A silicon-based surface code quantum computer

Abstract

Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: There is a basic conflict between nanometre separation desired for qubit-qubit interactions, and the much larger scales that would enable control and addressing in a manufacturable and fault tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid state spins, or 'data qubits', that are widely separated from one another. We employ a second set of 'probe' spins which are mechanically separate from the data qubits and move in-and-out of their proximity. The spin dipole-dipole interactions give rise to phase shifts; measuring a probe's total phase reveals the collective parity of the data qubits along the probe's path. We introduce a protocol to balance the systematic errors due to the spins being imperfectly located during device fabrication. Detailed simulations show that the surface code's threshold then corresponds to misalignments that are substantial on the scale of the array, indicating that it is very robust. We conclude that this simple 'orbital probe' architecture overcomes many of the difficulties facing solid state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.The code written for our numerical simulations is openly available online [1].

A surface code quantum computer in silicon

“…The accommodation of such qubit arrays and associated circuitry in spin-based systems of donors and/or quantum dots, where the pitch due to the qubit interaction is only tens of nanometers, is therefore problematic. Recently, approaches have been suggested based on physically moving qubits over large distances (25), or hybrid donor-dot transport systems (26). In general, the introduction of quantum interconnects (27) creates more fabrication, characterization, and control complexity in the overall problem and require careful inclusion into the fault-tolerant QEC protocol.…”

Intrinsic errors in transporting a single-spin qubit through a double quantum dot

“…One way or another, spin shuttling schemes have always featured in theoretical considerations of scalable spin qubit architectures [16,21]. Especially in recent proposals based on the two-dimensional surface code [22], it becomes necessary to move spins either as probes [23], or as qubit activators [18], or as qubits themselves [24]. Mathematically, the Hilbert space of the entire system is composed of many orthogonal two-dimensional subspaces with spatially localized support, and initializing a physical electron spin into a given dot/donor not only populates one of those subspaces, but labels it as the "logical" subspace (or, in a multi-qubit system, part of the logical subspace) where the information resides.…”