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arXiv:2607.07586

Fidelity Analysis of Adiabatically Driven Donor Spins as Two-Qubit and Ququart Systems

Brian Michon, James Keppens, Ashutosh Kinikar, George Simion, Kristof Moors, Bart Sorée

quant-phSubmitted Jul 8, 2026• Announced Jul 9, 2026• 0 citations
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Abstract

Donor spin systems host a native Hilbert space whose dimension exceeds that of a qubit, meaning they can be used as qudits. Here we study a \ce{Si{:}P} donor spin system through leakage-aware randomized benchmarking (RB) of native ququart $\mathcal{C}_4$ and encoded two-qubit $\mathcal{C}_2^{\otimes 2}$ Clifford groups. We implement adiabatic ramps to operate electron dipole spin resonance (EDSR) pulses at the ionization point, where the electron is shared halfway between the donor and the interface, and to operate electron spin resonance (ESR) pulses near the interface, motivated by the sensitivity of the effective magnetic field to charge noise at the ionization point. By placing the electron near the ionization point only during EDSR control and using sufficiently long displacement ramp durations, leakage outside the computational basis is strongly suppressed, which is crucial for optimized qudit control. We find in our analysis based on leakage RB that $\mathcal{C}_4$ consistently achieves $\sim 40$--$50\%$ lower (lower-bound) error rates $\varepsilon^{\mathrm{LB}}_\mathrm{PT}$ with respect to $\mathcal{C}_2^{\otimes 2}$, due to its reduced circuit complexity. These results indicate that donor spin qudits benefit from genuine qudit operation as opposed to imposed encoded qubit operation.

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Donor spin systems host a native Hilbert space whose dimension exceeds that of a qubit, meaning they can be used as qudits. Here we study a \ce{Si{:}P} donor spin system through leakage-aware randomized benchmarking (RB) of native ququart C4\mathcal{C}_4C4​ and encoded two-qubit C2⊗2\mathcal{C}_2^{\otimes 2}C2⊗2​ Clifford groups. We implement adiabatic ramps to operate electron dipole spin resonance (EDSR) pulses at the ionization point, where the electron is shared halfway between the donor and the interface, and to operate electron spin resonance (ESR) pulses near the interface, motivated by the sensitivity of the effective magnetic field to charge noise at the ionization point. By placing the electron near the ionization point only during EDSR control and using sufficiently long displacement ramp durations, leakage outside the computational basis is strongly suppressed, which is crucial for optimized qudit control. We find in our analysis based on leakage RB that C4\mathcal{C}_4C4​ consistently achieves ∼40\sim 40∼40--50%50\%50% lower (lower-bound) error rates εPTLB\varepsilon^{\mathrm{LB}}_\mathrm{PT}εPTLB​ with respect to C2⊗2\mathcal{C}_2^{\otimes 2}C2⊗2​, due to its reduced circuit complexity. These results indicate that donor spin qudits benefit from genuine qudit operation as opposed to imposed encoded qubit operation.
Two level quantum mechanical systems like spin 1/2 particles lend themselves as a natural qubit implementation. However, encoding a single qubit in several spins reduces the resources necessary for qubit control and can protect from decoherence channels. While several varieties of such encoded spin qubits have been implemented, accurate control remains challenging, and leakage out of the subspace of valid qubit states is a potential issue. Here, we realize high-fidelity single qubit operations for a qubit encoded in two electron spins in GaAs quantum dots by iterative tuning of the all-electrical control pulses. Using randomized benchmarking, we find an average gate fidelity of F=(98.5±0.1) %\mathcal{F} = (98.5 \pm 0.1)\,\%F=(98.5±0.1)% and determine the leakage rate between the computational subspace and other states to L=(0.4±0.1) %\mathcal{L} = (0.4\pm0.1)\,\%L=(0.4±0.1)%. These results also demonstrate that high fidelity gates can be realized even in the presence of nuclear spins as in III-V semiconductors.
Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual (31)P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized (31)P nucleus of a single P donor in isotopically purified (28)Si. We find average gate fidelities of 99.95% for the electron and 99.99% for the nuclear spin. These values are above certain error correction thresholds and demonstrate the potential of donor-based quantum computing in silicon. By studying the influence of the shape and power of the control pulses, we find evidence that the present limitation to the gate fidelity is mostly related to the external hardware and not the intrinsic behaviour of the qubit.
Hole spin qubits in semiconductor quantum dots (QDs) enable high-fidelity all-electric control, but conventional electric dipole spin resonance (EDSR) can require substantial rf drive power at the low magnetic fields that are favorable for qubit coherence and readout. In planar Ge hole spin qubits, this can reach -27 dBm at the device, posing challenges for scalable architectures due to heating and crosstalk. Here, we demonstrate a flopping-mode (FM) qubit in Ge, where a single spin is delocalized in a double QD, combining first-order protection against charge noise with exceptionally efficient electric driving. By mapping out coherence sweet-spots as a function of magnetic field orientation we achieve T2∗=1.4μsT_2^*= 1.4μ\mathrm{s}T2∗​=1.4μs, T2Hahn=11.5μsT_2^{\mathrm{Hahn}}= 11.5 μ\mathrm{s}T2Hahn​=11.5μs, T2φ,CPMG32=130μsT^{φ, \mathrm{CPMG32}}_2= 130 μ\mathrm{s}T2φ,CPMG32​=130μs, and T1=226μsT_1= 226 μ\mathrm{s}T1​=226μs, and a single-qubit gate fidelity of up to 99.76%\%% for a gate time tXπ=88t_{Xπ} = 88tXπ​=88 ns. Importantly, these results are obtained at a nearly in-plane magnetic field of 5 mT using only -52 dBm drive power at the device. We further find that qubit relaxation in this regime is consistent with a two-photon Orbach process, providing a route for further optimization. Our results demonstrate that FM-EDSR supports ultra-low-power, high-fidelity single-qubit operations, improvements that could benefit scalable hole-spin-based architectures and hybrid spin-photon interfaces.
We present a strategy for producing multiqubit gates that promise high fidelity with minimal tuning requirements. Our strategy combines gap protection from the adiabatic theorem with dynamical decoupling in a complementary manner. Energy-level transition errors are protected by adiabaticity and remaining phase errors are mitigated via dynamical decoupling. This is a powerful way to divide and conquer the various error channels. In order to accomplish this without violating a no-go theorem regarding black-box dynamically corrected gates [Phys. Rev. A 80, 032314 (2009)], we require a robust operating point (sweet spot) in control space where the qubits interact with little sensitivity to noise. There are also energy gap requirements for effective adiabaticity. We apply our strategy to an architecture in Si with P donors where we assume we can shuttle electrons between different donors. Electron spins act as mobile ancillary qubits and P nuclear spins act as long-lived data qubits. This system can have a very robust operating point where the electron spin is bound to a donor in the quadratic Stark shift regime. High fidelity single qubit gates may be performed using well-established global magnetic resonance pulse sequences. Single electron-spin preparation and measurement has also been demonstrated. Putting this all together, we present a robust universal gate set for quantum computation.
Quantum physics governs the world at the microscopic scale and determines the properties of matter. While classical computers exploit quantum phenomena passively by relying on transistor technology, the concept of a quantum computer with active control over quantum states promises unprecedented possibilities for information encoding and processing. Already developed quantum algorithms are known to perform certain tasks faster than any existing classical algorithms, and quantum computers also promise the possibility for precise simulations of complex quantum systems, a task infeasible for classical computers. These points emphasize the need for the development of quantum computers. Considering quantum computers, the fundamental unit of information is a qubit, a two-level quantum system. Qubits, in contrast to classical bits which are either in state 0 or 1, can exist in quantum superposition of the states 0 and 1, allowing for more complex and parallel computations. While there are many options to encode a logical qubit in a physical system, spin 1/2 particles are considered a natural choice because their spin degree of freedom defines a qubit intrinsically. Semiconductors are a promising platform for hosting spin qubits, as they enable the confinement of electrons with spin 1/2 either through gate-defined quantum dots (QDs) or donor atoms. Among the possible choices of donor atoms, phosphorous 31P is particularly noteworthy because its nucleus has nuclear spin 1/2. Nuclear spins are prime candidates for qubit implementation because they demonstrated exceptionally long coherence times, but the underlying good isolation from their environment is a challenge when it comes to readout and control. In this thesis, we face this challenge by proposing a hybrid quantum dot-donor (QDD) system consisting of a gate defined silicon (Si) QD and a thereto laterally displaced 31P phosphorous donor atom implanted in the Si host material. A single electron is presumed to be confined in the system, which can be moved between the QD and the donor on demand. If its wave function overlaps with the donor atom, electron spin and the donor nuclear spin interact via the hyperfine interaction and the electron can act as a mediator between the nuclear spin qubit and the environment for readout and control, whereas the nuclear spin qubit can be set in an idling mode by shifting the electron to the QD. Importantly, the proposed system can be embedded in circuit quantum electrodynamics (cQED) architectures enabling strong coupling between the system’s electron spin and microwave resonator photons. This coupling is fundamental for the research presented in this thesis. Analyzing the envisioned system, we first propose a novel method for nuclear-spin readout by probing the resonator transmission. This method is based on the observation that the signature of strong electron spin-photon coupling in the resonator transmission is altered due to the hyperfine interaction, in such a manner that well separated signatures for the electron spin-photon coupling conditioned on the state of the nuclear spin arise. As the next step, we turn our attention to the control of nuclear spin qubits and especially to the challenge of realizing a two-qubit gate between distant nuclear spins. In this course, we derive an effective nuclear spin-photon coupling. While expected to be weak, this interaction can be harnessed to couple the nuclear spins of two distant QDD systems dispersively to a microwave resonator resulting in an entangling nuclear spin two-qubit √iSWAP gate with a gate fidelity approaching 90%. These two key findings represent a significant and valuable contribution to the field of quantum information processing using nuclear spins.
Nuclear spins show exceptionally long coherence times but the underlying good isolation from their environment is a challenge when it comes to controlling nuclear spin qubits. A particular difficulty, not only for nuclear spin qubits, is the realization of two-qubit gates between distant qubits. Recently, strong coupling between an electron spin and microwave resonator photons as well as a microwave resonator mediated coupling between two electron spins both in the resonant and the dispersive regime have been reported and, thus, a microwave resonator mediated electron spin two-qubit gate seems to be in reach. Inspired by these findings, we theoretically investigate the interaction of a microwave resonator with a hybrid quantum dot-donor (QDD) system consisting of a gate-defined Si QD and a laterally displaced 31P^{31}\mathrm{P}31P phosphorous donor atom implanted in the Si host material. We find that driving the QDD system allows to compensate the frequency mismatch between the donor nuclear spin splitting in the MHz regime and typical superconducting resonator frequencies in the GHz regime, and also enables an effective nuclear spin-photon coupling. While we expect this coupling to be weak, we predict that coupling the nuclear spins of two distant QDD systems dispersively to the microwave resonator allows the implementation of a resonator-mediated nuclear spin two-qubit iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​ gate with a gate fidelity approaching 9090%90.