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Enrichment Lengthens Coherence but Barely Changes Circuit Success: A Model of Silicon Spin Qubits

WU Yi-fan

Published Oct 10, 2026• 0 citations
Publisher

Abstract

Abstract - Silicon spin qubits can be built in existing chip factories, but three physical mechanisms limit them: charge noise, hyperfine coupling to residual 29Si nuclear spins, and phonon-driven relaxation. Many groups enrich silicon to remove the 29Si, so I ask whether that is what limits a quantum circuit. I build a closed-form model of the three mechanisms and use it to predict the success probability of a width-8 mirror circuit (56 two-qubit gates). No spin-qubit hardware was available, so every silicon number is a model prediction, not a measurement. Enriching from 4.7% 29Si to 800 ppm lengthens the hyperfine-limited coherence time 7.6-fold, and to 50 ppm 31-fold, yet changes the predicted success probability by less than one percentage point. Charge noise on the two-qubit gate dominates the error, while magnetic field, temperature and relaxation time have no effect. The predicted success probability, 0.73, is lower than the 0.83 measured on a Rigetti superconducting device. The two-qubit error is calibrated to published results and not predicted, and crosstalk and leakage are left out, so this comparison is a rough guide only.

DOI
10.5281/zenodo.23284886

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Abstract - Silicon spin qubits can be built in existing chip factories, but three physical mechanisms limit them: charge noise, hyperfine coupling to residual 29Si nuclear spins, and phonon-driven relaxation. Many groups enrich silicon to remove the 29Si, so I ask whether that is what limits a quantum circuit. I build a closed-form model of the three mechanisms and use it to predict the success probability of a width-8 mirror circuit (56 two-qubit gates). No spin-qubit hardware was available, so every silicon number is a model prediction, not a measurement. Enriching from 4.7% 29Si to 800 ppm lengthens the hyperfine-limited coherence time 7.6-fold, and to 50 ppm 31-fold, yet changes the predicted success probability by less than one percentage point. Charge noise on the two-qubit gate dominates the error, while magnetic field, temperature and relaxation time have no effect. The predicted success probability, 0.73, is lower than the 0.83 measured on a Rigetti superconducting device. The two-qubit error is calibrated to published results and not predicted, and crosstalk and leakage are left out, so this comparison is a rough guide only.
Spin-12\frac{1}{2}21​ 119^{119}119Sn nuclei in a silicon semiconductor could make excellent qubits. Nuclear spins in silicon are known to have long coherence times. Tin is isoelectronic with silicon, so we expect electrons can easily shuttle from one Sn atom to another to propagate quantum information via a hyperfine interaction that we predict, from all-electron linearized augmented plane wave density functional theory calculations, to be roughly ten times larger than intrinsic 29^{29}29Si. A hyperfine-induced electro-nuclear controlled-phase (e-n-CPhase) gate operation, generated (up to local rotations) by merely holding an electron at a sweet-spot of maximum hyperfine strength for a specific duration of time, is predicted to be exceptionally resilient to charge/voltage noise. Diabatic spin flips are suppressed with a modest magnetic field (>15 >15~>15 mT for <10−6<10^{-6}<10−6 flip probabilities) and nuclear spin bath noise may be avoided via isotopic enrichment or mitigated using dynamical decoupling or through monitoring and compensation. Combined with magnetic resonance control, this operation enables universal quantum computation.
Silicon is promising for spin-based quantum computation because nuclear spins, a source of magnetic noise, may be eliminated through isotopic enrichment. Long spin decoherence times T2 have been measured in isotope-enriched silicon but come far short of the T2=2T1 limit. The effect of nuclear spins on T2 is well established. However, the effect of background electron spins from ever present residual phosphorus impurities in silicon can also produce significant decoherence. We study spin decoherence decay as a function of donor concentration, 29Si concentration, and temperature using cluster expansion techniques specifically adapted to the problem of a sparse dipolarly coupled electron spin bath. Our results agree with the existing experimental spin echo data in Si:P and establish the importance of background dopants as the ultimate decoherence mechanism in isotope-enriched silicon.
Logical qubits are essential for utility scale universal quantum computation and require stable, high-fidelity physical qubits. In this thesis we consider three factors that can affect the performance of phosphorus atom qubits in silicon. Specifically, we determined the number of phosphorus atoms in few-atom qubit registers using the charging energy. We then explored if a new silicon encapsulation recipe could reduce charge noise under realistic qubit operating conditions. Finally, we performed experiments on few qubit devices to identify the dominant causes of qubit decoherence. To attain high-fidelity control requires characterising the underlying atomic structure of qubit registers (≤4P). By combining precise (≤5% error) experimentally measured charging energies with high quality STM images and theoretically modelled charging energies, we show the number of phosphorus atoms present can be determined confidently. Previously, our all-epitaxial nat-Si devices have demonstrated record low charge noise (0.17µeV). In this thesis we consider a new Si-28 growth recipe to assess if introducing an annealed ∼1nm silicon locking layer grown at room temperature can further increase the silicon encapsulation quality, whilst minimising P segregation. We first optimised the geometry of SET charge sensors fabricated in Si-28 to obtain high current contrast (≫1nA). For the locking layer (standard recipe) single electron transistors we found high (low) levels of charge noise at 0V (2.1µeV) that increased with the applied voltage (at 0V (0.29µeV) and 0.5V (0.23µeV)). In addition, we found that the electrical behaviour of the locking layer sensors was highly sensitive to the applied voltage. Since qubits are typically operated at ∼0.5V, further work is needed to assess the viability of this new growth recipe. Finally, we investigated different charge and magnetic noise sources that cause qubit decoherence in a 3P register using a modified Hahn echo experiment. Here, we use resonant drive at the frequencies of different nuclear spin species to identify P-31 in the SET island as causing qubit decoherence. Further, we found that the dominant charge noise source for electron spin qubits was the Stark shift of the g-factor. We also found the spin flip rate of phosphorus nuclei in the spin bath was affected by a change in the mechanical noise coupling into the fridge. For nuclear spin qubits we found the dominant noise source to be the Stark shift of the hyperfine interaction.
In semiconductor single-spin qubits, high-fidelity quantum gates have been demonstrated; however, achieving consistent performance remains challenging due to variations in driven qubit coherence, which is less explored than free-evolution coherence such as T2∗T_2^*T2∗​. Here, we report single-qubit gate fidelities above 99.999%, achieved by dramatically extending the driven-spin coherence time and suppressing off-resonant driving effects that are detrimental to accurate fidelity benchmarking. We demonstrate that removing proximal reservoirs significantly enhances the spin-locking coherence time (T1ρT_{1ρ}T1ρ​), a critical metric for qubits under microwave driving. Furthermore, we reveal that in typical spin qubit setups using parity readout and rectangular pulses, off-resonant excitation of neighboring qubits causes substantial benchmarking artifacts. By optimizing device conditions to mitigate microwave-induced degradation and implementing spectrally tailored pulse shaping, we achieve a π/2π/2π/2 gate fidelity of 99.99920(2)%, with remaining errors primarily limited by incoherent noise. These results showcase the mechanisms that bound fidelity benchmarking in state-of-the-art silicon spin qubits and provide practical guidelines for achieving and verifying high fidelities in these systems.
Abstract Quantum computers offer a route to outperform classical methods in tasks such as molecular simulation, motivating hybrid algorithms like the variational quantum eigensolver (VQE) for near-term devices. Silicon spin qubits are a promising platform for scalable quantum computation, but their performance is limited by hardware imperfections—most notably charge-noise–induced potential fluctuations and static miscalibration of gate-electrode voltages—which degrade quantum gate fidelities and, ultimately, algorithmic accuracy. Here we develop a hardware–algorithm co-simulation framework for silicon quantum-dot processors that links 3D electrostatics to effective g -factors and exchange couplings, and propagates voltage-level noise through realistic control pulses. Using VQE for H 2 ground-state energy estimation as a circuit-level testbed, we study both static scaling/offset errors on the gate-electrode voltages and stochastic fluctuations modeled as random-telegraph noise with tunable amplitudes and switching times. At the gate level, we show that exchange-based two-qubit gates are roughly an order of magnitude more sensitive to these types of noise than ESR-driven single-qubit rotations. Quantum process tomography and Kraus-operator analysis further distinguish coherent and incoherent contributions and quantify the fraction of error that is, in principle, correctable by a compensating unitary. Embedding these noise models into the VQE circuit, we identify regimes of miscalibration strength and noise switching time compatible with chemically accurate energy estimates, and discuss how statistical post-processing based on the full distribution of noisy energy estimates could further improve accuracy.
Quantum computers offer a route to outperform classical methods in tasks such as molecular simulation, motivating hybrid algorithms like the Variational Quantum Eigensolver (VQE) for near-term devices. Silicon spin qubits are a promising platform for scalable quantum computation, but their performance is limited by hardware imperfections -- most notably charge-noise-induced potential fluctuations and static miscalibration of gate-electrode voltages -- which degrade quantum gate fidelities and, ultimately, algorithmic accuracy. Here we develop a hardware-algorithm co-simulation framework for silicon quantum-dot processors that links 3D electrostatics to effective ggg-factors and exchange couplings, and propagates voltage-level noise through realistic control pulses. Using VQE for H2\mathrm{H}_2H2​ ground-state energy estimation as a circuit-level testbed, we study both static scaling/offset errors on the gate-electrode voltages and stochastic fluctuations modeled as random-telegraph noise with tunable amplitudes and switching times. At the gate level, we show that exchange-based two-qubit gates are roughly an order of magnitude more sensitive to these types of noise than ESR-driven single-qubit rotations. Quantum process tomography and Kraus-operator analysis further distinguish coherent and incoherent contributions and quantify the fraction of error that is, in principle, correctable by a compensating unitary. Embedding these noise models into the VQE circuit, we identify regimes of miscalibration strength and noise switching time compatible with chemically accurate energy estimates, and discuss how statistical post-processing based on the full distribution of noisy energy estimates could further improve accuracy.