Current gate-based quantum computers have the potential to provide a
computational advantage if algorithms use quantum hardware efficiently. To make
combinatorial optimization more efficient, we introduce the Filtering
Variational Quantum Eigensolver (F-VQE) which utilizes filtering operators to
achieve faster and more reliable convergence to the optimal solution.
Additionally we explore the use of causal cones to reduce the number of qubits
required on a quantum computer. Using random weighted MaxCut problems, we
numerically analyze our methods and show that they perform better than the
original VQE algorithm and the Quantum Approximate Optimization Algorithm
(QAOA). We also demonstrate the experimental feasibility of our algorithms on a
Honeywell trapped-ion quantum processor.

本篇论文介绍了一种基于 F-VQE 算法和因果锥的方法，可在量子计算机上更高效地解决组合优化问题，实验结果表明该方法比原始的 VQE 算法和量子近似优化算法（QAOA）更加优秀。

用于组合优化的变分量子算法过滤

Filtering variational quantum algorithms for combinatorial optimization

The performance of the quantum approximate optimization algorithm is
evaluated by using three different measures: the probability of finding the
ground state, the energy expectation value, and a ratio closely related to the
approximation ratio. The set of problem instances studied consists of weighted
MaxCut problems and 2-satisfiability problems. The Ising model representations
of the latter possess unique ground states and highly-degenerate first excited
states. The quantum approximate optimization algorithm is executed on quantum
computer simulators and on the IBM Q Experience. Additionally, data obtained
from the D-Wave 2000Q quantum annealer is used for comparison, and it is found
that the D-Wave machine outperforms the quantum approximate optimization
algorithm executed on a simulator. The overall performance of the quantum
approximate optimization algorithm is found to strongly depend on the problem
instance.

本研究对量子近似优化算法的性能进行了评估，其中研究了加权 MaxCut 和 2-SAT 问题实例的概率、期望能值和近似比相关的比率三个不同的度量方式。研究表明，该算法的性能强烈依赖于问题实例，D-Wave 2000Q 量子退火器的性能表现优于在模拟器上执行的量子近似优化算法。

基准测试量子近似优化算法

Benchmarking the Quantum Approximate Optimization Algorithm

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
$O(\text{poly}(p))$ 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.

本文深入研究了混合量子 - 经典变分算法中外循环经典优化的有效途径，并在 MaxCut 问题上通过发现优化参数中的模式，提出了启发式策略以在 $O (poly (p) $) 的时间内，找到近似最优的 p 级 QAOA $o$ 参数。与量子退火比较发现 QAOA 可以通过优化学习利用非绝热机制来克服与湮灭光谱间隙相关的挑战。在资源分析中，揭示了仅当问题规模大于数字模拟但可在近期设备中访问时，优化才是重要的，并提出用 2D 中性原子系统实现大型 MaxCut 问题的可行方法，从而挑战最佳经典算法所达到的范畴。