Efficient synthesis of universal repeat-until-success quantum circuits.

Area of Science:

• Quantum Computing
• Quantum Circuit Synthesis
• Algorithm Development

Background:

• Repeat-until-success (RUS) circuits offer resource reduction for implementing quantum operations.
• Existing RUS circuit synthesis algorithms have prohibitive exponential classical runtime.
• A need exists for efficient synthesis of RUS circuits for practical quantum computation.

Purpose of the Study:

• To present a probabilistically polynomial-time algorithm for synthesizing RUS circuits.
• To approximate arbitrary single-qubit unitaries within the Clifford+T basis to a given precision.
• To investigate the resource requirements, particularly the T count, of synthesized RUS circuits.

Main Methods:

• Development of a novel probabilistic algorithm for RUS circuit synthesis.
• Approximation of single-qubit unitaries using the Clifford+T gate basis.
• Leveraging measurement and ancilla qubits within the RUS circuit framework.

Main Results:

• A probabilistically polynomial-time algorithm for synthesizing RUS circuits is presented.
• The synthesized RUS circuits achieve high precision for single-qubit unitary approximations.
• An expected T count of 1.15 log₂(1/ϵ) is achieved for single-qubit z rotations, surpassing theoretical bounds for purely unitary circuits.

Conclusions:

• The new algorithm significantly improves the efficiency of RUS circuit synthesis.
• RUS circuits, utilizing measurement and ancilla qubits, can achieve lower T counts than previously thought possible.
• The higher density of implementable unitaries in RUS protocols explains their efficiency advantage.