Singlet-triplet Spin Qubit Research Articles

Semiconductor spin qubits

Spin qubits, employing the fundamental quantum property of intrinsic angular momentum of individual electrons and nuclei, continue to develop and evolve. Lithographically patterned semiconductor chips play host to spin-qubit systems in which long coherence times, high-fidelity quantum gates, and single-shot quantum measurement are now routine. This review summarizes progress in four current qubit types: single spin qubits, donor spin qubits, singlet triplet spin qubits, and exchange-only spin qubits. All have been boosted by advances in mesoscopic physics. On the other hand, all systems still need to address challenges to further progress, such as the mitigation of noise and the establishment of long-distance quantum entanglement.

In-flight detection of few electrons using a singlet-triplet spin qubit

We investigate experimentally the capacitive coupling between a two-electron singlet-triplet spin qubit and flying electrons propagating in quantum Hall edge channels. After calibration of the spin qubit detector, we assess its charge sensibility and demonstrate experimentally the detection of less than five flying electrons with average measurement. This experiment demonstrates that the spin qubit is an ultrasensitive and fast charge detector with the perspective of a future single shot-detection of a single flying electron. This work opens the route toward quantum electron optics experiments at the single electron level in semiconductor circuits.

Parametric longitudinal coupling between a high-impedance superconducting resonator and a semiconductor quantum dot singlet-triplet spin qubit

Coupling qubits to a superconducting resonator provides a mechanism to enable long-distance entangling operations in a quantum computer based on spins in semiconducting materials. Here, we demonstrate a controllable spin-photon coupling based on a longitudinal interaction between a spin qubit and a resonator. We show that coupling a singlet-triplet qubit to a high-impedance superconducting resonator can produce the desired longitudinal coupling when the qubit is driven near the resonator’s frequency. We measure the energy splitting of the qubit as a function of the drive amplitude and frequency of a microwave signal applied near the resonator antinode, revealing pronounced effects close to the resonator frequency due to longitudinal coupling. By tuning the amplitude of the drive, we reach a regime with longitudinal coupling exceeding 1 MHz. This mechanism for qubit-resonator coupling represents a stepping stone towards producing high-fidelity two-qubit gates mediated by a superconducting resonator.

All-electrical control of hole singlet-triplet spin qubits at low-leakage points

We study the effect of the spin-orbit interaction on heavy holes confined in a double quantum dot in the presence of a magnetic field of arbitrary direction. Rich physics arise as the two hole states of different spin are not only coupled by the spin-orbit interaction but additionally by the effect of site-dependent anisotropic $g$ tensors. It is demonstrated that these effects may counteract in such a way as to cancel the coupling at certain detunings and tilting angles of the magnetic field. This feature may be used in singlet-triplet qubits to avoid leakage errors and implement an electrical spin-orbit switch, suggesting the possibility of task-tailored two-axes control. Additionally, we investigate systems with a strong spin-orbit interaction at weak magnetic fields. By exact diagonalization of the dominant Hamiltonian we find that the magnetic field may be chosen such that the qubit ground state is mixed only within the logical subspace for realistic system parameters, hence reducing leakage errors and providing reliable control over the qubit.

Designing arbitrary single-axis rotations robust against perpendicular time-dependent noise

Low-frequency time-dependent noise is one of the main obstacles on the road toward a fully scalable quantum computer. The majority of solid-state qubit platforms, from superconducting circuits to spins in semiconductors, are greatly affected by 1/f noise. Among the different control techniques used to counteract noise effects on the system, dynamical decoupling sequences are one of the most effective. However, most dynamical decoupling sequences require unbounded and instantaneous pulses, which are unphysical and can only implement identity operations. Among methods that do restrict to bounded control fields, there remains a need for protocols that implement arbitrary gates with lab-ready control fields. In this work, we introduce a protocol to design bounded and continuous control fields that implement arbitrary single-axis rotations while shielding the system from low-frequency time-dependent noise perpendicular to the control axis. We show the versatility of our method by presenting a set of non-negative-only control pulses that are immediately applicable to quantum systems with constrained control, such as singlet-triplet spin qubits. Finally, we demonstrate the robustness of our control pulses against classical 1/f noise and noise modeled with a random quantum bath, showing that our pulses can even outperform ideal dynamical decoupling sequences.

Charge Noise and Overdrive Errors in Dispersive Readout of Charge, Spin, and Majorana Qubits

Solid-state qubits incorporating quantum dots can be read out by gate reflectometry. Here, we theoretically describe physical mechanisms that render such reflectometry-based readout schemes imperfect. We discuss charge qubits, singlet-triplet spin qubits, and Majorana qubits. In our model, we account for readout errors due to slow charge noise, and due to overdriving, when a too strong probe is causing errors. A key result is that for charge and spin qubits, the readout fidelity saturates at large probe strengths, whereas for Majorana qubits, there is an optimal probe strength which provides a maximized readout fidelity. We also point out the existence of severe readout errors appearing in a resonance-like fashion as the pulse strength is increased, and show that these errors are related to probe-induced multi-photon transitions. Besides providing practical guidelines toward optimized readout, our study might also inspire ways to use gate reflectometry for device characterization.

Closed-loop control of a GaAs-based singlet-triplet spin qubit with 99.5% gate fidelity and low leakage

Semiconductor spin qubits have recently seen major advances in coherence time and control fidelities, leading to a single-qubit performance that is on par with other leading qubit platforms. Most of this progress is based on microwave control of single spins in devices made of isotopically purified silicon. For controlling spins, the exchange interaction is an additional key ingredient which poses new challenges for high-fidelity control. Here, we demonstrate exchange-based single-qubit gates of two-electron spin qubits in GaAs double quantum dots. Using careful pulse optimization and closed-loop tuning, we achieve a randomized benchmarking fidelity of (99.50±0.04)% and a leakage rate of 0.13% out of the computational subspace. These results open new perspectives for microwave-free control of singlet-triplet qubits in GaAs and other materials.

High-fidelity gate set for exchange-coupled singlet-triplet qubits

In order to enable semiconductor-based quantum computing with many qubits, issues like residual interqubit coupling and constraints from scalable control hardware need to be tackled to retain the high gate fidelities demonstrated in current single-qubit devices. Here, we focus on two exchange-coupled singlet-triplet spin qubits, considering realistic control hardware as well as Coulomb and exchange coupling that cannot be fully turned off. Using measured noise spectra, we optimize realistic control pulses and show that two-qubit (single-qubit) gate fidelities of 99.90\% ($\ge 99.69\%$) can be reached in GaAs, while 99.99\% ($\ge 99.95\%$) can be achieved in Si.

Resonantly Driven Singlet-Triplet Spin Qubit in Silicon.

We report implementation of a resonantly driven singlet-triplet spin qubit in silicon. The qubit is defined by the two-electron antiparallel spin states and universal quantum control is provided through a resonant drive of the exchange interaction at the qubit frequency. The qubit exhibits long T_{2}^{*} exceeding 1 μs that is limited by dephasing due to the ^{29}Si nuclei rather than charge noise thanks to the symmetric operation and a large micromagnet Zeeman field gradient. The randomized benchmarking shows 99.6% single gate fidelity which is the highest reported for singlet-triplet qubits.

Bandwidth-Limited and Noisy Pulse Sequences for Single Qubit Operations in Semiconductor Spin Qubits

Spin qubits are very valuable and scalable candidates in the area of quantum computation and simulation applications. In the last decades, they have been deeply investigated from a theoretical point of view and realized on the scale of few devices in the laboratories. In semiconductors, spin qubits can be built confining the spin of electrons in electrostatically defined quantum dots. Through this approach, it is possible to create different implementations: single electron spin qubit, singlet–triplet spin qubit, or a three-electron architecture, e.g., the hybrid qubit. For each qubit type, we study the single qubit rotations along the principal axis of Bloch sphere including the mandatory non-idealities of the control signals that realize the gate operations. The realistic transient of the control signal pulses are obtained by adopting an appropriate low-pass filter function. In addition. the effect of disturbances on the input signals is taken into account by using a Gaussian noise model.

Device Architecture for Coupling Spin Qubits via an Intermediate Quantum State

We demonstrate a scalable device architecture that facilitates indirect exchange between singlet-triplet spin qubits, mediated by an intermediate quantum state. The device comprises five quantum dots, which can be independently loaded and unloaded via tunneling to adjacent reservoirs, avoiding charge latch-up common in linear dot arrays. In a step towards realizing two-qubit entanglement based on indirect exchange, the architecture permits precise control over tunnel rates between the singlet-triplet qubits and the intermediate state. We show that by separating qubits by 1 um, the residual capacitive coupling between them is reduced to 7 ueV.

Phonon-assisted relaxation and decoherence of singlet-triplet qubits in Si/SiGe quantum dots

We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.

Neural-network-designed pulse sequences for robust control of singlet-triplet qubits

Composite pulses are essential for universal manipulation of singlet-triplet spin qubits. In the absence of noise, they are required to perform arbitrary single-qubit operations due to the special control constraint of a singlet-triplet qubits; while in a noisy environment, more complicated sequences have been developed to dynamically correct the error. Tailoring these sequences typically requires numerically solving a set of nonlinear equations. Here we demonstrate that these pulse sequences can be generated by a well-trained, double-layer neural network. For sequences designed for the noise-free case, the trained neural network is capable of producing almost exactly the same pulses known in the literature. For more complicated noise-correcting sequences, the neural network produces pulses with slightly different line-shapes, but the robustness against noises remains comparable. These results indicate that the neural network can be a judicious and powerful alternative to existing techniques, in developing pulse sequences for universal fault-tolerant quantum computation.

Crosstalk error correction through dynamical decoupling of single-qubit gates in capacitively coupled singlet-triplet semiconductor spin qubits

In addition to magnetic field and electric charge noise adversely affecting spin qubit operations, performing single-qubit gates on one of multiple coupled singlet-triplet qubits presents a new challenge---crosstalk, which is inevitable (and must be minimized) in any multiqubit quantum computing architecture. We develop a set of dynamically-corrected pulse sequences that are designed to cancel the effects of both types of noise (i.e., field and charge) as well as crosstalk to leading order, and provide parameters for these corrected sequences for all 24 of the single-qubit Clifford gates. We then provide an estimate of the error as a function of the noise and capacitive coupling to compare the fidelity of our corrected gates to their uncorrected versions. Dynamical error correction protocols presented in the current work are important for the next generation of singlet-triplet qubit devices where coupling among many qubits will become relevant.

Magic angle for barrier-controlled double quantum dots

We show that the exchange interaction of a singlet-triplet spin qubit confined in double quantum dots, when being controlled by the barrier method, is insensitive to a charged impurity lying along certain directions away from the center of the double-dot system. These directions differ from the polar axis of the double dots by the magic angle, equaling $\arccos\left(1/\sqrt{3}\right)\approx 54.7^\circ$, a value previously found in atomic physics and nuclear magnetic resonance. This phenomenon can be understood from an expansion of the additional Coulomb interaction created by the impurity, but also relies on the fact that the exchange interaction solely depends on the tunnel coupling in the barrier-control scheme. Our results suggest that for a scaled-up qubit array, when all pairs of double dots rotate their respective polar axes from the same reference line by the magic angle, cross-talks between qubits can be eliminated, allowing clean single-qubit operations. While our model is a rather simplified version of actual experiments, our results suggest that it is possible to minimize unwanted couplings by judiciously designing the layout of the qubits.

Fast pulse sequences for dynamically corrected gates in singlet-triplet qubits

We present a set of experimentally feasible pulse sequences that implement any single-qubit gate on a singlet-triplet spin qubit and demonstrate that these new sequences are up to three times faster than existing sequences in the literature. We show that these sequences can be extended to incorporate built-in dynamical error correction, yielding gates that are robust to both charge and magnetic field noise and up to twice as fast as previous dynamically corrected gate schemes. We present a thorough comparison of the performance of our new sequences with that of several existing ones using randomized benchmarking, considering both quasistatic and $1/f^\alpha$ noise models. We provide our results both as a function of evolution time and as a function of the number of gates, which respectively yield both an effective coherence time and an estimate of the number of gates that can be performed within this coherence time. We determine which set of pulse sequences gives the best results for a wide range of noise strengths and power spectra. Overall, we find that the traditional, slower sequences perform best when there is no field noise or when the noise contains significant high-frequency components; otherwise, our new, fast sequences exhibit the best performance.

Decoherence of two coupled singlet-triplet spin qubits

We study a pair of capacitively coupled singlet-triplet spin qubits. We characterize the two-qubit decoherence through two complementary measures, the decay time of coupled-qubit oscillations and the fidelity of entangled state preparation. We provide a quantitative map of their dependence on charge noise and field noise, and we highlight the magnetic field gradient across each singlet-triplet qubit as an effective tool to suppress decoherence due to charge noise.

Suppression of charge noise using barrier control of a singlet-triplet qubit

It has been recently demonstrated that a singlet-triplet spin qubit in semiconductor double quantum dots can be controlled by changing the height of the potential barrier between the two dots ("barrier control"), which has led to a considerable reduction of charge noises as compared to the traditional tilt control method. In this paper we show, through a molecular-orbital-theoretic calculation of double quantum dots influenced by a charged impurity, that the relative charge noise for a system under the barrier control not only is smaller than that for the tilt control, but actually decreases as a function of an increasing exchange interaction. This is understood as a combined consequence of the greatly suppressed detuning noise when the two dots are symmetrically operated, as well as an enhancement of the inter-dot hopping energy of an electron when the barrier is lowered which in turn reduces the relative charge noise at large exchange interaction values. We have also studied the response of the qubit to charged impurities at different locations, and found that the improvement of barrier control is least for impurities equidistant from the two dots due to the small detuning noise they cause, but is otherwise significant along other directions.

Energy spectrum, exchange interaction, and gate crosstalk in a system with a pair of double quantum dots: A molecular-orbital calculation

We present a theoretical study of a four-electron four-quantum-dot system based on molecular orbital methods, which hosts a pair of singlet-triplet spin qubits. We explicitly take into account of the admixture of electron wave functions in all dots, and have found that this mixing of wave functions has consequences on the energy spectrum, exchange interaction and the gate crosstalk of the system. Specifically, we have found that when the two singlet-triplet qubits are close enough, some of the states are no longer dominated by the computational basis states and the exchange interaction can not simply be understood as the energy difference between the singlet and triplet states. Using the Hund-Mulliken calculation of the Hubbard parameters, we characterize the effective exchange interaction of the system and have found good agreement with results calculated by taking energy differences where applicable. We have studied the two commonly conceived schemes coupling two qubits, the exchange and capacitive coupling, and have found that when the inter-qubit distance is at certain intermediate values, the two kinds of coupling are comparable in strength, complicating analyses of the evolution of the two qubits. We also investigate the gate crosstalk in the system due to the quantum mechanical mixing of electron states and have found that while this effect is typically very weak, it should not be ignored if the spacing between the qubits are similar to or less than the distance between the double dots that constitute the qubit.

Spectrum of the Nuclear Environment for GaAs Spin Qubits.

Using a singlet-triplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over 6 orders of magnitude in frequency, from 1mHz to 1kHz, is flat below 10mHz, and falls as 1/f^{2} for frequency f≳1 Hz. Increasing the applied magnetic field from 0.1 to 0.75T suppresses electron-mediated spin diffusion, which decreases the spectral content in the 1/f^{2} region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the few-pulse regime (≲16π pulses), where transverse Overhauser fluctuations dominate dephasing, to the many-pulse regime (≳32 π pulses), where longitudinal Overhauser fluctuations with a 1/f spectrum dominate.