Singlet-triplet Spin Qubit Research Articles

Noise-compensating pulses for electrostatically controlled silicon spin qubits

We study the performance of SUPCODE---a family of dynamically correcting pulses designed to cancel simultaneously both Overhauser and charge noise for singlet-triplet spin qubits---adapted to silicon devices with electrostatic control. We consider both natural Si and isotope-enriched Si systems, and in each case we investigate the behavior of individual gates under static noise and perform randomized benchmarking to obtain the average gate error under realistic 1/f noise. We find that in most cases SUPCODE pulses offer roughly an order of magnitude reduction in gate error, and especially in the case of isotope-enriched Si, SUPCODE yields gate operations of very high fidelity. We also develop a version of SUPCODE that cancels the charge noise only, "$\delta J$-SUPCODE", which is particularly beneficial for isotope-enriched Si devices where charge noise dominates Overhauser noise, offering a level of error reduction comparable to the original SUPCODE while yielding gate times that are 30% to 50% shorter. Our results show that the SUPCODE noise-compensating pulses provide a fast, simple, and effective approach to error suppression, bringing gate errors well below the quantum error correction threshold in principle.

Suppressing qubit dephasing using real-time Hamiltonian estimation.

Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and materials engineering, quantum error correction and dynamical decoupling can mitigate decoherence, but generally increase experimental complexity. Here we improve coherence in a qubit using real-time Hamiltonian parameter estimation. Using a rapidly converging Bayesian approach, we precisely measure the splitting in a singlet-triplet spin qubit faster than the surrounding nuclear bath fluctuates. We continuously adjust qubit control parameters based on this information, thereby improving the inhomogenously broadened coherence time from tens of nanoseconds to >2 μs. Because the technique demonstrated here is compatible with arbitrary qubit operations, it is a natural complement to quantum error correction and can be used to improve the performance of a wide variety of qubits in both meteorological and quantum information processing applications.

Magnetically tunable singlet-triplet spin qubit in a four-electron InGaAs coupled quantum dot.

A pair of self-assembled InGaAs quantum dots filled with two electrons can act as a singlet-triplet spin qubit that is robust against nuclear spin fluctuations as well as charge noise. This results in a T2* coherence time two orders of magnitude longer than that of a single electron, provided the qubit is operated at a particular “sweet spot” in gate voltage. However, at this fixed operating point the ground-state splitting can no longer be tuned into resonance with e.g. another qubit, limiting the options for coupling multiple qubits. Here, we propose using a four-electron coupled quantum dot to implement a singlet-triplet qubit that features a magnetically tunable level splitting. As a first step towards full experimental realization of this qubit design, we use optical spectroscopy to demonstrate the tunability of the four-electron singlet-triplet splitting in a moderate magnetic field.

Noise-protected gate for six-electron double-dot qubit

Singlet-triplet spin qubits in six-electron double quantum dots, in moderate magnetic fields, can show superior immunity to charge noise. This immunity results from the symmetry of orbitals in the second energy shell of circular quantum dots: singlet and triplet states in this shell have identical charge distributions. Our phase-gate simulations, which include $1/f$ charge noise from fluctuating traps, show that this symmetry is most effectively exploited if the gate operation switches rapidly between sweet spots deep in the (3,3) and (4,2) charge stability regions; fidelities very close to one are predicted if subnanosecond switching can be performed.

Automated synthesis of dynamically corrected quantum gates

We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches unfeasible. By focusing on the important case of singlet-triplet electron spin qubits, we show how ideas from optimal control theory may be used to automate the synthesis of dynamically corrected gates that simultaneously minimize the system's sensitivity against both decoherence and control errors. Explicit sequences for effecting robust single-qubit rotations subject to realistic timing and pulse-shaping constraints are provided, which can deliver substantially improved gate fidelity for state-of-the-art experimental capabilities.

Dynamical decoupling of a singlet-triplet qubit afflicted by a charge fluctuator

The efficiency of dynamical decoupling pulse sequences in removing noise due to a charge fluctuator is studied for a singlet-triplet spin qubit. We develop a numerical method to solve the dynamical equations for all three components of the Bloch vector under a general pulse protocol, and with an arbitrary rotation axis. The qubit is shown to undergo both dephasing and dissipative dynamics, pending on its working point. Analytical solutions are found for the limits of weakly and strongly coupled fluctuators, shedding light on the distinct dynamics in the different parameter regimes. Scaling of the qubit decay time with the number of control pulses is found to follow a power law over a wide range of TLF parameters and qubit bias points.

Scaling of Dynamical Decoupling for Spin Qubits

We investigate the scaling of coherence time T(2) with the number of π pulses n(π) in a singlet-triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law T(2) is proportional to (n(π))(γ(e)), with γ(e)=0.72±0.01, essentially independent of the envelope function used to extract T(2). From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S(ω)~ω(-β), yields β=γ(e)/(1-γ(e))=2.6±0.1. Model values for T(2)(n(π)) using β=2.6 for CPMG with both even and odd n(π) up to 32 and CDD orders 3 through 6 compare very well with the experiment.

Composite pulses for robust universal control of singlet–triplet qubits

Precise qubit manipulation is fundamental to quantum computing, yet experimental systems generally have stray coupling between the qubit and the environment, which hinders the necessary high-precision control. Here, we report the first theoretical progress in correcting an important class of errors stemming from fluctuations in the magnetic field gradient, in the context of the singlet-triplet spin qubit in a semiconductor double quantum dot. These errors are not amenable to correction via control techniques developed in other contexts, as here the experimenter has precise control only over the rotation rate about the z axis of the Bloch sphere, and this rate is furthermore restricted to be positive and bounded. Despite these strong constraints, we construct simple electrical pulse sequences that, for small gradients, carry out z axis rotations while cancelling errors up to the sixth order in gradient fluctuations, and for large gradients, carry out arbitrary rotations while cancelling the leading order error.

Screening of charged impurities with multielectron singlet-triplet spin qubits in quantum dots

Charged impurities in semiconductor quantum dots comprise one of the main obstacles to achieving scalable fabrication and manipulation of singlet-triplet spin qubits. We theoretically show that using dots that contain several electrons each can help to overcome this problem through the screening of the rough and noisy impurity potential by the excess electrons. We demonstrate how the desired screening properties turn on as the number of electrons is increased, and we characterize the properties of a double quantum dot singlet-triplet qubit for small odd numbers of electrons per dot. We show that the sensitivity of the multi-electron qubit to charge noise may be an order of magnitude smaller than that of the two-electron qubit.

Electrically controlled quantum gates for two-spin qubits in two double quantum dots

Exchange-coupled singlet-triplet spin qubits in two gate-defined double quantum dots are considered theoretically. Using charge density operators to describe the double-dot orbital states, we calculate the Coulomb couplings between the qubits and identify optimal bias points for single- and two-qubit operations, as well as convenient idle positions. The same intuitive formulation is used to derive dephasing rates of these qubits due to the fluctuating charge environment, thereby providing the main considerations for a quantum computation architecture that is within current experimental capabilities.

Charge-State Conditional Operation of a Spin Qubit

We report coherent operation of a singlet-triplet qubit controlled by the spatial arrangement of two confined electrons in an adjacent double quantum dot that is electrostatically coupled to the qubit. This four-dot system is the specific device geometry needed for two-qubit operations of a two-electron spin qubit. We extract the strength of the capacitive coupling between qubit and adjacent double quantum dot and show that the present geometry allows fast conditional gate operation, opening pathways toward implementation of a universal set of gates for singlet-triplet spin qubits.

Phenomenological study of decoherence in solid-state spin qubits due to nuclear spin diffusion

We present a study of the prospects for coherence preservation in solid-state spin qubits using dynamical decoupling protocols. Recent experiments have provided the first demonstrations of multipulse dynamical decoupling sequences in this qubit system, but quantitative analyses of potential coherence improvements have been hampered by a lack of concrete knowledge of the relevant noise processes. We present calculations of qubit coherence under the application of arbitrary dynamical decoupling pulse sequences based on an experimentally validated semiclassical model. This phenomenological approach bundles the details of underlying noise processes into a single experimentally relevant noise power spectral density. Our results show that the dominant features of experimental measurements in a two-electron singlet-triplet spin qubit can be replicated using a $1/{\ensuremath{\omega}}^{2}$ noise power spectrum associated with nuclear spin flips in the host material. Beginning with this validation, we address the effects of nuclear programming, high-frequency nuclear spin dynamics, and other high-frequency classical noise sources, with conjectures supported by physical arguments and microscopic calculations where relevant. Our results provide expected performance bounds and identify diagnostic metrics that can be measured experimentally in order to better elucidate the underlying nuclear spin dynamics.