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Nano Letters

Characterization of a Scalable Donor-Based Singlet–Triplet Qubit Architecture in Silicon

Prasanna Pakkiam, Matthew Gregory House, Matthias Koch, Michelle Yvonne Simmons

Published May 24, 2018• 12 citations
Publisher

Abstract

We present a donor-based quadruple-quantum-dot device, designed to host two singlet–triplet qubits fabricated by scanning tunnelling microscope lithography, with just two leads per qubit. The design is geometrically compact, with each pair of dots independently controlled via one gate and one reservoir. The reservoirs both supply electrons for the dots and measure the singlet–triplet state of each qubit via dispersive sensing. We verify the locations of the four phosphorus donor dots via an electrostatic model of the device. We study one of the observed singlet–triplet states with a tunnel coupling of 39 GHz and a S 0 -to- T – decay of 2 ms at zero detuning. We measure a 5 GHz electrostatic interaction between two pairs of dots separated by 65 nm. The results outline a low-gate-density pathway to a scalable 1D building block of atomic-precision singlet–triplet qubits using donors with dispersive readout.

DOI
10.1021/acs.nanolett.8b00006

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We present a donor-based quadruple-quantum-dot device, designed to host two singlet–triplet qubits fabricated by scanning tunnelling microscope lithography, with just two leads per qubit. The design is geometrically compact, with each pair of dots independently controlled via one gate and one reservoir. The reservoirs both supply electrons for the dots and measure the singlet–triplet state of each qubit via dispersive sensing. We verify the locations of the four phosphorus donor dots via an electrostatic model of the device. We study one of the observed singlet–triplet states with a tunnel coupling of 39 GHz and a S 0 -to- T – decay of 2 ms at zero detuning. We measure a 5 GHz electrostatic interaction between two pairs of dots separated by 65 nm. The results outline a low-gate-density pathway to a scalable 1D building block of atomic-precision singlet–triplet qubits using donors with dispersive readout.
The search for a sweet spot, the locus in qubit parameters where quantum control is first-order insensitive to noises, is key to achieve high-fidelity quantum gates. Efforts to search for such a sweet spot in conventional double-quantum-dot singlet-triplet qubits where each dot hosts one electron (``two-electron singlet-triplet qubit''), especially for two-qubit operations, have been unsuccessful. Here we consider singlet-triplet qubits allowing each dot to host more than one electron, with a total of four electrons in the double quantum dots (``four-electron singlet-triplet qubit''). We theoretically demonstrate, using configuration interaction calculations, that sweet spots appear in this coupled qubit system. We further demonstrate that, under realistic charge noise and hyperfine noise, a two-qubit operation at the proposed sweet spot could offer gate fidelities ($\ensuremath{\sim}99%$) that are higher than the conventional two-electron singlet-triplet qubit system ($\ensuremath{\sim}90%$). Our results should facilitate realization of high-fidelity two-qubit gates in singlet-triplet qubit systems.
We propose two schemes to coherently transfer arbitrary quantum states of the two electron singlet-triplet qubit across an empty chain of quantum dots. The schemes are based on electrical control over the detuning energy of the quantum dots. The first scheme is a pulse-gating scheme, requiring dc pulses and engineering of inter- and intra-dot Coulomb energies. The second scheme is based on the adiabatic theorem, requiring time-dependent linear control of the detuning energy through avoided crossings at a rate that the system remains in the ground state. We simulate the transfer fidelity for 3 dots using typical experimental parameters for silicon quantum dots, then generalize our results to arbitrary number of dots. Our results give state transfer fidelities in excess of 98.7% and 99.3%, and at sub-nanosecond and tens of nanosecond timescales, for the pulse-gated and adiabatic schemes, respectively.
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Semiconductor quantum dot arrays are a promising platform to perform spin-based error-corrected quantum computation with large numbers of qubits. However, due to the diverging number of possible charge configurations combined with the limited sensitivity of large-footprint charge sensors, achieving single-spin occupancy in each dot in a growing quantum dot array is exceedingly complex. Therefore, to scale-up a spin-based architecture we must change how individual charges are readout and controlled. Here, we demonstrate single-spin occupancy of each dot in a foundry-fabricated array by combining two methods. 1/ Loading a finite number of electrons into the quantum dot array; simplifying electrostatic tuning by isolating the array from the reservoirs. 2/ Deploying multiplex gate-based reflectometry to dispersively probe charge tunneling and spin states without charge sensors or reservoirs. Our isolated arrays probed by embedded multiplex readout can be readily electrostatically tuned. They are thus a viable, scalable approach for spin-based quantum architectures. Large-footprint, low-sensitivity charge sensors hinder scaling semiconductor quantum dot arrays for quantum computation. Here the authors present a potentially scalable approach using multiplexed gate-based readout and operation in a foundry-fabricated quantum dot array, demonstrating single-electron occupancy.
We show how single quantum dots, each hosting a singlet–triplet qubit, can be placed in arrays to build a spin quantum cellular automaton. A fast (∼10 ns) deterministic coherent singlet–triplet filtering, as opposed to current incoherent tunneling/slow-adiabatic based quantum gates (operation time ∼300 ns), can be employed to produce a two-qubit gate through capacitive (electrostatic) couplings that can operate over significant distances. This is the coherent version of the widely discussed charge and nano-magnet cellular automata, and would increase speed, reduce dissipation, and perform quantum computation while interfacing smoothly with its classical counterpart. This combines the best of two worlds—the coherence of spin pairs known from quantum technologies, and the strength and range of electrostatic couplings from the charge-based classical cellular automata. Significantly our system has zero electric dipole moment during the whole operation process, thereby increasing its charge dephasing time.
We describe high-fidelity entangling gates between singlet-triplet qubits (STQs) which are coupled via one quantum state (QS). The QS can be provided by a quantum dot itself or by another confined system. The orbital energies of the QS are tunable using an electric gate close to the QS, which changes the interactions between the STQs independent of their single-qubit parameters. Short gating sequences exist for controlled not (cnot) operations. We show that realistic quantum dot setups permit excellent entangling operations with gate infidelities below ${10}^{\ensuremath{-}3}$, which is lower than the quantum error correction threshold of the surface code. We consider limitations from fabrication errors, hyperfine interactions, spin-orbit interactions, and charge noise in GaAs and Si heterostructures.