Heralded high-dimensional module-based quantum computation

Area of Science:

• Quantum Information Science
• Quantum Computing Architectures
• Quantum Optics

Background:

• Parity measurements are crucial for quantum information processing tasks.
• Entangled states and quantum computation rely on effective parity measurement techniques.
• Existing methods for quantum computing face challenges in scalability and determinism.

Purpose of the Study:

• To develop novel high-dimensional generalized parity modules.
• To propose a deterministic method for constructing module-based controlled-NOT gates.
• To explore optical implementation of generalized parity modules using quantum nondemolition measurements.

Main Methods:

• Development of two alternative high-dimensional generalized parity modules.
• Proposal of a procedure for constructing high-dimensional generalized module-based controlled-NOT gates.
• Design of an optical nondestructive scheme utilizing quantum nondemolition measurements.

Main Results:

• Identified two specific parity modules, P=(j⊖i)mod d and P=(j⊕i)mod d, as essential building blocks for high-dimensional quantum computing.
• Demonstrated that the proposed module-based quantum computing construction is deterministic, heralded, and does not require postselection.
• Successfully proposed an optical scheme for implementing generalized parity modules using photon-number-resolving and single-photon detectors.

Conclusions:

• The identified parity modules are fundamental for high-dimensional quantum computing.
• The proposed deterministic and heralded construction method simplifies quantum gate implementation.
• Optical implementation using quantum nondemolition measurements offers a viable path for realizing these quantum modules.