Solving Gauss's law on digital quantum computers with loop-string-hadron digitization

Indrakshi Raychowdhury, Jesse R. Stryker
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引用次数: 50

Abstract

We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,'"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how that is digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.
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环弦强子数字化在数字量子计算机上求解高斯定律
我们证明,使用SU(2)晶格规范理论(arXiv:1912.06133)的环弦强子(LSH)公式作为数字量子计算的基础,很容易解决一个重要的基本问题:精确实现规范不变性(或高斯定律)。我们首先讨论了LSH希尔伯特空间在d空间维度上的结构,它的截断,以及它的量子位的数字化。规范理论模拟中的错误检测和缓解将受益于物理“预言器”,因此我们分解标记规范不变波函数的电路。然后,我们分析了协议涉及的逻辑量子比特成本和纠缠门计数。LSH基可以比kogut - susskind型表示基节省或花费更多的量子位,这取决于它是如何数字化的以及空间维度。许多其他明显的好处鼓励未来的研究应用这一框架。
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