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Mean Field Analysis of Quantum Annealing Correction
Shunji Matsuura1,2, Hidetoshi Nishimori3, Tameem Albash4,5,6
1Niels Bohr International Academy and Center for Quantum Devices, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark.
Physical Review Letters
|June 18, 2016
Summary
Quantum annealing correction (QAC) protects quantum annealers from errors by adjusting energy penalties. This study reveals QAC
Area of Science:
- Quantum Computing
- Statistical Mechanics
- Optimization Problems
Background:
- Quantum annealing correction (QAC) is a technique to mitigate errors in quantum annealers.
- Experimental demonstrations show QAC's success, but its underlying mechanism remains unclear.
Purpose of the Study:
- To elucidate the operating mechanism of Quantum Annealing Correction (QAC).
- To analyze QAC's effectiveness in different quantum system models.
Main Methods:
- Employed quantum statistical mechanics tools for analysis.
- Utilized mean-field analysis on analytically tractable models.
- Studied the p-body ferromagnetic infinite-range transverse-field Ising model and the quantum Hopfield model.
Main Results:
- For second-order phase transitions (p=2), QAC shifts the transition to higher transverse field strengths.
- For first-order phase transitions (p≥3), QAC softens or prevents gap closure near quantum critical points.
- Similar protective effects of QAC were observed in the disordered quantum Hopfield model.
Conclusions:
- QAC provides robust protection against errors near quantum critical points.
- The findings offer a deeper theoretical understanding of QAC's error suppression capabilities.
- The study confirms QAC's efficacy across different models, including those with disorder.
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