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Physica Scripta

Thermal CNOT gate based on Silicon quantum dots using Tsallis statistics

Behzad Lari, E. Mohammadikhabaz, elham eilkhas, HASSAN HASSANABADI

Published Oct 1, 2025• 2 citations
Publisher

Abstract

Abstract We consider a CNOT gate based on Silicon semiconductor quantum dots in thermal non-equilibrium conditions (TNEC). By applying Tsallis statistics, we analyze the time evolution of fidelity between the dot state and Bell state in TNEC, considering the effects of control magnetic fields on the left and right dots, exchange interaction, and microwave frequencies in the presence of environmental exposure. We present a thermal model for the time-dependent behavior of exchange interaction in silicon and compare our findings with experimental data. Our model incorporates physical dimensions and highlights the trade-off between achieving high fidelity near absolute zero temperatures and generating strong, high-frequency point magnetic fields to stabilize the CNOT gate. We determine that q > 1 is the optimal geometric region for extending gate lifetime. Utilizing quantum materials to generate strong point fields and topological manipulation of the qubit could be a viable approach to achieve such a gate. We aim to manipulate states to achieve high fidelity using control magnetic fields to create a functional CNOT gate in thermal noise, simultaneously ensuring strong entanglement between the dots.

DOI
10.1088/1402-4896/ae0ed4

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arXiv:1902.02350•Physical review. B./Physical review. B•Jul 9, 2019•32 citations
Abstract We consider a CNOT gate based on Silicon semiconductor quantum dots in thermal non-equilibrium conditions (TNEC). By applying Tsallis statistics, we analyze the time evolution of fidelity between the dot state and Bell state in TNEC, considering the effects of control magnetic fields on the left and right dots, exchange interaction, and microwave frequencies in the presence of environmental exposure. We present a thermal model for the time-dependent behavior of exchange interaction in silicon and compare our findings with experimental data. Our model incorporates physical dimensions and highlights the trade-off between achieving high fidelity near absolute zero temperatures and generating strong, high-frequency point magnetic fields to stabilize the CNOT gate. We determine that q > 1 is the optimal geometric region for extending gate lifetime. Utilizing quantum materials to generate strong point fields and topological manipulation of the qubit could be a viable approach to achieve such a gate. We aim to manipulate states to achieve high fidelity using control magnetic fields to create a functional CNOT gate in thermal noise, simultaneously ensuring strong entanglement between the dots.
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.
Achieving high-fidelity two-qubit gates is crucial for spin qubits in silicon-based double quantum dots. However, these gates are sensitive to charge noise in experimental settings, which remains a significant challenge. Geometric gates, which utilize pure geometric phases for gate operations, are a promising approach to achieving robust control. In this work, we theoretically propose a feasible strategy to implement geometric two-qubit gates for silicon-based spin qubits considering experimental control environments. By operating in the suitable region where the local magnetic field gradient is significantly larger than the exchange interaction, we can implement both entangling and nonentangling geometric gates through analytical and numerical methods. It is found that the geometric gates obtained are highly compatible with existing experimental techniques using electric dipole spin resonance in silicon. Moreover, the implemented geometric controlled-ZZZ (CZ) gates can achieve fidelities exceeding 99% under experimental noise levels and the gate times are as short as 20 ns. Our work paves the way for the realization of high-fidelity geometric two-qubit gates for spin qubits in silicon.
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work, we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters, we present simple control pulses that generate CNOT, CPHASE, and CZ gates with average fidelities greater than 99.99% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a CNOT gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to CNOT\sqrt{CNOT}CNOT​ and CZ\sqrt{CZ}CZ​ that are used to implement simple two-piece pulse sequences that produce high-fidelity CNOT and CZ gates in the presence of low-frequency noise.
We model a controlled-NOT (CNOT) gate mediated by exchange interactions in a realistic Ge/GeSi hole spin-qubit device. We use for that purpose a computationally efficient framework based on a compact dressed basis of many-body singlet and triplet states, which enables fast time-dependent simulations that would be prohibitive within a conventional configuration-interaction approach. We discuss the dominant sources of infidelity in ideal (noise-free) devices. On the one hand, the nonadiabaticity of the tunnel barrier ramps, enhanced by the transverse component of the exchange interaction, imposes limits on the speed of the CNOT gate. On the other hand, the AC Stark shift of the conditional resonance and the off-resonant driving of the complementary transition can significantly degrade the gate fidelity and call for a careful optimization of the driving conditions. Finally, we investigate the impact of quasi-static charge noise on the fidelity of the CNOT gate. We find that the capture of charges near the qubits can strongly disrupt the conditional operation, while the nanometer-scale motion of charges results in a loss of fidelity that sensitively depends on the position and strength of the corresponding dipole. Our results quantify the requirements on barrier control, microwave driving, and charge-noise stability for high-fidelity two-qubit operations in Ge/GeSi hole-spin qubits.
Single-qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. Although high-fidelity single-qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been challenging because of rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities greater than 99%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 nanoseconds. We used the CNOT gate to generate a Bell state with 78% fidelity (corrected for errors in state preparation and measurement). Our quantum dot device architecture enables multi-qubit algorithms in silicon.
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate cnot, cphase, and cz gates with average fidelities greater than 99.99% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a cnot gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to CNOT\sqrt{\mathrm{CNOT}}CNOT​ and CZ\sqrt{\mathrm{CZ}}CZ​ that are used to implement simple two-piece pulse sequences that produce high-fidelity cnot and cz gates in the presence of low-frequency noise.