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Optical and Quantum Electronics

A QND-based Toffoli gate for polarization qubits and its applications

Samy C. Policarpo, João Batista Rosa Silva

Published Feb 5, 2023• 1 citation
Publisher
DOI
10.1007/s11082-023-04601-6

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Reversible photonic computing is a promising research field that seeks to develop computers that can perform calculations without loss of information by means of the controlled manipulation of light. Reversibility is an important property of a computational system, as it allows the system to be restored to its initial state after the calculation. This can be useful for applications such as cryptography, security, and image processing. This work presents a theoretical optical apparatus (cS) for polarization qubits based on quantum nondemolition measurements (QND) which through analytical and comparable calculations, presented an efficiency greater than 90% that is capable of performing the Toffoli gate function. The proposed optical system is configurable, based on prior configuration and combination, and reversible AND, NAND, Toffoli, CNOT, Peres, Fredkin, HNG, and ALG gates can be obtained, as well as any other reversible gate based on C n+1 -NOT gates. The cS system can be configured to function as a sequential binary comparator and the same can be used as a Bell state generator.

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Reversible photonic computing is a promising research field that seeks to develop computers that can perform calculations without loss of information by means of the controlled manipulation of light. Reversibility is an important property of a computational system, as it allows the system to be restored to its initial state after the calculation. This can be useful for applications such as cryptography, security, and image processing. This work presents a theoretical optical apparatus (cS) for polarization qubits based on quantum nondemolition measurements (QND) which through analytical and comparable calculations, presented an efficiency greater than 90% that is capable of performing the Toffoli gate function. The proposed optical system is configurable, based on prior configuration and combination, and reversible AND, NAND, Toffoli, CNOT, Peres, Fredkin, HNG, and ALG gates can be obtained, as well as any other reversible gate based on C n+1 -NOT gates. The cS system can be configured to function as a sequential binary comparator and the same can be used as a Bell state generator.
Abstract We propose a method for efficient mixed polarity multiple controlled Toffoli (MPMCT) gate decomposition from the perspective of a cost metric related to Toffoli gates, namely Toffoli-depth. When using the technique presented in a previous study, there is a range in which Toffoli-depth (consequently T-depth) of the implemented circuit increases proportionally as the number of provided (clean) work qubits increases. In other words, using the previous technique may result in more inefficient MPMCT gates even though the number of helpful work qubits has increased. In this work, a technique is devised to provide sufficient help from clean work qubits at the central part of the implemented circuit as many as possible, thereby addressing the issues with the previous technique. Meanwhile, one of the representative algorithms that use MPMCT gates is Grover’s algorithm. We show the implementation results for MPMCT gates according to the number of work qubits, using Grover’s algorithm as an example. It is experimentally demonstrated that T-depth decreases much more quickly when using our method than the previous method.
Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive to performing complex quantum algorithms. Here, we propose and present an experimental demonstration of a quantum Toffoli gate fully exploiting the polarization and orbital angular momentum of a single photon. The Toffoli gate is implemented using the polarized diffractive neural networks scheme, achieving a mean truth table visibility of 97.27±0.20%. We characterize the gate's performance through quantum state tomography on 216 different input states and quantum process tomography, which yields a process fidelity of 94.05±0.02%. Our method offers a novel approach for realizing the Toffoli gate without requiring exponential optical elements while maintaining extensibility to the implementation of other three-qubit gates.