Session L45: Semiconductor Qubits: Quantum Dot Entanglement and Control

One- and two-qubit logic using silicon-MOS quantum dots

Spin qubits in silicon are excellent candidates for scalable quantum information processing [1] due to their long coherence times and the enormous investment in silicon CMOS technology. While our Australian effort in Si QC has largely focused on spin qubits based upon phosphorus dopant atoms implanted in Si [2,3], we are also exploring spin qubits based on single electrons confined in SiMOS quantum dots [4]. Such qubits can have long spin lifetimes T1 $=$ 2 s, while electric field tuning of the conduction-band valley splitting removes problems due to spin-valley mixing [5]. In isotopically enriched Si-28 these SiMOS qubits have a control fidelity of 99.6{\%} [6], consistent with that required for fault-tolerant QC. By gate-voltage tuning the electron g*-factor, the ESR operation frequency can be Stark shifted by \textgreater 10 MHz [6], allowing individual addressability of many qubits. Most recently we have coupled two SiMOS qubits to realize a CNOT gate [7] using exchange-based controlled phase (CZ) operations. The speed of the two-qubit CZ-operations is controlled electrically via the detuning energy and over 100 two-qubit gates can be performed within a coherence time of 8 $\mu $s. [1] D.D. Awschalom et al., ``Quantum Spintronics'', Science 339, 1174 (2013). [2] J.J. Pla et al., ``A single-atom electron spin qubit in silicon'', Nature 489, 541 (2012). [3] J.T. Muhonen et al., ``Storing quantum information for 30 seconds in a nanoelectronic device'', Nature Nanotechnology 9, 986 (2014). [4] S.J. Angus et al., ``Gate-defined quantum dots in intrinsic silicon'', Nano Lett. 7, 2051 (2007). [5] C.H. Yang et al., ``Spin-valley lifetimes in a silicon quantum dot with tunable valley splitting'', Nature Comm. 4, 2069 (2013). [6] M. Veldhorst et al., ``An addressable quantum dot qubit with fault-tolerant control fidelity'', Nature Nanotechnology 9, 981 (2014). [7] M. Veldhorst et al., ``A two-qubit logic gate in silicon'', Nature 526, 410 (2015).   

Silicon quantum processor with robust long-distance qubit coupling

Recent demonstration of high-fidelity quantum operations using donors in silicon [1] has ignited an urge in scaling up these systems to a multi-qubit device. However, multi-qubit operations and long-distance donor coupling remain a formidable challenge. We will present a novel scalable design for a silicon quantum processor [2] that allows for long-distance fast 2-qubit gates and does not require precise donor placement. Quantum information is encoded into either the nuclear-spin or the flip-flop states of electron and nucleus. It can be manipulated by biasing the electron wavefunction to be shared between donor and interface, in such a way that the hyperfine interaction strongly depends on electric fields. The qubits are spaced by hundreds of nanometers and coupled through direct electric dipole interactions and/or photonic links. All operations are performed at second-order clock transitions, preserving the qubits' outstanding coherence times. A large number of qubits can then be interconnected in a network robust against errors. Prototypical devices are fabricated to demonstrate the processor's basic units. [1] J. T. Muhonen, et.al. Nature Nanotechnol. 9, 986 (2014). [2] G. Tosi, et.al. arXiv:1509.08538 (2015).   

Towards optimizing two-qubit operations in three-electron double quantum dots

The successful implementation of single-qubit gates in the quantum dot hybrid qubit motivates our interest in developing a high fidelity two-qubit gate protocol. Recently, extensive work has been done to characterize the theoretical limitations and advantages in performing two-qubit operations at an operation point located in the charge transition region. Additionally, there is evidence to support that single-qubit gate fidelities improve while operating in the so-called ``far-detuned" region, away from the charge transition. Here we explore the possibility of performing two-qubit gates in this region, considering the challenges and the benefits that may present themselves while implementing such an operational paradigm. This work was supported in part by ARO (W911NF-12-0607) (W911NF-12-R-0012), NSF (PHY-1104660), ONR (N00014-15-1-0029). The authors gratefully acknowledge support from the Sandia National Laboratories Truman Fellowship Program, which is funded by the Laboratory Directed Research and Development (LDRD) Program. Sandia is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.   

High-Fidelity Entangling Gates for Two-Electron Spin Qubits

High fidelity gate operations for manipulating individual and multiple qubits are a prerequisite for fault-tolerant quantum information processing. Recently, we have shown that single-qubit gates for singlet-triplet qubits in GaAs can be pulse-engineered to reduce systematic errors and mitigate magnetic field fluctuations from the abundant nuclear spins, leading to experimentally demonstrated gate fidelities of 98.5\% [1]. We expect that a similar approach will be successful for two-qubit gates. We now describe short gating sequences for exchange-based two-qubit gates, showing that gate infidelities below 0.1\% can be reached in realistic quantum dot setups [2]. Additionally, we perform numerical pulse optimization to fully take the experimentally important imperfections into account, minimizing systematic errors and noise sensitivity. Since transferring the optimal control pulses to an experimental setting will inevitably incur systematic errors, we discuss how these errors can be calibrated on the experiment. [1] P. Cerfontaine, T. Botzem, D. Schuh, D. Bougeard, H. Bluhm, in preparation. [2] S. Mehl, H. Bluhm, D. P. DiVincenzo, PRB 90 (2014).   

Error-reducing sequence for capacitively coupled singlet-triplet qubits

Two-qubit gates can be implemented by capacitively coupling singlet-triplet qubits, which has been experimentally demonstrated to be capable of generating entangling operations. However, the fidelity of the entangling two-qubit gates is still far from optimum. In this light, we propose a two-qubit entangling echo sequence that reduces drastically the two-qubit decoherence due to the Overhauser field fluctuation and improves the fidelity of two-qubit gates under charge noise.   

Decoherence of two electron spin qubit in Si double quantum dot with g-factor modulations

The rapid progress in the manipulation and detection of semiconductor spin qubits enables the experimental demonstration of high fidelity two qubit gates that are necessary for universal quantum computing. Here, we consider the decoherence of two electron spin due to phonon emission in a Si double quantum dot (DQD). In the large detuning regime, where the two qubit gate is operated, we find that the decoherence depends strongly on the g-factor modulation and the asymmetry of the two dots. The estimated two qubit decoherence rate is comparable to the experimental measured results. We discuss the impact of the decoherence on the single/two qubit operations and ways to reduce the gate errors for the addressable semiconductor spin qubit.   

Valley dependent g-factor anisotropy in Silicon quantum dots

Silicon (Si) quantum dots (QD) provide a promising platform for a spin based quantum computer, because of the exceptionally long spin coherence times in Si and the existing industrial infrastructure. Due to the presence of an interface and a vertical electric field, the two lowest energy states of a Si QD are primarily composed of two conduction band valleys. Confinement by the interface and the E-field not only affect the charge properties of these states, but also their spin properties through the spin-orbit interaction (SO), which differs significantly from the SO in bulk Si. Recent experiments have found that the g-factors of these states are different and dependent on the direction of the B-field. Using an atomistic tight-binding model, we investigate the electric and magnetic field dependence of the electron g-factor of the valley states in a Si QD. We find that the g-factors are valley dependent and show 180-degree periodicity as a function of an in-plane magnetic field orientation. However, atomic scale roughness can strongly affect the anisotropic g-factors. Our study helps to reconcile disparate experimental observations and to achieve better external control over electron spins in Si QD, by electric and magnetic fields.   

Strong spin relaxation anisotropy in a single-electron quantum dot

Spin coherence and relaxation is of crucial importance in operating spin based qubits. In a magnetic field, spins relax predominately through spin-phonon coupling mediated by spin-orbit interaction (SOI) [1]. Here we present measurements of the spin relaxation rate anisotropy in a gate defined single-electron GaAs quantum dot. The spin relaxation rate W is measured at applied magnetic fields of 4 T in the plane of the 2D electron gas. W exhibits strong anisotropy: a sinusoidal dependence on the B-field angle $\varphi $ with a period of 180 degrees, as reported recently [2]. The extrema are observed at fields pointing nearly along the [110] and [1-10] crystal axes, modulated by a factor of about 14 from minimum to maximum. The periodicity is attributed to the interplay of Rashba and Dresselhaus SOIs. To decipher the role of SOI, we perform pulsed-gate spectroscopy to extract orbital excited-state energies, and obtain very good agreement with theory also for the angular dependence W($\varphi )$, indicating that $\alpha $ and $\beta $, Rashba and Dresselhaus coefficients respectively, have the same relative sign and are within 20{\%} of each other. With controllable manipulations of the dot orbitals by varying gate voltages, it is possible to precisely extract values of $\alpha $ and $\beta $. Meanwhile, top- and back gates have been implemented on the device structure, which allows full electrical control over the Rashba SOI in the 2D electron gas [3]. [1] V. N. Golovach et al., Phys. Rev. Lett. \textbf{93}, 016601 (2004). [2] P. Scarlino et al., Phys. Rev. Lett. \textbf{113}, 256802 (2014). [3] F. Dettwiler et al., arXiv:1403.3518 (2014).   

Electron Spin Resonance Characterization of Damage and Recovery of Si/SiO$_{2}$ Interfaces from Electron Beam Lithography

Electron beam lithography (EBL) is an essential tool for the fabrication of few electron silicon quantum devices. However, high-energy electrons and photons from the EBL process create shallow traps and other defects at the Si/SiO$_{2}$ interface, inhibiting the control of electron populations through electrostatic gating. To reduce defect densities, high temperature and forming gas anneals are commonly used. We studied the effect of these anneals on the reduction of shallow traps created by EBL by fabricating two sets of large area ($\sim$1cm$^{2}$) MOSFETs and characterizing them using transport and electron spin resonance (ESR) measurements. One set was exposed to a typical EBL dosage (10kV, 40$\mu$C/cm$^{2}$) and the other remained unexposed. All MOSFETs were fabricated from the same commercially grown gate stack (30nm dry thermal oxide, 200nm amorphous silicon gate layer) and were annealed at 900C in N$_{2}$ and at 435C in forming gas. Our transport data indicate that these annealing steps recover the EBL exposed sample's low temperature (4.2K) peak mobility to 85$\%$ of the unexposed sample's. Additionally, our ESR data indicate that annealing the EBL exposed sample reduces its density of shallow traps (2-4 meV) to the same density as the unexposed sample.   

Assessing MOS Interface Quality for Silicon Quantum Dot Device Fabrication

Defects at the Si-SiO2 interface are capable of trapping electrons and degrading the operation of silicon-based quantum dot devices. To improve device performance, we are working to characterize the interface quality in MOSCAPs and MOSFETs fabricated at NIST by comparing industry standard defect measurements, such as capacitance-voltage (CV), conductance, and mobility, to electron spin resonance (ESR) measurements. This comparison will give insight into the relative role of defects near the band edge and those distributed throughout the gap in degrading device performance. We will discuss our progress toward this goal as well as our latest data and interpretations.   

First-principles hyperfine tensors for electrons and holes in silicon and GaAs

Knowing (and controlling) hyperfine interactions in silicon and III-V semiconductor nanostructures is important for quantum information processing with electron and nuclear spin states. We have performed density-functional theory (DFT) calculations that fully account for spin structure of the Bloch states (in contast with approaches that rely on the density alone). Using this method, we confirm the known value for the contact hyperfine coupling in the conduction band of silicon, but find a significant deviation in the value for the conduction band of GaAs relative to the accepted value, estimated in ref. [1]. Moreover, this method can be used to calculate the full hyperfine tensor for the valence band, where spin-orbit effects may be strong, precluding methods that determine hyperfine couplings from the density alone. This general method can be applied to a broad class of materials with strong combined spin-orbit and hyperfine interactions. [1] D. Paget, G. Lampel, B. Sapoval, and V. I. Safarov Phys. Rev. B 15, 5780 (1977)   

Quantum quench dynamics of a central-spin system

Quantum effects can significantly influence equilibration dynamics. In quantum annealing, a local tunneling mechanism may accelerate the approach to equilibrium. Similarly, long-range quantum coherence can allow for rapid transitions between macroscopically distinct states of a quantum system. An experimentally relevant example of this is given by a 'central' electron spin coupled to an ensemble of nuclear spins in a quantum dot. This system admits a superradiance-like burst of current through ferromagnetic leads due to long-range nuclear spin coherence [1] with a simultaneous inversion of the nuclear-spin polarization. Here, we study this system coupled to normal leads. In particular, we study quench dynamics of the nuclear spin polarization after passing through a quantum phase transition controlled by an applied magnetic field. As a function of dephasing controlled by a magnetic field gradient, we find a crossover from rapid equilibration via collective states to slow dynamics described by classical (product-state) spin configurations. This understanding may allow us to better control dynamic nuclear spin polarization processes in quantum dots and to control more general quantum states of nuclear-spin ensembles. [1] S. Chesi and W. A. Coish PRB 91, 245306 (2015)