No-iteration of unknown quantum gates

Abstract

We propose a new no-go theorem by proving the impossibility of constructing a deterministic quantum circuit that iterates a unitary oracle by calling it only once. Different schemes are provided to bypass this result and to approximately realize the iteration. The optimal scheme is also studied. An interesting observation is that for large number of iterations, a trivial strategy like using the identity channel has the optimal performance, and preprocessing, postprocessing, or using resources like entanglement does not help at all. Intriguingly, the number of iterations, when being large enough, does not affect the performance of the proposed schemes.

13 pages, 7 figures; added references, revised argument in section 3, accepted for publication in Physical Review A

References in corpus (6)

• Quantum Circuits Architecture
• Transforming quantum operations: quantum supermaps
• Computational advantage from quantum-controlled ordering of gates
• Implementing quantum control for unknown subroutines
• Optimal cloning of unitary transformations
• Minimal computational-space implementation of multi-round quantum protocols

Cited by in corpus (6)

• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Optimal universal quantum circuits for unitary complex conjugation
• Universal construction of decoders from encoding black boxes
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• A Quantum Approach to the Unique Sink Orientation Problem