Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation

Abstract

Repeat-until-success strategy is a standard method to obtain success with a probability which grows exponentially in the number of iterations. However, since quantum systems are disturbed after a quantum measurement, it is not straightforward how to perform repeat-until-success strategies in certain quantum algorithms. In this paper, we propose a new structure for probabilistic higher-order transformation named success-or-draw, which allows a repeat-until-success implementation. For that we provide a universal construction of success-or-draw structure which works for any probabilistic higher-order transformation on unitary operations. We then present a semidefinite programming approach to obtain optimal success-or-draw protocols and analyze in detail the problem of inverting a general unitary operation.

17 pages, 4 figures

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Cited by in corpus (15)

• Quantum metrology for non-Markovian processes
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly
• Energy-Consumption Advantage of Quantum Computation
• Simulating noisy quantum channels via quantum state preparation algorithms
• Optimal universal quantum circuits for unitary complex conjugation
• Universal construction of decoders from encoding black boxes
• The quantum switch is uniquely defined by its action on unitary operations
• Quantum Supermaps are Characterized by Locality
• No-signalling constrains quantum computation with indefinite causal structure
• Readout Error Mitigation for Mid-Circuit Measurements and Feedforward
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Causality in Higher Order Process Theories
• Saving resources through repeat-until-success positive-operator-valued-measure measurements in quantum computation
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations