Simulating Many-Body Systems with a Projective Quantum Eigensolver
Simulating Many-Body Systems with a Projective Quantum Eigensolver
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DOI：
10.1103/prxquantum.2.030301
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发表时间：
2021-01
期刊：
影响因子：
9.7
通讯作者：
Nicholas H Stair;Francesco A. Evangelista
中科院分区：
文献类型：
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作者：
Nicholas H Stair;Francesco A. Evangelista
我们提出了一种新的混合量子经典算法，用于优化幺正耦合簇（UCC）波函数，被认为是射影量子特征解算器（PQE），适用于近期噪声量子硬件。与变分量子算法相反，PQE使用残差（Schrödinger方程的投影）而不是能量梯度来优化试验状态。我们表明，残差可以通过简单地测量每个元素的两个能量期望值来评估。我们还介绍了PQE的一个选择变体（SPQE），它使用由任意阶粒子空穴算子构建的自适应分析，并绕过了自适应变分量子算法中使用的昂贵的基于梯度的选择过程。PQE和SPQE在一组分子体系上进行了测试，包括弱相关和强相关体系，包括4-10原子的氢簇和BeH2分子。当使用固定方差时，我们发现PQE可以将UCC波函数收敛到与变分优化基本相同的能量，同时需要更少的计算资源。SPQE和自适应变分量子算法的比较表明，对于含有相同数量参数的ansätze，两种方法产生的结果精度相当。最后，我们证明了SPQE在1-3维强相关H10系统上的表现与选择的构型相互作用和密度矩阵重整化群相似，在某些情况下甚至更好。
We present a new hybrid quantum-classical algorithm for optimizing unitary coupled-cluster (UCC) wave functions deemed the projective quantum eigensolver (PQE), amenable to near-term noisy quantum hardware. Contrary to variational quantum algorithms, PQE optimizes a trial state using residuals (projections of the Schrödinger equation) rather than energy gradients. We show that the residuals may be evaluated by simply measuring two energy expectation values per element. We also introduce a selected variant of PQE (SPQE) that uses an adaptive ansatz built from arbitrary-order particle-hole operators and circumvents the expensive gradient-based selection procedures used in adaptive variational quantum algorithms. PQE and SPQE are tested on a set of molecular systems covering both the weak and strong correlation regimes, including hydrogen clusters with 4–10 atoms and the BeH2 molecule. When employing a fixed ansatz, we find that PQE can converge UCC wave functions to essentially identical energies as variational optimization while requiring fewer computational resources. A comparison of SPQE and adaptive variational quantum algorithms shows that—for ansätze containing the same number of parameters—the two methods yield results of comparable accuracy. Finally, we show that SPQE performs similar to, and in some cases, better than selected configuration interaction and the density matrix renormalization group on 1–3 dimensional strongly correlated H10 systems.