Counterdiabaticity and the quantum approximate optimization algorithm
Counterdiabaticity and the quantum approximate optimization algorithm
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DOI：
10.22331/q-2022-01-27-635
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发表时间：
2021-06
期刊：
影响因子：
6.4
通讯作者：
J. Wurtz;P. Love
中科院分区：
文献类型：
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作者：
J. Wurtz;P. Love
量子近似优化算法（QAOA）是一种近期的混合算法，旨在解决诸如MaxCut之类的组合优化问题，例如模仿QAOA。根据绝热定理，在这项工作中，QAOA和绝热性之间的连接是通过检查Q型但有限的QAOA来明确的。抵绝热（CD）进化，我们构建了CD-QAOA角度，通过将Trotter的“误差”项与近似的绝热规格电位相匹配，这些术语抑制了抑制了由有限的ramp速度引起的绝热量表。 ，不是有害的，使用此匹配来将QAOA与量子绝热算法（QAA）联系起来，我们表明近似值收敛到一个至少是1-c（p）〜1/pμ。优化连续的绝热时间表。绝热的演变。
The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the p→∞ limit the final state is an exact maximal eigenstate in accordance with the adiabatic theorem. In this work, the connection between QAOA and adiabaticity is made explicit by inspecting the regime of p large but finite. By connecting QAOA to counterdiabatic (CD) evolution, we construct CD-QAOA angles which mimic a counterdiabatic schedule by matching Trotter "error" terms to approximate adiabatic gauge potentials which suppress diabatic excitations arising from finite ramp speed. In our construction, these "error" terms are helpful, not detrimental, to QAOA. Using this matching to link QAOA with quantum adiabatic algorithms (QAA), we show that the approximation ratio converges to one at least as 1−C(p)∼1/pμ. We show that transfer of parameters between graphs, and interpolating angles for p+1 given p are both natural byproducts of CD-QAOA matching. Optimization of CD-QAOA angles is equivalent to optimizing a continuous adiabatic schedule. Finally, we show that, using a property of variational adiabatic gauge potentials, QAOA is at least counterdiabatic, not just adiabatic, and has better performance than finite time adiabatic evolution. We demonstrate the method on three examples: a 2 level system, an Ising chain, and the MaxCut problem.