrew Pocklington, Aashish A. Clerk

Published Feb 6, 2025• 9 citations
arXivHTMLPDF

Abstract

A wide variety of dissipative state preparation schemes suffer from a basic time-entanglement tradeoff: the more entangled the steady state, the slower the relaxation to the steady state. Here, we show how a minimal kind of adaptive dynamics can be used to completely circumvent this tradeoff, and allow the dissipative stabilization of maximally entangled states with a finite timescale. Our approach takes inspiration from simple fermionic stabilization schemes, which surprisingly are immune to entanglement-induced slowdown. We describe schemes for accelerated stabilization of many-body entangled qubit states (including spin squeezed states), both in the form of discretized Floquet circuits, as well as continuous time dissipative dynamics. Our ideas are compatible with a number of experimental platforms.

DOI
10.1103/physrevlett.134.050603

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A wide variety of dissipative state preparation schemes suffer from a basic time-entanglement tradeoff: the more entangled the steady state, the slower the relaxation to the steady state. Here, we show how a minimal kind of adaptive dynamics can be used to completely circumvent this tradeoff, and allow the dissipative stabilization of maximally entangled states with a finite timescale. Our approach takes inspiration from simple fermionic stabilization schemes, which surprisingly are immune to entanglement-induced slowdown. We describe schemes for accelerated stabilization of many-body entangled qubit states (including spin squeezed states), both in the form of discretized Floquet circuits, as well as continuous time dissipative dynamics. Our ideas are compatible with a number of experimental platforms.
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We demonstrate a surprising connection between pure steady-state entanglement and relaxation time scales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems, A and B , interact locally with a common dissipative environment. This setup also encompasses a broad class of adaptive quantum dynamics based on continuous measurement and feedback. As steady-state entanglement increases, there is generically an emergent strong symmetry that leads to a dynamical slow-down. Using this, we can prove rigorous bounds on relaxation times set by steady-state entanglement. We also find that this time must necessarily diverge for maximal entanglement. To test our bound, we consider the dynamics of a random ensemble of local Lindbladians that support pure steady states, finding that the bound does an excellent job of predicting how the dissipative gap varies with the amount of entanglement. Our work provides general insights into how dynamics and entanglement are connected in open systems and has specific relevance to quantum reservoir engineering. Published by the American Physical Society 2024
We describe an optimal-control strategy designed to accelerate the dissipative preparation of complex, highly entangled quantum many-body states. Analogous to optimal steering of isolated quantum systems, our scheme identifies control pulses that guide the evolution of open quantum systems along trajectories of instantaneous steady states while minimizing leakage resulting from non-adiabatic transitions. In many cases of interest, these control parameters can be derived analytically and without the need for computationally expensive numerical simulations of the full many-body master equation. We apply this technique for the preparation of bi- and multipartite entangled states in qubit systems coupled to a common photonic waveguide or a distributed squeezed reservoir. In both scenarios, our optimal-control strategy significantly outperforms the bare relaxation dynamics after a quench, reducing preparation times of near-maximally entangled states by orders of magnitude. This drastic speedup makes dissipative entanglement distribution protocols compatible with high-fidelity quantum information processing applications and illustrates more broadly the potential of leakage minimization for accelerating reservoir-engineering schemes.
The controlled preparation of quantum many-body states is a central challenge for quantum technologies. While preparing target states coherently is possible in principle, it is often fragile and experimentally demanding. Dissipative state preparation, where engineered environments drive the system toward desired steady states, provides a complementary and powerful paradigm. This thesis explores dissipative methods for preparing complex many-body states along three distinct directions. First, we investigate the dissipative stabilization of injective matrix product states (MPS). Injective MPS are particularly well suited for dissipative preparation because they arise as ground states of frustration-free parent Hamiltonians, allowing for tailored jump operators to steer the system directly into the target state. We showcase the surprising result that such state preparation works even in the dilute limit where steering only acts on a single link. Moreover, we introduce a formalism for engineering additional coherent interactions, extending the set of accessible states. Second, and complementary to steering, we develop and analyze a universal cooling scheme capable of preparing ground states even in frustrated quantum systems. In contrast to steering methods, universal cooling can overcome the glass floor that forbids steering methods to prepare such frustrated ground states. A key insight here is that the presented cooling scheme is completely system-agnostic making it extremely robust. Finally, we pursue dressing of the system eigenstates by means of either classical drives or coherent interactions as a means to influence the action of dissipation on the system. Focusing first on time-dependent systems, we propose a generalized numerical implementation of non-adiabatic master equations suitable for the use of optimal control tools. Additionally, we investigate how the collective coupling between a spin ensemble and a cavity can steer the system into a spin-squeezed steady state. Together, these three avenues illustrate how tailored dissipative dynamics can extend the frontier of many-body state preparation, from stabilizing injective MPS to cooling complex frustrated systems and generating non-classical steady states in the dressed framework.
We present a scheme for the dissipative preparation of an entangled steady state of two superconducting qubits in a circuit quantum electrodynamics (QED) setup. Combining resonator photon loss---a dissipative process already present in the setup---with an effective two-photon microwave drive, we engineer an effective decay mechanism which prepares a maximally entangled state of the two qubits. This state is then maintained as the steady state of the driven, dissipative evolution. The performance of the dissipative state preparation protocol is studied analytically and verified numerically. In view of the experimental implementation of the presented scheme we investigate the effects of potential experimental imperfections and show that our scheme is robust to small deviations in the parameters. We find that high fidelities with the target state can be achieved both with state-of-the-art three-dimensional, as well as with the more commonly used two-dimensional transmons. The promising results of our study thus open a route for the demonstration of a highly entangled steady state in circuit QED.