2025/10/18 by Adam Husted Kjelstrøm, Kjelstrøm, Adam Husted, Andreas Pavlogiannis +3
Computer Science · #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2510.16420
openalex publication_date 2025/10/18 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit C, computing a circuit C' which behaves equivalently on a desired subspace, and that minimizes a quantum resource type, expressed as the count or depth of (i) arbitrary gates, or (ii) non-Clifford gates, or (iii) superposition gates, or (iv) entanglement gates. We show that, when C is expressed over any gate set that can implement the H and TOF gates exactly, each of the above optimization problems is hard for co-NQP, and hence outside the Polynomial Hierarchy, unless the Polynomial Hierarchy collapses. This complements recent results in the literature which established an NP-hardness lower bound when equivalence is over the full state space, and tightens the gap to the corresponding NPNQP upper bound known for cases (i)-(iii) over Clifford+T and (i)-(iv) over H+TOF circuits.