From String Detection to Orthogonal Vector Problem

• DOI: 10.48550/arxiv.2209.11452
• Publication Date: 2022-01-01
• Authors: Yunhao Wang; Tianyuan Zheng; Lior Horesh
• Keywords: Intuition

Considering Grover's Search Algorithm (GSA) with the standard diffuser stage applied, we revisit $3$-qubit unique String Detection Problem (SDP) and extend algorithm to $4$-qubit SDP multiple winners. We then investigate unstructured search problems non-uniform distributions define Orthogonal Vector (OVP) under quantum settings. Although no numerically stable results is reached original GSA framework, provide intuition behind our implementation further observations on OVP. perform a special case analysis modified framework which aims stabilize final measurement arbitrary initial distribution. Based result of analysis, generalize condition neither nor modification works. Instead utilizing GSA, also propose short-depth circuit that can calculate orthogonal pair for given vector represented as binary string constant runtime.