Square-root rule of two-dimensional bandwidth problem

Lin, Lan; Yao, Lin

doi:10.1051/ita/2011120

Cited by 7 publications

(1 citation statement)

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“…While this still requires quite a long interaction range in 1D, the bandwidth problem can also be generalized to higher dimensions. In 2D arrangements, we then expect the diameter of interaction to be B 2D ∼ √ 100 for N = 400 3-regular graphs [51], which seems within reach for nearterm quantum devices. A detailed study of the 2D bandwidth problem is beyond the scope of this work.…”

Section: Reducing Interaction Rangementioning

confidence: 81%

Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices

Zhou,

Wang,

Choi

et al. 2018

Preprint

137

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The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently understood about QAOA's performance beyond its lowest-depth variant. An essential but missing ingredient for understanding and deploying QAOA is a constructive approach to carry out the outer-loop classical optimization. We provide an in-depth study of the performance of QAOA on MaxCut problems by developing an efficient parameter-optimization procedure and revealing its ability to exploit non-adiabatic operations. Building on observed patterns in optimal parameters, we propose heuristic strategies for initializing optimizations to find quasi-optimal p-level QAOA parameters in O(poly(p)) time, whereas the standard strategy of random initialization requires 2 O(p) optimization runs to achieve similar performance. We then benchmark QAOA and compare it with quantum annealing, especially on difficult instances where adiabatic quantum annealing fails due to small spectral gaps. The comparison reveals that QAOA can learn via optimization to utilize non-adiabatic mechanisms to circumvent the challenges associated with vanishing spectral gaps. Finally, we provide a realistic resource analysis on the experimental implementation of QAOA. When quantum fluctuations in measurements are accounted for, we illustrate that optimization will be important only for problem sizes beyond numerical simulations, but accessible on near-term devices. We propose a feasible implementation of large MaxCut problems with a few hundred vertices in a system of 2D neutral atoms, reaching the regime to challenge the best classical algorithms.

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Section: Reducing Interaction Rangementioning

confidence: 81%