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Dissipative Preparation of Many-Body Quantum States: Towards Practical Quantum Advantage

Lin Lin

TL;DR

The paper addresses the challenge of preparing complex quantum many-body states on quantum devices by framing dissipative state preparation via Lindblad dynamics as a practical alternative to postselected coherent methods. It develops a concrete algorithmic framework using algorithmically constructed jump operators and fixed-point convergence, with rigorous discussions of simulation on fault-tolerant quantum computers, mixing times, and locality constraints. The work provides detailed schemes for ground-state, Gibbs-state, excited-state, and eigenvector preparation, including frequency-filtered jumps, KMS/Detailed Balance structure, and quantum singular value transformations, along with cost and implementation considerations. Together, these results illuminate how engineered dissipation can yield robust routes to practical quantum advantage on early fault-tolerant hardware, and they chart a path toward experimental realizations and co-design across platforms.

Abstract

While dissipation has traditionally been viewed as an obstacle to quantum coherence, it is increasingly recognized as a powerful computational resource. Dissipative protocols can prepare complex many-body quantum states by leveraging engineered system-environment interactions. This essay focuses on a class of algorithms that utilize algorithmically constructed Lindblad generators, and highlight recent advances enabling the preparation of ground and thermal states for certain non-commuting Hamiltonians with rigorous performance guarantees. We also propose extensions of these protocols to prepare excited and resonance states, which may offer new pathways toward realizing practical quantum advantage on early fault-tolerant quantum computing platforms.

Dissipative Preparation of Many-Body Quantum States: Towards Practical Quantum Advantage

TL;DR

The paper addresses the challenge of preparing complex quantum many-body states on quantum devices by framing dissipative state preparation via Lindblad dynamics as a practical alternative to postselected coherent methods. It develops a concrete algorithmic framework using algorithmically constructed jump operators and fixed-point convergence, with rigorous discussions of simulation on fault-tolerant quantum computers, mixing times, and locality constraints. The work provides detailed schemes for ground-state, Gibbs-state, excited-state, and eigenvector preparation, including frequency-filtered jumps, KMS/Detailed Balance structure, and quantum singular value transformations, along with cost and implementation considerations. Together, these results illuminate how engineered dissipation can yield robust routes to practical quantum advantage on early fault-tolerant hardware, and they chart a path toward experimental realizations and co-design across platforms.

Abstract

While dissipation has traditionally been viewed as an obstacle to quantum coherence, it is increasingly recognized as a powerful computational resource. Dissipative protocols can prepare complex many-body quantum states by leveraging engineered system-environment interactions. This essay focuses on a class of algorithms that utilize algorithmically constructed Lindblad generators, and highlight recent advances enabling the preparation of ground and thermal states for certain non-commuting Hamiltonians with rigorous performance guarantees. We also propose extensions of these protocols to prepare excited and resonance states, which may offer new pathways toward realizing practical quantum advantage on early fault-tolerant quantum computing platforms.

Paper Structure

This paper contains 15 sections, 30 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Lindblad dynamics and its quantum simulation
  3. Lindblad dynamics as an algorithmic tool
  4. Simulation of Lindblad dynamics on fault-tolerant quantum computers
  5. Dissipative state preparation as a fixed-point process and cost analysis
  6. Dissipative state preparation via Lindblad dynamics
  7. Ground state preparation
  8. Local versus quasi-local jump operators for preparing pure states
  9. Gibbs state preparation
  10. Excited state preparation
  11. Ground singular vector preparation and eigenvector preparation of general matrices
  12. Opportunities towards quantum advantage and experimental realization
  13. Potential quantum advantage from dissipative state preparation
  14. Experimental realization
  15. Outlook

Figures (1)

  • Figure 1: Schematic representation of (a) coherent state preparation via unitary evolution and post-selection, (b) dissipative state preparation via measurement and trace-over of ancillary degrees of freedom, and (c) conceptually equivalent implementation of dissipative state preparation by introducing more ancilla registers and deferring all measurements to the end. The initial state is $\rho_0$, and the target state is $\sigma$. Both $\rho_0$ and $\sigma$ can be pure or mixed states.