Efficient Mean-Field Simulation of Quantum Circuits Inspired by Density Functional Theory
Efficient Mean-Field Simulation of Quantum Circuits Inspired by Density Functional Theory
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DOI：
10.1021/acs.jctc.3c00607
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发表时间：
2023-11-10
影响因子：
5.5
通讯作者：
Bernardi，Marco
中科院分区：
文献类型：
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作者：
Bernardi，Marco
量子电路（QC）的精确模拟目前仅限于250个量子位，因为存储QC波函数所需的内存和计算成本随量子位数呈指数级变化。因此，开发有效的近似QC模拟方案是当前的研究热点。在这里，我们展示了量子化学的模拟与密度泛函理论（DFT），一种广泛使用的方法，用于研究多电子系统的启发。我们的计算可以预测边际单量子比特概率（SQP）在几类具有通用门集的QC中具有超过90%的准确度，使用量子比特数线性的内存和计算资源，尽管SQP的形式指数成本。这是通过开发QC的平均场描述和制定最佳单量子位和双量子位门泛函（DFT中交换相关泛函的类似物）来实现的，以在不计算QC波函数的情况下发展SQP。目前的局限性和未来的扩展，这种形式主义进行了讨论。
Exact simulations of quantum circuits (QCs) are currently limited to ∼50 qubits because the memory and computational cost required to store the QC wave function scale exponentially with qubit number. Therefore, developing efficient schemes for approximate QC simulations is a current research focus. Here, we show simulations of QCs with a method inspired by density functional theory (DFT), a widely used approach for studying many-electron systems. Our calculations can predict marginal single-qubit probabilities (SQPs) with over 90% accuracy in several classes of QCs with universal gate sets, using memory and computational resources linear in qubit number despite the formal exponential cost of the SQPs. This is achieved by developing a mean-field description of QCs and formulating optimal single- and two-qubit gate functionals─analogues of exchange-correlation functionals in DFT─to evolve the SQPs without computing the QC wave function. Current limitations and future extensions of this formalism are discussed.