Session B45: Semiconductor Qubits: Multidot Qubits and Dynamical Control

Multiple quantum dot spin qubits

To date various techniques of implementing spin qubits and entangling gates have been developed with quantum dos (QDs). The necessary step for further scaling up the qubit system is to increase the number of QDs with a well-controlled charge state to prepare multiple qubits and improve the fidelity of the qubit gates as well. I will first review spin-1/2 qubit gates with triple QDs for operating three qubits, local and non-local entangling gates, and SWAP gates. I show that the fidelity of these spin manipulations is significantly increased by decreasing the data acquisition time. Secondly I will refer to quadruple and quintuple QDs to implement multiple spin qubits. For the triple QD we use two sets of two coupled dots in the spin blockade regime to demonstrate operation of three individual spin qubits. We use an exchange coupling between the neighboring dots to make two sets of SWAPs and an inhomogeneous Zeeman field difference between the neighboring dots (between the remote dots) to make local (non-local) control of S-T$_{0}$ oscillations. We apply the same technique for the quadruple QD to coherently manipulate individual four spins. We finally discuss a way to further scale up the qubit system using multiple QDs.   

A new look at encoded-qubit quantum dot quantum computing in silicon

Although the properties of spin-based qubits are specified by the material system they reside in, it's possible to modify those properties by encoding a qubit into multiple physical spins. Here we consider new operating regimes for encoded spin qubits and discuss their relevance to spin-based quantum computing and qubit-qubit coupling, especially in silicon quantum dot systems. We will also briefly discuss recent developments in g-factor theory in silicon quantum dots and their possible implications.   

High quality exchange rotations in spin qubits using symmetric gating

We present results on a singlet-triplet qubit implemented in a GaAs/AlGaAs heterostructure and we show that exchange oscillations can be realized either by tilting the double well potential, the conventional method, or by symmetrically lowering the barrier, as originally suggested by Loss and DiVincenzo. The two methods are compared here. We find that lowering the barrier between dots has much less relative exchange noise compared to tilting the potential. Since exchange rotations are sensitive to electrical noise and relatively insensitive to nuclear noise, this yields significantly enhanced free induction decay times and quality factors. Our results are comparable to those reported recently in silicon quantum dot devices, obtained using similar techniques.   

Charge noise mitigation in triple-dot encoded spin qubits

The immediate scalability of electrons confined to semiconductor quantum dots makes them one of the most attractive platforms for quantum information processing; however, 1/f charge noise associated with electrical confinement has been a leading source of noise in quantum dot systems.   Recently, there has been a surge of experimental and theoretical work aimed at charge noise mitigation in quantum dot systems implementing AC- or DC- control of triple dots at "sweet spots''.  In this talk, we compare the symmetric operation point (SOP) DC control technique implemented in Reed, et al. [arXiv:1508.01223] to the resonant exchange (RX) AC control technique [Medford, et al., PRL 111, 050501 (2013), Taylor, et al., PRL 111, 050502 (2013), Russ, et al., Phys. Rev. B 91, 235411 (2015)] .  Numerical results suggest that both DC and AC triple-dot control can offer a comparably substantial reduction in charge noise; however, the validity of the rotating wave approximation forces a trade-off between speed and accuracy for RX qubits, while the performance of SOP qubits actually improves at shorter gate times.     

The validity of the RWA and gate operation speedup by violating RWA in resonant-driven qubit systems

The rotating wave approximation (RWA) is ubiquitously used in understanding (quasi)resonant driven systems and designing pulses for state evolution. Following the practice in atomic and NMR physics, a wide range of semiconducting qubit systems are driven resonantly to manipulate the qubit, including single-spin/resonant exchange (RX)/various singlet-triplet(ST)/spin-charge hybrid qubits. The purpose of this talk is twofold: (I) Examine the validity of RWA in different qubit systems and analyze the error in terms of quantum computation; (II) Present faster gate operations by going into RWA-invalid regime for resonant-driven qubits (esp. for ST and RX types). We measure the RWA-induced infidelity and discuss it in view of the fault-tolerant error correction threshold and operation speeds. Applying the analytical extension (two orders higher than RWA) greatly reduces the infidelity, in the regime where the RWA is attempted to be used. Moreover, we show that the resonant-driven system is not limited by the Rabi-like weak coupling limit and the associated slow gate speed, much smaller than the level splitting (e.g., the small Zeeman energy gradient in ST qubits). We demonstrate the universal one qubit gates for driving strength up to a few level splitting, achieving fast control with only simple sinusoidal pulses. We also solve for the `shifted sinusoidal' pulses needed for ST qubits where the exchange coupling cannot change signs.   

Leakage of The Quantum Dot Hybrid Qubit in The Strong Driving Regime

Recent experimental demonstrations of high-fidelity single-qubit gates suggest that the quantum dot hybrid qubit is a promising candidate for large-scale quantum computing. The qubit is comprised of three electrons in a double quantum dot, and can be protected from charge noise by operating in an extended sweet-spot regime. Gate operations are based on exchange interactions mediated by an excited state. However, strong resonant driving causes unwanted leakage into the excited state. Here, we theoretically analyze leakage caused by strong driving, and explore methods for increasing gate fidelities.   

Tenfold increase in the Rabi decay time of the quantum dot hybrid qubit

The quantum dot hybrid qubit is formed from three electrons in a double quantum dot. In previous work, we showed that the hybrid qubit has the speed of a charge qubit and the stability of a spin qubit. Here, we show that the hybrid qubit is also highly tunable, and can be tuned into regimes with desirable coherence properties. By changing the interdot tunnel rate by only 25\%, from 5 GHz to 6.25 GHz, we are able to increase the Rabi decay time by a factor of ten, from 18 ns to 177 ns. We attribute this improvement to the refinement of an extended “sweet spot” in the energy dispersion of the hybrid qubit, where the qubit is less susceptible to charge noise, which is a dominant source of decoherence. This work was supported in part by ARO (W911NF-12-0607) and NSF (DMR-1206915 and PHY-1104660). Development and maintenance of the growth facilities used for fabricating samples is sup- ported by DOE (DE-FG02-03ER46028). This research utilized NSF-supported shared facilities at the University of Wisconsin-Madison.   

Effect of Charge Noise on Landau-Zener Interferometry in double quantum dots

We study the effect of charge noise on the dynamics of semiconductor quantum dot qubits. Recent experiments have demonstrated relatively long coherence times in these systems; however at the same time, the visibility of the Landau-Zener interference pattern is relatively low. We argue that the electromagnetic noise of the environment affects the coherence of the qubit near the charge degeneracy point, including the singlet-triplet avoided level crossing, and results in the reduced visibility of the Landau-Zener interferometry when the singlet-triplet avoided level crossing happens in the vicinity of the charge degeneracy point. Using a master equation, we describe the evolution of the density matrix for the qubit assuming weak coupling of the quantum dot to its electromagnetic environment and compare our results to experimental data.   

Noise-induced collective quantum state preservation in spin qubit arrays

The hyperfine interaction with nuclear spins (or, Overhauser noise) has long been viewed as a leading source of decoherence in individual quantum dot spin qubits. We show that in a coupled multi-qubit system consisting of as few as four spins, interactions with nuclear spins can have the opposite effect where they instead preserve the collective quantum state of the system. This noise-induced state preservation can be realized in a linear spin qubit array using current technological capabilities. Our proposal requires no control over the Overhauser fields in the array; only experimental control over the average interqubit coupling between nearest neighbors is needed, and this is readily achieved by tuning gate voltages. Our results illustrate how the role of the environment can transform from harmful to helpful in the progression from single-qubit to multi-qubit quantum systems.   

Decoupling a spin qubit from high-frequency Larmor dynamics of a GaAs nuclear spin bath

We present a technique of decoupling a spin qubit in a GaAs/AlGaAs heterostructure from low- and high-frequency noise arising from hyperfine interaction of electrons with nuclear spins. We use Carr-Purcell-Meiboom-Gill sequences in which we synchronize the repetition rate of $\pi$ pulses to difference Larmor frequencies of $^{69}$Ga, $^{71}$Ga and $^{75}$As nuclei. This decouples the qubit both from low-frequency noise due to diffusion of nuclear spins and from noise at selected high frequencies, allowing us to apply more than a thousand $\pi$ pulses in a sequence. We demonstrate a coherence time of a singlet-triplet qubit of 0.87 ms, i.e. five orders of magnitude longer than the inhomogeneous dephasing time intrinsic to GaAs.   

Noise filtering of composite pulses for singlet-triplet qubits

Dynamically corrected gates are useful measures to combat decoherence in spin qubit systems. They are, however, mostly designed assuming the static-noise model and may thus be considered low-frequency noise filters. In this talk we carefully examine the applicability of a particular type of dynamically corrected gates, namely the \textsc{supcode} designed for singlet-triplet qubits, under realistic $1/f^\alpha$ noises. Through randomized benchmarking, we have found that \textsc{supcode} offers improvement of the gate fidelity for $\alpha>1$ and the improvement becomes exponentially more pronounced with the increase of the noise exponent $\alpha$ up to 3. On the other hand, for small $\alpha$ \textsc{supcode} will not offer any improvement. We also present the computed filter transfer functions for the \textsc{supcode} gates for nuclear and charge noise respectively and have found that they are consistent with the finding from the benchmarking.   

Dynamical Decoupling with pulse errors for ensembles of interacting spins

Dynamical decoupling (DD) is a well-known approach for decoupling quantum (spin) systems from their environments. Theoretically, the performance of DD pulse sequences is often analyzed using a single spin approximation in which environmental noise is included through single spin operators. This approach has successfully analyzed the effectiveness of many popular DD pulse sequences (like CPMG and XY4) to cancel environmental noise even in the presence of unavoidable pulse errors. However, this methodology does not describe the effect of DD on the spin-spin interactions present in experiments involving large numbers of spins. Here, we go beyond the usual single-spin model, extending the analysis of DD sequences to include such spin-spin interactions. We find that when using certain popular DD sequences (like CPMG), coherence times of ensembles with dipolar interactions between spins can be drastically influenced by pulse errors. While sequences with ideal pulses do not decouple the spin-spin interactions, the presence of even small pulse errors can partially (or even greatly) decouple the spin-spin interactions thus leading to longer coherence times. Furthermore, the extent that these interactions are decoupled is highly dependent on the type of DD sequence used, and not necessarily the number of pulses involved. These calculations explain results of past experiments (Tyryshkin et al, arxiv: 1011.1903).   

Dynamic field-frequency lock for tracking magnetic field fluctuations in electron spin resonance experiments

Global magnetic field fluctuations present significant challenges to pulsed electron spin resonance experiments on systems with long spin coherence times. We will discuss results from experiments in which we follow instantaneous changes in magnetic field by locking to the free induction decay of a proton NMR signal using a phase-locked loop. We extend conventional field-frequency locking techniques used in NMR to follow slow magnetic field drifts by using a modified Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence in which the phase of the pi-pulses follows the phase of the proton spins at all times. Hence, we retain the ability of the CPMG pulse sequence to refocus local magnetic field inhomogeneities without refocusing global magnetic field fluctuations. In contrast with conventional field-frequency locking techniques, our experiments demonstrate the potential of this method to dynamically track global magnetic field fluctuations on timescales of about 2 seconds and with rates faster than a kHz. This frequency range covers the dominant noise frequencies in our electron spin resonance experiments as previously reported.