Dissipative State Preparation and the Dissipative Quantum Eigensolver
summary
Constructs a Dissipative Quantum Eigensolver that uses weak local measurements and a conditional stopping rule (stop after n successive “good” outcomes) to provably converge to the ground-state subspace of any k‑local Hamiltonian without needing gap or energy bounds. Provides an analytic runtime formula (expected time is exponential) and shows numerical gains from local resampling (smaller exponent than global restart). Algorithm is immune to initial-state errors and provably fault‑resilient without error‑correction; Chebyshev AGSPs give polytime fixed‑point maps but require QMA‑hard spectral advice.
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chapters (15)
- 0:00Introduction and motivation
- 1:26The ground state problem
- 4:42Dissipative state preparation
- 10:36Distance quantum eigensolver
- 13:40AGSPs and implementation
- 20:10The DQE algorithm mechanism
- 23:24Theoretical convergence proofs
- 28:20Runtime analysis
- 36:41Convergence with decreasing epsilon
- 40:04Fault resilience
- 43:28Discussion and Q&A
- 50:17Resampling and optimization
- 55:08Chebyshev AGSPs and complexity
- 1:02:28Dissipative Gibbs sampling
- 1:05:47Concluding remarks
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