A Silicon Surface Code Architecture Resilient Against Leakage Errors

Abstract

Spin qubits in silicon quantum dots are one of the most promising building blocks for large scale quantum computers thanks to their high qubit density and compatibility with the existing semiconductor technologies. High fidelity single-qubit gates exceeding the threshold of error correction codes like the surface code have been demonstrated, while two-qubit gates have reached 98% fidelity and are improving rapidly. However, there are other types of error -such as charge leakage and propagation -that may occur in quantum dot arrays and which cannot be corrected by quantum error correction codes, making them potentially damaging even when their probability is small. We propose a surface code architecture for silicon quantum dot spin qubits that is robust against leakage errors by incorporating multi-electron mediator dots. Charge leakage in the qubit dots is transferred to the mediator dots via charge relaxation processes and then removed using charge reservoirs attached to the mediators. A stabiliser-check cycle, optimised for our hardware, then removes the correlations between the residual physical errors. Through simulations we obtain the surface code threshold for the charge leakage errors and show that in our architecture the damage due to charge leakage errors is reduced to a similar level to that of the usual depolarising gate noise. Spin leakage errors in our architecture are Zhenyu Cai: zhenyu.cai@materials.ox.ac.uk John J. L. Morton: jjl.morton@ucl.ac.uk constrained to only ancilla qubits and can be removed during quantum error correction via reinitialisations of ancillae, which ensure the robustness of our architecture against spin leakage as well. Our use of an elongated mediator dots creates spaces throughout the quantum dot array for charge reservoirs, measuring devices and control gates, providing the scalability in the design.

Remote capacitive sensing in two-dimension quantum-dot arrays

“…In addition to applications for sensing, capacitive coupling have been used to realise local multi-qubit interactions in a variety of systems, including singlettriplet qubits [25] and charge qubits [26,27]. Meanwhile, several approaches to scaling quantum dot arrays pursue long-range coupling between qubits to facilitate the integration and fan-out of control electronics and suppress charge leakage [6,11]-solutions to realising such two-qubit gates include exploiting a RKKY mediating exchange interaction [11,28] or coupling via a superconducting resonator [29]. Multi-qubit operations utilising capacitive coupling via floating gates, coupling two singly-occupied planar dot structures, have been proposed to produce a spin-spin coupling Hamiltonian H S−S J 12 (σ 1…”

“…The promise of a highly developed materials system and mature fabrication industry, together with the success of laboratory, and industry-grade prototype silicon-metal-oxidesemiconductor (SiMOS) quantum-dot based devices [8] has led to the proposition of several approaches to foundry-compatible scaling into grid-based architectures of quantum dot arrays. These approaches range from densely-packed qubits with next-nearest-neighbour couplings [9], dot arrays partially-populated with qubits [10] and arrays with qubit sites linked via mediating structures for remote qubit-qubit coupling [11].…”

Materials for Silicon Quantum Dots and their Impact on Electron Spin Qubits

“…In its simplest form, flushing the electron out of the quantum dot and loading another electron into the quantum dot ground state (separated from the spin excited state by the Zeeman splitting) is an effective strategy for initialization, [ 42 ] but requires the dot to be near a reservoir. For a dense arrangement of quantum dots, only the dots at the perimeter of the array can be connected to a reservoir (unless 3D integration of reservoirs is made possible through vias [ 56 ] ). It is, therefore, desirable to create a route for initialization that does not rely on coupling most qubits to a bath of electrons.…”

Materials for Silicon Quantum Dots and their Impact on Electron Spin Qubits

“…In its simplest form, flushing the electron out of the quantum dot and loading another electron into the quantum dot ground state (separated from the spin excited state by the Zeeman splitting) is an effective strategy for initialisation [42], but requires the dot to be near a reservoir. For a dense arrangement of quantum dots, only the dots at the perimeter of the array can be connected to a reservoir (unless 3D integration of reservoirs is made possible through vias [56]). It is, therefore, desirable to create a route for initialisation that does not rely on coupling most qubits to a bath of electrons.…”