Private Quantum Signal Processing

Quantum signal processing (QSP), which is a general technique for construction of 1-qubit rotation operators, is a strong framework for quantum algorithm design. We consider a scenario of information-theoretically secure computation for QSP: n parties who have private angle parameters make the evaluator perform the QSP from the sum of their angles in a privacy-preserving manner through noninteractive communication. In this scenario, we construct a private simultaneous messages (PSM) protocol for QSP, named Private QSP (PQSP). As an application, we construct an efficient PSM protocol for symmetric Boolean functions with an evaluator of 1-qubit workspace by adapting PQSP to the 1-qubit quantum algorithm for symmetric Boolean functions of Maslov et al. [1]. We also show that the technique of PQSP works for the 1-qubit program for Boolean functions of Cosentino et al. [2]. We construct an efficient PSM protocol for Boolean functions computable by O(log n)-depth circuits with an evaluator of 1-qubit writable workspace from their 1-qubit program [3]. Such efficient PSM protocols with space-bounded classical evaluators have not been known so far.