arXiv subjects

Wayne M. Witzel

Publications and source records attributed to Wayne M. Witzel.

15 recordsLinked to original sources

arXiv2026

Noise-resilient and Scalable Quantum Error Correction for Nuclear Spin Qubits in Silicon with Electron Shuttling

Nuclear spin qubits in silicon are well-isolated from their environment. Consequently, they have very long lifetimes and low sensitivity to noise, but this also suggests that control and measurement is challenging. We introduce electron pair interferometry (EPI), a protocol to overcome this challenge and maintain robustness to noise. EPI is implemented using an array of quantum dots with isoelectronic nuclear spin qubits located in the dots. A pair of electrons are initialized into a singlet ground state, split apart, and shuttled to the dots containing nuclear spin qubits. We show it is possible to coherently transfer the parity of the nuclei onto the measurable state of singlet/triplet-encoded electrons. Global nuclear magnetic resonance (NMR) can be used to change bases and implement dynamical decoupling (DD). Combined with selective hyperfine-induced $Z_π$ rotations, our gate set is complete for universal quantum computation, tailored to Calderbank-Shor-Steane (CSS) quantum error correction, and robust to noise. We discuss very low sensitivity to charge noise and study the sensitivity to both DC and AC magnetic field inhomogeneity which depends strongly on their relative strengths.

quant-ph↗

arXiv2026

Predicting the Slow Drift of Nuclear Spin Noise in Semiconductor Spin Qubits

The dynamics of a nuclear spin bath generates magnetic noise that is a key contributor to the decoherence of electron spin qubits in electrostatically-defined quantum dots. In this paper, we extend the cluster correlation expansion (CCE) technique, which has proven useful for predicting solid-state qubit coherence times across various settings but is limited to shorter time scales, to incorporate stochastic treatments of cluster dynamics in order to efficiently predict slow drifting Overhauser fields over longer time scales. This approach combines quantum evolution with classical rate matrices to enable simulation across a wide range of temporal regimes required to simulate, for example, the long-time convergence of the ergodic $T_2^*$ from Ramsey experiments. Our methodology is validated against experimental data from various silicon spin qubit systems, demonstrating a strong agreement between simulation and measurement of Ramsey experiments presented in the form of $T_2^*$ versus averaging time, autocorrelation functions, as well as power spectral densities. Furthermore, we demonstrate significant back-action effects through modeling and experiment; specifically, the dynamics of the nuclear spin bath depends upon the electron spin occupation schedule. Finally, our modeling quantitatively predicts the benefits from compensating for the slow drift of Overhauser fields in qubit operations. Our findings indicate that compensating for an Overhauser rotation measured $Δt$ in the past results in an effective $T_2^*$, which we denote $\tilde{T}_2^*(Δt)$ for clarity, under certain scenarios of interest, can be one or two orders of magnitude larger than the ergodic $T_2^*$ if the Overhauser rotation is re-characterized every 100 milliseconds; that is, $\tilde{T}_2^*(Δt = 100~{\rm ms})$ can be $10$ to $100$ times larger than $T_2^*$.

cond-mat.mes-hall↗

arXiv2026

Correcting coherent quantum errors by going with the flow

The performance of a given quantum error correction (QEC) code depends upon the noise model that is assumed. Independent Pauli noise, applied after each quantum operation, is a simplistic noise model that is easy to simulate and understand in the context of stabilizer codes. Although such a noise model is artificial, it is equivalent to independent, random, unbiased qubit rotations. What about spatially or temporally correlated qubit rotations? Such a noise model is applicable to global operations (e.g., NMR or ESR), common control sources (e.g., lasers), or slow drift (e.g., charge or magnetic noise) in various qubit technologies. In the worst case, such errors can combine constructively and result in a post-correction failure rate that increases with the number of error correction cycles. However, we show that this worst case does not generally arise unless taking active corrective actions while performing QEC. That is, by employing virtual Pauli frame updates ("passive" error correction) rather than physical corrections ("active" error correction), coherent errors do not compound appreciably. Starting in a random Pauli frame is also advantageous. In fact, through perturbation theory arguments and supporting numerical simulations, we show that the logical qubit performance beyond distance 3 for correlated single-qubit Hamiltonian noise models (i.e., global errant qubit rotations), when employing these "lazy" strategies, essentially matches the performance of Pauli noise model with the same process fidelity (fidelity after one application). In a more general circuit model of noise, correlations may add constructively within syndrome extraction rounds but Pauli frame randomization from passive error correction mitigates this effect across multiple rounds.

quant-ph↗

arXiv2023

Verifying Quantum Phase Estimation (QPE) using Prove-It

The general-purpose interactive theorem-proving assistant called Prove-It was used to verify the Quantum Phase Estimation (QPE) algorithm, specifically claims about its outcome probabilities. Prove-It is unique in its ability to express sophisticated mathematical statements, including statements about quantum circuits, integrated firmly within its formal theorem-proving framework. We demonstrate our ability to follow a textbook proof to produce a formally certified proof, highlighting useful automation features to fill in obvious steps and make formal proving nearly as straightforward as informal theorem proving. Finally, we make comparisons with formal theorem-proving in other systems where similar claims about QPE have been proven.

quant-ph↗

arXiv2022

The remarkable prospect for quantum-dot-coupled tin qubits in silicon

Spin-$\frac{1}{2}$ $^{119}$Sn 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 $^{29}$Si. 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 ($>15~$mT for $<10^{-6}$ 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.

quant-ph↗

arXiv2020

Prove-It: A Proof Assistant for Organizing and Verifying General Mathematical Knowledge

We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a highly-flexible Jupyter notebook-based user interface that documents interactions and proof steps using LaTeX. We review Prove-It's highly expressive representation of expressions, judgments, theorems, and proofs; demonstrate the system by constructing a traditional proof-by-contradiction that $\sqrt{2}\notin\mathbb{Q}$; and discuss how the system avoids inconsistencies such as Russell's and Curry's paradoxes. Extensive documentation is provided in the appendices about core elements of the system. Current development and future work includes promising applications to quantum circuit manipulation and quantum algorithm verification.

cs.LO↗

arXiv2017

Probing low noise at the MOS interface with a spin-orbit qubit

The silicon metal-oxide-semiconductor (MOS) material system is technologically important for the implementation of electron spin-based quantum information technologies. Researchers predict the need for an integrated platform in order to implement useful computation, and decades of advancements in silicon microelectronics fabrication lends itself to this challenge. However, fundamental concerns have been raised about the MOS interface (e.g. trap noise, variations in electron g-factor and practical implementation of multi-QDs). Furthermore, two-axis control of silicon qubits has, to date, required the integration of non-ideal components (e.g. microwave strip-lines, micro-magnets, triple quantum dots, or introduction of donor atoms). In this paper, we introduce a spin-orbit (SO) driven singlet-triplet (ST) qubit in silicon, demonstrating all-electrical two-axis control that requires no additional integrated elements and exhibits charge noise properties equivalent to other more model, but less commercially mature, semiconductor systems. We demonstrate the ability to tune an intrinsic spin-orbit interface effect, which is consistent with Rashba and Dresselhaus contributions that are remarkably strong for a low spin-orbit material such as silicon. The qubit maintains the advantages of using isotopically enriched silicon for producing a quiet magnetic environment, measuring spin dephasing times of 1.6 $μ$s using 99.95% $^{28}$Si epitaxy for the qubit, comparable to results from other isotopically enhanced silicon ST qubit systems. This work, therefore, demonstrates that the interface inherently provides properties for two-axis control, and the technologically important MOS interface does not add additional detrimental qubit noise.

cond-mat.mes-hall↗

arXiv2015

Multi-qubit gates protected by adiabaticity and dynamical decoupling applicable to donor qubits in silicon

We present a strategy for producing multi-qubit 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. To avoid degenerate states and maximize the benefit of the gap protection, the scheme is best suited when there are two different kinds of qubits (not mutually resonant). Furthermore, we require a robust operating point in control space where the qubits interact with little sensitivity to noise. This allows us to circumvent a No-Go theorem that prevents block-box dynamically corrected gates [Phys. Rev. A 80, 032314 (2009)]. We show how to 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.

quant-ph↗

arXiv2014

Converting a real quantum bath to an effective classical noise

We present a cluster expansion method for approximating quantum spin-bath dynamics in terms of a classical Gaussian stochastic process. The cluster expansion produces the two-point correlation function of the approximate classical bath, permitting rapid evaluation of noise-mitigating quantum control strategies without resorting to computationally intensive dynamical decoupling models. Our approximation is valid for the wide class of models possessing negligible back-action and nearly-Gaussian noise. We study several instances of the central spin decoherence problem in which the central spin and randomly-located bath spins are alike and dipolarly coupled. For various pulse sequences, we compare the coherence echo decay computed explicitly quantum mechanically versus those computed using our approximate classical model, and obtain agreement in most, but not all, cases. We demonstrate the utility of these classical noise models by efficiently searching for the 4-pulse sequences that maximally mitigate decoherence in each of these cases, a computationally expensive task in the explicit quantum model.

cond-mat.mes-hall↗

arXiv2012

Quantum Decoherence of the Central Spin in a Sparse System of Dipolar Coupled Spins

The central spin decoherence problem has been researched for over 50 years in the context of both nuclear magnetic resonance and electron spin resonance. Until recently, theoretical models have employed phenomenological stochastic descriptions of the bath-induced noise. During the last few years, cluster expansion methods have provided a microscopic, quantum theory to study the spectral diffusion of a central spin. These methods have proven to be very accurate and efficient for problems of nuclear-induced electron spin decoherence in which hyperfine interactions with the central electron spin are much stronger than dipolar interactions among the nuclei. We provide an in-depth study of central spin decoherence for a canonical scale-invariant all-dipolar spin system. We show how cluster methods may be adapted to treat this problem in which central and bath spin interactions are of comparable strength. Our extensive numerical work shows that a properly modified cluster theory is convergent for this problem even as simple perturbative arguments begin to break down. By treating clusters in the presence of energy detunings due to the long-range (diagonal) dipolar interactions of the surrounding environment and carefully averaging the effects over different spin states, we find that the nontrivial flip-flop dynamics among the spins becomes effectively localized by disorder in the energy splittings of the spins. This localization effect allows for a robust calculation of the spin echo signal in a dipolarly coupled bath of spins of the same kind, while considering clusters of no more than 6 spins. We connect these microscopic calculation results to the existing stochastic models. We, furthermore, present calculations for a series of related problems of interest for candidate solid state quantum bits including donors and quantum dots in silicon as well as nitrogen-vacancy centers in diamond.

cond-mat.mes-hall↗

arXiv2012

Optimized pulses for the control of uncertain qubits

Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for π/2- and π-pulses, and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from π/2- and π-pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter, to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, post facto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.

quant-ph↗

arXiv2012

SiGe/Si quantum dot electron spin decoherence dependence on $^{73}$Ge

We theoretically study the nuclear spin induced decoherence of a quantum dot in Si that is confined at a SiGe interface. We calculate decoherence time dependence on $^{73}$Ge in the barrier layer to evaluate the importance of Ge as well as Si enrichment for long decoherence times. We use atomistic tight-binding modeling for an accurate account of the electron wavefunction which is particularly important for determining the contact hyperfine interactions with the Ge nuclear spins. We find decoherence times due to Ge spins at natural concentrations to be milliseconds. This suggests SiGe/Si quantum dot devices employing enriched Si will require enriched Ge as well in order to benefit from long coherence times. We provide a comparison of $T_2$ times for various fractions of nonzero spin isotopes of Si and Ge.

cond-mat.mes-hall↗

arXiv2011

Quantum control of hybrid nuclear-electronic qubits

Pulsed magnetic resonance is a wide-reaching technology allowing the quantum state of electronic and nuclear spins to be controlled on the timescale of nanoseconds and microseconds respectively. The time required to flip either dilute electronic or nuclear spins is orders of magnitude shorter than their decoherence times, leading to several schemes for quantum information processing with spin qubits. We investigate instead the novel regime where the eigenstates approximate 50:50 superpositions of the electronic and nuclear spin states forming "hybrid nuclear-electronic" qubits. Here we demonstrate quantum control of these states for the first time, using bismuth-doped silicon, in just 32 ns: this is orders of magnitude faster than previous experiments where pure nuclear states were used. The coherence times of our states are five orders of magnitude longer, reaching 4 ms, and are limited by the naturally-occurring 29Si nuclear spin impurities. There is quantitative agreement between our experiments and no-free-parameter analytical theory for the resonance positions, as well as their relative intensities and relative Rabi oscillation frequencies. In experiments where the slow manipulation of some of the qubits is the rate limiting step, quantum computations would benefit from faster operation in the hybrid regime.

quant-ph↗

arXiv2010

Electron spin decoherence in isotope-enriched silicon

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, $T_2$, have been measured in isotope-enriched silicon but come far short of the $T_2 = 2 T_1$ limit. The effect of nuclear spins on $T_2$ 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, $^{29}$Si 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.

cond-mat.mes-hall↗

arXiv2010

Quantum simulation of multiple-exciton generation in a nanocrystal by a single photon

We have shown theoretically that efficient multiple exciton generation (MEG) by a single photon can be observed in small nanocrystals (NCs). Our quantum simulations that include hundreds of thousands of exciton and multi-exciton states demonstrate that the complex time-dependent dynamics of these states in a closed electronic system yields a saturated MEG effect on a picosecond timescale. Including phonon relaxation confirms that efficient MEG requires the exciton--biexciton coupling time to be faster than exciton relaxation time.

cond-mat.mes-hall↗