Researchers at the University of Maryland have detailed the performance of SAGE spin qubits, a novel qubit design encoding a single qubit in the spins of four electrons within four tunnel-coupled quantum dots. The work characterizes how these qubits, inherently protected from magnetic noise due to their singlet-only encoding and always-on exchange couplings, respond to fluctuations caused by charge noise.

While the always-on operation increases sensitivity to charge noise, the team demonstrates that realistic pulse sequences can extend single-qubit coherence times and improve two-qubit gate fidelity even with experimentally relevant noise levels. The results, based on a Hubbard model, propose a refocusing strategy and optimized pulse timings to mitigate these effects.

SAGE Qubit Resilience to Magnetic Field Gradients

Modeling each SAGE qubit as a Hubbard-like system, researchers characterized performance in the presence of 1/f charge noise, specifically fluctuations impacting both dot chemical potentials and interdot tunnel couplings. This approach uses a description of four electrons contained within four quantum dots, acknowledging the established effectiveness of the Hubbard model for spin qubits due to its accurate representation of exchange coupling originating from the quantum dots.

The work details how these fluctuations act as a source of decoherence, a critical factor in qubit stability and operational lifespan. The team accounted for magnetic field gradients as random, quasistatic fluctuations of the local magnetic field, represented by an equation incorporating the magnetic disorder and the Pauli z matrix acting on each electron’s spin.

These fluctuations were sampled from a normal distribution, centered around a value of negative delta h and a standard deviation of delta h, acknowledging the influence of local nuclear environments and g-factor variations on qubit behavior. The magnetic disorder was polarized along the z-direction, a consequence of the large background magnetic field applied during operation. All leakage states beyond the primary SAGE qubit subspace were deemed negligible due to the strong background magnetic field, simplifying the effective Hamiltonian used to describe the qubit’s behavior.

Projecting this Hamiltonian onto the SAGE basis states resulted in an equation defining the effective SAGE qubit Hamiltonian, incorporating Pauli matrices and exchange couplings between the dots. Throughout the analysis, the researchers consistently operated the SAGE qubit at a “charge noise sweet spot,” setting all dot chemical potentials to zero to streamline single-qubit rotations by modulating the effective tunneling strengths between neighboring dots. This strategy, while enhancing control, simultaneously introduces a trade-off, as the always-on exchange couplings that protect against magnetic noise increase the qubit’s susceptibility to charge noise.

Singlet-Only Encoding and Leakage Suppression in SAGE Qubits

The SAGE qubit design achieves inherent protection from magnetic-gradient-induced errors through its singlet-only encoding, a characteristic that sets it apart from conventional exchange-only (EO) qubits susceptible to local magnetic field variations and g-factor fluctuations. This resilience stems from the qubit’s encoding being invariant under magnetic field gradients, while always-on exchange couplings energetically suppress leakage from the computational subspace. Analysis of this effective qubit Hamiltonian revealed a maximized gap between qubit and leakage states when interdot couplings are equal, a condition the researchers termed the ‘leakage-protected idle’ (LPI) point.

The team modeled the underlying electronic structure using a Hubbard model, allowing them to quantify the impact of 1/f charge noise on qubit coherence. Their calculations demonstrate that the LPI point, indicated in figures within the study, defines the ideal operating condition for minimizing leakage.

Hubbard Model Characterization of SAGE Qubit Performance

The approach incorporates 1/f charge noise, a common source of decoherence, by simulating its effects on gate potentials controlling detunings between the quantum dots and the strength of the tunnel couplings between them. Calculations of idle coherence times show that applying pulse sequences similar to those used in Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling can significantly extend the time SAGE qubits maintain quantum information.

Specifically, the team found these pulses can enhance the T2 coherence times, a key metric for qubit stability, to hundreds of microseconds for realistic levels of charge noise. “Using a Hubbard model description of the coupled quantum dots, we have demonstrated that the deleterious effects of time-dependent 1/f charge noise on the performance of singlet-only always-on gapless exchange (SAGE) spin qubits can be mitigated through simple refocusing pulses reminiscent of CPMG,” the study reports.

Impact of 1/f Charge Noise on SAGE Coherence

This dynamic decoupling approach directly addresses the increased sensitivity to charge noise inherent in the always-on operation of SAGE qubits, a trade-off previously identified as a key challenge. The team’s analysis of energy spectra reveals that a specific configuration, where the chemical potential is balanced across all four quantum dots, represents a “charge noise sweet spot,” minimizing sensitivity to fluctuations in chemical potentials. This point corresponds to a condition where the qubit is, to first order, insensitive to these fluctuations.

The study’s modeling, based on a Hubbard model, also demonstrates that the fidelity of SAGE two-qubit gates is less affected by charge noise amplitudes than by magnetic-gradient-induced leakage. The SAGE qubit subspace is inherently protected from magnetic-gradient-induced Pauli errors by virtue of the singlet-only encoding, which is invariant under magnetic field gradients, and the always-on exchange couplings, which provide energetic leakage protection.

CPMG Pulse Sequences for Extended SAGE Coherence

Dynamical decoupling techniques can extend the coherence of SAGE spin qubits to hundreds of microseconds, even with significant charge noise, bringing their performance in line with conventional spin qubits in charge-noise dominated environments. Researchers demonstrated that pulse sequences resembling the Carr-Purcell-Meiboom-Gill (CPMG) method effectively cancel low-frequency charge fluctuations, maintaining a performance advantage in magnetic-noise dominated regimes. The team’s analysis, based on a four-dot Hubbard model, focused on characterizing the behavior of SAGE qubits under both quasistatic magnetic and 1/f charge noise.

Calculations of SAGE idle coherence times with and without dynamical decoupling revealed that CPMG-type pulse sequences substantially enhance the T₂ times, a metric for qubit coherence, of SAGE qubits. Pulse lengths of approximately 20 nanoseconds were achieved by reducing exchange couplings to J₀/2, and the idling time between neighboring pulses was set to zero for initial calculations.

Realistic CPMG-like pulse sequences can be used to significantly extend SAGE single-qubit coherence times for experimentally relevant charge noise strengths. Because the SAGE qubit is gapless, there is no inherent distinction between energy relaxation time (T₁) and dephasing time (T₂), and the study measured dephasing time in the qubit’s x basis as a measure of overall coherence.

SAGE Two-Qubit Gate Fidelity Under Charge Noise

Calculations reveal that refocusing pulses can significantly improve the fidelity of two-qubit gates in SAGE spin qubits, mitigating the impact of charge noise. Further analysis of CZ gate fidelity as a function of charge noise strength revealed an interesting trade-off. The simulations show that a larger maximum exchange interaction, $J_{m a x}$ , enables faster gate operation but simultaneously amplifies the effects of single-qubit charge noise, leading to approximately constant infidelity with varying $J_{m a x}$ .

This suggests that achieving high-fidelity two-qubit gates does not necessarily require maximizing $J_{m a x}$ , but rather optimizing the balance between gate speed and noise mitigation. The results indicate that realistic levels of charge noise can be overcome with careful pulse engineering.

Refocusing Strategies to Mitigate Noise in SAGE Gates

Calculations reveal these sequences can significantly improve coherence times, key for performing complex quantum computations with these qubits under realistic conditions. This approach focuses on applying repeated π-pulses around the qubit’s y-axis, mirroring the principles of Carr-Purcell-Meiboom-Gill (CPMG) sequences, to counteract the disruptive effects of fluctuating charge. These high-fidelity gates were achieved even when accounting for imperfections in the pulses used to perform rotations, demonstrating the robustness of the technique.

The team’s analysis demonstrates that this refocusing scheme does not require correction of noise within the entangling interaction itself, a significant advantage. Simulations using finite-width pulses, representing realistic experimental conditions, show that the refocusing strategy substantially improves overall qubit performance, rather than introducing detrimental overhead.

These results suggest that dynamical decoupling approaches will meaningfully improve key performance metrics as SAGE qubits progress toward experimental realization, positioning them as a potentially attractive building block for scalable, all-electrical spin qubit architectures. The work clarifies that SAGE qubits, while inherently protected from magnetic noise, benefit from active mitigation of charge noise to achieve optimal performance.

Ramp Time Optimization for SAGE Entangling Pulses

These parameters define the foundation for exploring how pulse shaping impacts qubit fidelity and leakage. A smoothly varying exchange coupling, achieved through carefully controlled pulse shapes, ensures adiabatic evolution and minimizes population of these unwanted leakage states. The team modeled these pulses as square waves with raised-cosine edges, using a ramp time parameter to fine-tune performance.

👉 More information
🗞 Singlet-only always-on gapless exchange spin qubits: Charge noise effects and two-qubit gates
✍️ Nathan L. Foulk, Katharina Laubscher, Silas Hoffman and Sankar Das Sarma
🧠 DOI: http://link.aps.org/doi/10.1103/8bzz-rw2j

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