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Bulletin of the American Physical Society

Thermodynamic implications of $^{29}$Si spin impurities on scalability of silicon-based quantum computing

Pavel Lougovski, Nicholas A. Peters

Published Mar 14, 2017• 0 citations
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Silicon–germanium (Si/SiGe) quantum dots represent a preeminent architecture for scalable quantum computing; however, their performance remains fundamentally constrained by environmental decoherence. This work presents a comparative simulation study of a two-qubit system in Si/SiGe, evaluating the fidelity of various noise modeling frameworks under realistic conditions, including 1/f charge noise and phonon-mediated relaxation. We benchmark the Lindblad Master Equation against the Bloch–Redfield Master Equation, the Semiclassical Stochastic Hamiltonian method and the Monte Carlo Wavefunction (Quantum Jumps). Our analysis reveals that while semiclassical models effectively capture pure dephasing (T2*) dynamics, they fail to account for energy relaxation (T1) at cryogenic temperatures, erroneously driving the system toward a high-entropy maximally mixed state. We propose the Quantum Trajectories method to resolve this discrepancy by incorporating discrete dissipation events, providing a thermodynamically consistent semi-classical framework. To demonstrate the scalability of our approach, we extend the simulation to a 4-qubit register, showing that the Quantum Trajectories method remains numerically robust and thermodynamically consistent as the Hilbert space dimension increases. Furthermore, we perform a magnetic field optimization analysis, identifying an operational “sweet spot” within the 0.1–0.5 T range that optimally balances the trade-offs between relaxation and dephasing.

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Statistical exchange-coupling errors and the practicality of scalable silicon donor qubits

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Recent experimental efforts have led to considerable interest in donor-based localized electron spins in Si as viable qubits for a scalable silicon quantum computer. With the use of isotopically purified 28Si and the realization of extremely long spin coherence time in single-donor electrons, the recent experimental focus is on two-coupled donors with the eventual goal of a scaled-up quantum circuit. Motivated by this development, we simulate the statistical distribution of the exchange coupling J between a pair of donors under realistic donor placement straggles, and quantify the errors relative to the intended J value. With J values in a broad range of donor-pair separation (5<|R|<60 nm), we work out various cases systematically, for a target donor separation R0 along the [001], [110] and [111] Si crystallographic directions, with |R0|=10,20 or 30 nm and standard deviation σR=1,2,5 or 10 nm. Our extensive theoretical results demonstrate the great challenge for a prescribed J gate even with just a donor pair, a first step for any scalable Si-donor-based quantum computer.

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Towards scalable silicon quantum computing

M. Vinet, Louis Hutin, Benoît Bertrand +14 more

Qubits can be made out of a variety of experimental platforms, fig. 1. Small processors have already been demonstrated in trapped ions and superconductors but in both cases, the constraints for coherent manipulation and the effective large size of the qubits including all quantum functionalities are hardly compatible with very large-scale architecture. When it comes to the crucial issue of large-scale integration, Si spin qubits are well positioned due to their long coherence times and compatibility with semiconductor fabrication techniques. Indeed, dephasing times of the order of 1s have been achieved in Si-based spin qubits and single-qubit gate fidelities are high enough for scalable, fault-tolerant quantum computing.

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Thermodynamic And Quantum Constraints On Scalable Quantum Computing

Rowan Brad Quni-Gudzinas

•Jan 1, 2025•0 citations
Thermodynamic implications of 29^{29}29Si spin impurities on scalability of silicon-based quantum computing
Silicon–germanium (Si/SiGe) quantum dots represent a preeminent architecture for scalable quantum computing; however, their performance remains fundamentally constrained by environmental decoherence. This work presents a comparative simulation study of a two-qubit system in Si/SiGe, evaluating the fidelity of various noise modeling frameworks under realistic conditions, including 1/f charge noise and phonon-mediated relaxation. We benchmark the Lindblad Master Equation against the Bloch–Redfield Master Equation, the Semiclassical Stochastic Hamiltonian method and the Monte Carlo Wavefunction (Quantum Jumps). Our analysis reveals that while semiclassical models effectively capture pure dephasing (T2*) dynamics, they fail to account for energy relaxation (T1) at cryogenic temperatures, erroneously driving the system toward a high-entropy maximally mixed state. We propose the Quantum Trajectories method to resolve this discrepancy by incorporating discrete dissipation events, providing a thermodynamically consistent semi-classical framework. To demonstrate the scalability of our approach, we extend the simulation to a 4-qubit register, showing that the Quantum Trajectories method remains numerically robust and thermodynamically consistent as the Hilbert space dimension increases. Furthermore, we perform a magnetic field optimization analysis, identifying an operational “sweet spot” within the 0.1–0.5 T range that optimally balances the trade-offs between relaxation and dephasing.
Recent experimental efforts have led to considerable interest in donor-based localized electron spins in Si as viable qubits for a scalable silicon quantum computer. With the use of isotopically purified 28Si and the realization of extremely long spin coherence time in single-donor electrons, the recent experimental focus is on two-coupled donors with the eventual goal of a scaled-up quantum circuit. Motivated by this development, we simulate the statistical distribution of the exchange coupling J between a pair of donors under realistic donor placement straggles, and quantify the errors relative to the intended J value. With J values in a broad range of donor-pair separation (5<|R|<60 nm), we work out various cases systematically, for a target donor separation R0 along the [001], [110] and [111] Si crystallographic directions, with |R0|=10,20 or 30 nm and standard deviation σR=1,2,5 or 10 nm. Our extensive theoretical results demonstrate the great challenge for a prescribed J gate even with just a donor pair, a first step for any scalable Si-donor-based quantum computer.
Qubits can be made out of a variety of experimental platforms, fig. 1. Small processors have already been demonstrated in trapped ions and superconductors but in both cases, the constraints for coherent manipulation and the effective large size of the qubits including all quantum functionalities are hardly compatible with very large-scale architecture. When it comes to the crucial issue of large-scale integration, Si spin qubits are well positioned due to their long coherence times and compatibility with semiconductor fabrication techniques. Indeed, dephasing times of the order of 1s have been achieved in Si-based spin qubits and single-qubit gate fidelities are high enough for scalable, fault-tolerant quantum computing.