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Physica A Statistical Mechanics and its Applications

Quantum gates based on two strongly coupled harmonic oscillators in thermal non-equilibrium conditions

Behzad Lari, Won Sang Chung, HASSAN HASSANABADI

Published Jan 27, 2024• 2 citations
Publisher
DOI
10.1016/j.physa.2024.129561

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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.
We consider a Squeezed Harmonic Oscillator (SHO) dissipated as a Dekker oscillator and exposed to an environment under Thermal Non-Equilibrium Conditions (TNEC). The eigenvalues and eigenvectors of the system are obtained to determine the thermal distribution. Using Tsallis statistics under TNEC, the oscillator is constrained to its two lowest energy levels as a quasi-qubit and its thermal state is represented as a qutrit based on a simple harmonic oscillator basis. The Hadamard operation on the environmental entanglement with quasi-qubit is analyzed. This analysis examines the impact of temperature, the frequencies of the system and the environment. The fidelity of the Dekker state with the superposition state is compared with that of its environmental entanglement. We find that reducing the entanglement with the environment increases the fidelity up to 99%, and this increase is directly linked to a reduction in system-environment entanglement. These results may be beneficial for the control of single-qubit gates exposed to environmental effects.
In this dissertation, we studied the generation of squeezed states induced by a timedependent interaction and the in uence of temperature on the strength of the squeezing in a condensed matter model. The model studied comprised two quantum harmonic oscillators, with a time-dependent, non-linear coupling between them. The in uence of the thermal bath on the non-equilibrium dynamics of the model was represented in terms of non-Hamiltonian thermostats and a collection of independent harmonic oscillators with Ohmic spectral density. The equations of motion were studied in the Wigner representation, which introduces a phase space description for the model. The representation of the system in quantum phase space allowed us to investigate the di erence between purely classical evolution and the relative importance of quantum corrections with respect to the dynamics. The dynamics was studied by means of computer simulation techniques. The numerical simulation of the non-equilibrium statistical mechanics of both time-dependent and non-linear interactions allowed us to investigate conditions beyond those in recent literature [1, 2].