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Searching for quantum speedup in quasistatic quantum annealers
Mohammad Amin
TL;DR
The paper asks whether performance measurements from suboptimal quantum annealers can reveal quantum speedup, given that long anneals may produce quasistatic, equilibrium-like populations. Using an open quantum master equation with realistic parameters, it shows that freeze-out distributions can correlate with classical simulations while concealing the underlying quantum dynamics.
Problem
Whether quantum speedup can be identified from suboptimal quantum-annealer performance remains unresolved because equilibrium populations do not reveal the dynamics that may generate a speedup.
Method
The authors model a 16-qubit quantum annealer with a Redfield open-quantum master equation and realistic environmental parameters to analyze quasistatic evolution and freeze-out.
Results
Long anneals can yield final populations close to a Boltzmann distribution at a single freeze-out point, potentially correlating with quantum Monte Carlo or simulated annealing without demonstrating classical dynamics or QMC simulability.
Takeaways & Limitations
Computation times derived from quasistatic equilibrium distributions provide no information about the underlying quantum dynamics, complicating searches for quantum speedup in suboptimal annealers.
Takeaways & Limitations
The counterexample is not claimed to be generic, and long-anneal final populations need not be equilibrium populations when different relaxation rates produce distributed freeze-out.
Abstract
from arXiv · showhide
We argue that a quantum annealer at very long annealing times is likely to experience a quasistatic evolution, returning a final population that is close to a Boltzmann distribution of the Hamiltonian at a single (freeze-out) point during the annealing. Such a system is expected to correlate well with a proper quantum Monte Carlo simulation. It may also correlate with simulated annealing if at the freeze-out point the quantum energy eigenvalues are close to the classical ones. These correlations are just signatures of equilibration and do not mean that the evolution of the quantum annealer is classical or can be simulated by quantum Monte Carlo. The computation time extracted from such a distribution reflects the equilibrium behavior and therefore provides no information about the underlying quantum dynamics. This makes the search for quantum speedup in suboptimal quantum annealers problematic. We use an open quantum master equation with realistic parameters to illustrate quasistatic evolution in a 16 qubit quantum annealer and discuss its implication for quantum speedup.