Session W39: Spin Qubit Arrays I

Away from voltages: Generating and using abstractions to operate arrays of quantum dots

As quantum dot qubits mature as a technology, operation and characterization of larger and larger devices must become robust and routine.  This talk describes automated tuning and characterization methods that focus on extracting and storing relevant and physically-meaningful information contained in measurements of dot devices.  These methods, which use a combination of machine learning techniques and simple physical models, are shown to work with a variety of data types of varying quality acquired from Si/SiGe SLEDGE arrays of quantum dots.  The resulting information forms a high-level 'device API' that allows interaction with, e.g., quantities of charge and tunnel coupling rather than applied gate voltages.      

Simulation Aided Design of a Six Dot Si/SiGe Spin Qubit Device

High fidelity single and two-qubit gates have been achieved in small Si/SiGe quantum processors [1,2]. In larger quantum dot arrays, the quantum dot charge detectors can have an appreciable impact on the confinement potential of the adjacent spin qubit array [3], complicating device tune-up. Optimization of the charge detector placement to maximize charge sensing fidelity and minimize undesired impacts on the spin qubit array is an outstanding challenge. We simulate the electron density of a six dot linear array in Si/SiGe to characterize the impact of the adjacent charge sensors using a Schrödinger-Poisson based device model.

[1] Yoneda et al., Nature Nanotechnology 13, 102 (2018) 

[2] Zajac et al., Science 359, 439 (2018)

[3] Mills et al., Nature Communications 10, 1063 (2019)    

Approaching Unit Readout Visibility in a Loss-DiVincenzo Spin Qubit with >99.9% Control Fidelity

High fidelity gate operations and high visibility readout are required for fault-tolerant implementations of spin-based quantum computing. Typical measurement fidelities for quantum dot and donor spin qubits using coupling to a reservoir for readout range from 68% to 99.5%, with the quantum dot based systems largely limited to <99% [1]. Here we control a single spin qubit in a six-dot linear array using electric dipole spin resonance and achieve single qubit gate fidelities exceeding 99.9%, as verified by randomized benchmarking and gate set tomography [2]. Optimization of the spin-to-charge conversion and electrical charge detection process yields a measurement fidelity exceeding 99% [3,4]. Our results bring the total operation fidelity of a silicon spin qubit above 99%.

[1] Keith et al., New J. Phys. 21, 063011 (2019)

[2] Nielsen et al., Quantum 5, 557 (2021)

[3] Elzerman et al., Nature 430, 431 (2004)

[4] Mills et al. (unpublished)   

Large coupling in a silicon quantum dot array

Gate-defined silicon quantum dots have been successfully used to encode two-qubit devices [1]. Central to attaining this multi-qubit control is the method used for inter-qubit coupling, where qubits may be coupled through capacitive or tunneling (exchange) interactions. Previous works have studied the capacitive coupling between two adjacent double quantum dots (DQDs) in accumulation-mode, overlapping gate architectures in SiGe [2,3] and have achieved capacitive couplings on the order of 20-50 GHz. In this talk, we examine the charge dynamics between two DQDs in a similar depletion-mode SiGe device we have fabricated. This device contains a linear array of four coupled QDs, and we study the inter-dot coupling’s transition from 45 GHz to measurements exceeding 200 GHz. We explore the mechanism responsible for the observed trend in inter-dot coupling as the barrier separating the two DQDs is decreased and remark on the device’s ability to reach such large couplings.

1]         M. Veldhorst, C. H. Yang, J. C. C. Hwang, W. Huang, J. P. Dehollain, J. T. Muhonen, S. Simmons, A. Laucht, F. E. Hudson, K. M. Itoh, A. Morello, and A. S. Dzurak, A Two-Qubit Logic Gate in Silicon, Nature 526, 410 (2015).

[2]       S. F. Neyens, E. R. MacQuarrie, J. P. Dodson, J. Corrigan, N. Holman, B. Thorgrimsson, M. Palma, T. McJunkin, L. F. Edge, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, Measurements of Capacitive Coupling Within a Quadruple-Quantum-Dot Array, Physical Review Applied 12, (2019).

[3]       D. M. Zajac, T. M. Hazard, X. Mi, E. Nielsen, and J. R. Petta, Scalable Gate Architecture for a One-Dimensional Array of Semiconductor Spin Qubits, Physical Review Applied 6, (2016).   

Nearly-Heisenberg precision scaling in spatiotemporally correlated noise environments by optimized sensor geometry

 We study the influence of non-collective couplings on frequency

  estimation by Ramsey interferometry in the presence of spatiotemporally

  correlated Gaussian quantum noise. For the relevant case of a bosonic

  environment, we previously found [1] that randomizing the probe positions

  makes their spatial correlations vanish on average, leading to

  super-classical, Zeno-like precision scaling in a suitable parameter

  regime and a metrological gain over the sub-SQL scaling reported in the

  collective noise limit [2]. Building up on these results, we consider a

  setup where the qubit sensors are placed in a one-dimensional regular

  lattice with noise-optimized separation. This allows us to improve the

  performance by creating negative spatial correlations between the qubits,

  and to beat the Zeno limit with both the paradigmatic GHZ state and the

  experimentally relevant one-axis-twisted state, reaching near-Heisenberg N^-35/36

  scaling with the former, and N^-7/9  scaling with the latter.   

A sparse quantum dot crossbar with sublinear scaling of interconnects at cryogenic temperature

A practical spin-based quantum computer will require millions of qubits that operate at cryogenic temperature and interface to room temperature with only a few electrical wires. Sublinear scaling of interconnects is also required for a high-throughput fabrication-measurement cycle of quantum devices. We demonstrate a 36x36 gate electrode crossbar that supports 648 narrow-channel field effect transistors (FET) for gate-defined quantum dots and enables a quadratic increase in quantum dot device count with a linear increase in control lines. The multi-gate FET are fabricated on industrial ²⁸Si-MOS stacks and integrate two tunable tunnel barriers per device, with interleaved ohmic contacts and cryo-CMOS control circuitry to measure each device independently from all others. Electrical characterisation at 1.7 K of a grid with geometry variations demonstrates 100% device yield and shows a decreasing threshold voltage for narrow channel devices. Statistical data obtained in this way provide means for device optimisation by design as a stepping stone towards large quantum dot spin-qubit arrays.   

A 16 quantum dot crossbar array in germanium

Quantum dots in semiconductors are a promising platform for quantum information. The steady advancement in the material growth and in the electrical control of gate-defined quantum dots in germanium quantum wells enabled the demonstration of quantum logic in a one-, then two- and recently in a four-spin qubit processor. Scaling up to larger quantum systems presents outstanding challenges such as solving the interconnect bottleneck caused by the high number of degrees of freedom of the circuits. Here, we take this step and demonstrate the operation of the first 4x4 quantum dot crossbar array. Despite the reduced input voltages, the shared control of plunger and barrier gates enables the definition of 16 quantum dots with similar occupancy and addressable interdot coupling. This result is a crucial milestone for scaling and controlling spin qubits in two dimensions.   

Benchmarking single-electron transistor charge sensitivity using machine learning

As silicon quantum device manufacturing shifts from academic laboratories to industrial settings, metrics to assess fabrication processes and optimal geometries will need to be developed. Preferentially, these metrics should be extracted using automated protocols to facilitate the large-scale characterisation required to obtain statistical evidence of improvement. In this talk, we propose a device characterisation strategy that aims to compare device performance across different quantum dot technologies. We present this approach applied to charge sensing, where the objective is to sample from the volume in gate voltage space in which the device can be operated with a satisfactory charge sensitivity, this allows us to efficiently quantify this volume we denote the charge sensitivity volume. This volume is determined by a uniform sampling algorithm that searches gate voltage space to identify regions where the charge sensor’s Coulomb blockade oscillations are measured to have a charge sensitivity exceeding a user defined satisfactory threshold. With the increasing demand for fast automatic testing of entire wafers of devices, this characterisation strategy could provide a universal benchmark through which to compare single-electron transistor technologies.   

Synthetic spin-1 chain in an array of InAsP quantum dots embedded in an InP nanowire

Here we describe the potential realization of a synthetic spin-1 Haldane chain in an array of InAs­P quantum dots embedded in an InP nanowire for the possible construction of a topologically protected singlet-triplet qubit. Using an ab-initio derived tight-binding Hamiltonian for a single and a double InAsP quantum dot containing millions of atoms, the single particle states were obtained. Though the distribution of As atoms in each quantum dot is random, the conduction band states of a quantum dot array can still be understood in terms of s, p, and d quantum dot orbitals with interdot tunneling. We then constructed the many-body Hamiltonian in the basis of N-electron configurations with the single particle states from the tight-binding model. Using exact diagonalization, we determined that the ground state of a single quantum dot with a half filled p­-shell has a total electronic spin of S = 1 and that the ground state for a double dot is a singlet with total spin S = 0, which is consistent with Heisenberg model¹. The low-energy spectrum of the double quantum dot array was then successfully fitted to both the Hubbard-Kanamori and Heisenberg model Hamiltonians to confirm that the quantum dot array with 4 electrons in each dot hosts the Haldane quasipartcles of a spin-1 chain.   

Flip-flop Qubits for Scalable Quantum Computing Architectures

Flip-flop qubits (FFQ) are a promising qubit type based on a mixture of nuclear and bonded electron spin states of a ³¹P atom in a spin-free ²⁸Si substrate [1]. High-fidelity one-qubit operations can be obtained by exploiting electric dipole spin resonance and two-qubit ones are created by using electric dipole interaction [1,2]. The long-range dipole-dipole interaction between FFQs could relax the usually stringent fabrication requirements for spin-based qubits, particularly for the lateral positioning of gates/donors thus moving the specs from some tens of nm to few hundreds of nm range. The simultaneous application of gates, i.e. parallel gating, is a central ingredient for quantum computation, but gate parallelism is inevitably limited by unwanted inter-qubit interactions. The effects on gate fidelities of those unwanted mutual interactions, due to multi one-qubit and multi two-qubit gates executed in parallel, is simulated in different arrays embedded in a realistic noisy environment [3]. Such information helps to infer those for logical qubits defined by a quantum error correction code, also providing insights for system scaling-up in view of long-term silicon-based quantum computers. [1] Tosi et al., Nat. Comm. 2017, 8450. [2] Ferraro et al., arXiv:2104.14341v12021. [3] Rei et al., arXiv:2110.12982.   

Two-body Wigner molecularization in asymmetric quantum dot spin qubits

We model the effects of Coulomb repulsion in doubly-occupied anisotropic quantum dots. Indeed, Coulomb interactions strongly influence the spectrum and the wave functions of a few electrons/holes confined in a quantum dot. When the confinement potential is not too strong, the Coulomb repulsion triggers the formation of a correlated state, the Wigner molecule, where the particles tend to split apart. We show that the anisotropy of the confinement potential strongly enhances the molecularization process. We support this conclusion with a simple harmonic potential model as well as full configuration-interaction calculations in realistic qubit devices. We highlight the exponential suppression of the singlet-triplet gap with increasing anisotropy and discuss how molecularization effects specifically hamper Pauli spin blockade readout and reduce the exchange interactions in two-qubit gates. We compare trends in different semiconductor materials and show that the molecularization effects are much stronger in silicon than in germanium, due to the heavier effective masses.   

Steady-State Tunable Entanglement Switch with Quantum Dots

SV acknowledges support from a DST-SERB Early Career Research Award (ECR/2018/000957) and DST-QUEST grant number DST/ICPS/QuST/Theme-4/2019. BM acknowledges Science and Engineering Research Board (SERB), Government of India, Grant No. STR/2019/000030.