Quantum conditional operations

Abstract

An essential element of classical computation is the "if-then" construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand, quantum theory prevents the existence of an analogous universal construct accepting a control qubit and an arbitrary quantum gate as its input. Nevertheless, there are controllable sets of quantum gates for which such a construct exists. Here we provide a necessary and sufficient condition for a set of unitary transformations to be controllable, and we give a complete characterization of controllable sets in the two dimensional case. This result reveals an interesting connection between the problem of controllability and the problem of extracting information from an unknown quantum gate while using it.

7 pages

References in corpus (7)

• Quantum Circuits Architecture
• Adding control to arbitrary unknown quantum operations
• Creation of superposition of unknown quantum states
• Coherent controlization using superconducting qubits
• Quantum Networks: general theory and applications
• Information - Disturbance Tradeoff in the Estimation of a Unitary Transformation
• Minimal computational-space implementation of multi-round quantum protocols

Cited by in corpus (13)

• Communication through coherent control of quantum channels
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Complex conjugation supermap of unitary quantum maps and its universal implementation protocol
• Quantum correlations in composite systems
• Controlled quantum operations and combs, and their applications to universal controllization of divisible unitary operations
• Experimental superposition of time directions
• Universal control of quantum processes using sector-preserving channels
• 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
• Quantum Circuits Are Just a Phase
• Operational models of temperature superpositions
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations