Diagonal Catalysts in Quantum Adiabatic Optimization
- URL: http://arxiv.org/abs/2009.05726v2
- Date: Mon, 15 Feb 2021 15:26:25 GMT
- Title: Diagonal Catalysts in Quantum Adiabatic Optimization
- Authors: Tameem Albash, Matthew Kowalsky
- Abstract summary: We show how a diagonal Hamiltonian can bias the energy landscape towards a given spin configuration.
We present examples where biasing towards low energy states that are nonetheless very far in Hamming distance from the ground state can severely worsen the efficiency of the algorithm.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose a protocol for quantum adiabatic optimization, whereby an
intermediary Hamiltonian that is diagonal in the computational basis is turned
on and off during the interpolation. This `diagonal catalyst' serves to bias
the energy landscape towards a given spin configuration, and we show how this
can remove the first-order phase transition present in the standard protocol
for the ferromagnetic $p$-spin and the Weak-Strong Cluster problems. The
success of the protocol also makes clear how it can fail: biasing the energy
landscape towards a state only helps in finding the ground state if the Hamming
distance from the ground state and the energy of the biased state are
correlated. We present examples where biasing towards low energy states that
are nonetheless very far in Hamming distance from the ground state can severely
worsen the efficiency of the algorithm compared to the standard protocol. Our
results for the diagonal catalyst protocol are analogous to results exhibited
by adiabatic reverse annealing, so our conclusions should apply to that
protocol as well.
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