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Lecture notes in electrical engineering

Effect of Noise on Concurrence of Compact Photonic CNOT Gate Designed Using Universal Cloner

Amit Kumar Sharma, Shishir Kumar Sharma, Ritu Sharma

Published Jan 1, 2022• 1 citation
Publisher
DOI
10.1007/978-981-19-0252-9_22

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Strongly-coupled two harmonics-oscillators CNOT gate under Wigner-parity decoherence in non-equilibrium thermal noise

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Abstract We explore how the Wigner-parity operator affects a system of strongly coupled two-harmonic oscillators (SCTHO) interacting with a bosonic bath under thermal non-equilibrium conditions (TNEC). By deforming the Lindblad equation with the Wigner-parity algebra, we model the system’s time evolution, constraining each oscillator to its two lowest energy levels. We use non-Gaussian Tsallis statistics to describe TNEC and examine the time development of concurrence both before and after a CNOT gate operation. Our findings indicate that parity is a strong marker of non-classical behavior in SCTHO exposed to thermal noise. Parity dependent Wigner negativities measure the loss of quantum coherence during CNOT gate operations. This loss is confirmed by Lindblad dynamics. We observe that the parity framework increases concurrence between oscillators after the CNOT, and we analyze how concurrence depends on Wigner parity and system frequency across different Tsallis q -regions. Our analysis reveals that Wigner parity deformation dramatically suppresses decoherence, enhancing concurrence longevity, while Tsallis statistics introduce a distinct hierarchy in thermal resilience. The CNOT gate’s operation induces a frequency dependent entanglement crossover, with parity protection proving most effective at high frequencies. This model offers potential for optimizing thermal solid-state quantum gates (QGs) and provides insights into fault-tolerant encoding in noisy oscillator-based qubits. Furthermore, by extending the analysis to a microscopic model with temperature-dependent decay rates derived from a Tsallis-distributed bath, we demonstrate how non-Gaussian environmental statistics directly shape the decoherence pathways and concurrence dynamics.

Physica Scripta•Feb 9, 2026•0 citations
The Controlled-NOT (CNOT) quantum gate associated with single qubit gates is universal for building all quantum circuits. Although CNOTs based on trapped ions and superconducting qubits have become experimentally feasible, the deterministically functioning quantum CNOT gate with photonic qubits will lead to practical realization of quantum computers in a deterministic manner, and will therefore provide an exponential increase in processing power with lowest decoherence time. Based on a previously proposed CNOT model utilizing a quantum cloner (with a fidelity of 78 %), we present in this work our design of the Compact CNOT gate providing a fidelity of 90.31 %, and give physical realization constraints for building CNOT based decomposition of the Toffoli gate and more generalized photonic CnNOT gates. The photonic qubits are encoded by circularly polarized single photons and the design of the gate is based on copying the polarization degree of freedom by quantum cloners. Our model is based on spin of electron in a quantum dot embedded in a double sided optical microcavity which behaves like a beam splitter. Circularly polarizing beam splitters, beam splitters, delay lines, photonic circulators, single qubit operations and other photonic devices are used for the design and decomposition. We show that the fidelity of the decomposed CnNOT gates is highly dependent on the errors of the non-perfect photonic devices used and more specifically to the theoretical optimal limit of 5/6 of the quantum cloners required for each CNOT in the decomposition.
Abstract We explore how the Wigner-parity operator affects a system of strongly coupled two-harmonic oscillators (SCTHO) interacting with a bosonic bath under thermal non-equilibrium conditions (TNEC). By deforming the Lindblad equation with the Wigner-parity algebra, we model the system’s time evolution, constraining each oscillator to its two lowest energy levels. We use non-Gaussian Tsallis statistics to describe TNEC and examine the time development of concurrence both before and after a CNOT gate operation. Our findings indicate that parity is a strong marker of non-classical behavior in SCTHO exposed to thermal noise. Parity dependent Wigner negativities measure the loss of quantum coherence during CNOT gate operations. This loss is confirmed by Lindblad dynamics. We observe that the parity framework increases concurrence between oscillators after the CNOT, and we analyze how concurrence depends on Wigner parity and system frequency across different Tsallis q -regions. Our analysis reveals that Wigner parity deformation dramatically suppresses decoherence, enhancing concurrence longevity, while Tsallis statistics introduce a distinct hierarchy in thermal resilience. The CNOT gate’s operation induces a frequency dependent entanglement crossover, with parity protection proving most effective at high frequencies. This model offers potential for optimizing thermal solid-state quantum gates (QGs) and provides insights into fault-tolerant encoding in noisy oscillator-based qubits. Furthermore, by extending the analysis to a microscopic model with temperature-dependent decay rates derived from a Tsallis-distributed bath, we demonstrate how non-Gaussian environmental statistics directly shape the decoherence pathways and concurrence dynamics.