2024/11/06 by Eddie Schoute, Schoute, Eddie, Dmitry Grinko +5
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2411.03648
openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Similar to a classical processor, which is an algorithm for reading a program and executing its instructions on input data, a universal programmable quantum processor is a fixed quantum channel that reads a quantum program |ψU⟩ that causes the processor to approximately apply an arbitrary unitary U to a quantum data register. The present work focuses on a class of simple programmable quantum processors for implementing reflection operators, i.e. U = ei π|ψ⟩⟨ψ| for an arbitrary pure state |ψ⟩ of finite dimension d. Unlike quantum programs that assume query access to U, our program takes the form of independent copies of the state to be reflected about |ψU⟩ = |ψ⟩⊗ n. We then identify the worst-case optimal algorithm among all processors of the form trProgram[V (|ϕ⟩⟨ϕ| ⊗ (|ψ⟩⟨ψ|)⊗ n) V^†] where the algorithm V is a unitary linear combination of permutations. By generalizing these algorithms to processors for arbitrary-angle rotations, ei α|ψ⟩⟨ψ| for α∈ \mathbb R, we give a construction for a universal programmable processor with better scaling in d. For programming reflections, we obtain a tight analytical lower bound on the program dimension by bounding the Holevo information of an ensemble of reflections applied to an entangled probe state. The lower bound makes use of a block decomposition of the uniform ensemble of reflected states with respect to irreps of the partially transposed permutation matrix algebra, and two representation-theoretic conjectures based on extensive numerical evidence.