One-dimensional quantum computing with a ‘segmented chain’ is feasible with today’s gate fidelities

Abstract

Building a quantum computer with a one-dimensional (1D) architecture, instead of the typical two-dimensional (2D) layout, could be significantly less difficult experimentally. However such a restricted topology necessitates a large overhead for shuffling qubits and consequently the fault tolerance threshold is far lower than in 2D architectures. Here we identify a middle ground: a 1D segmented chain which is a linear array of segments, each of which is a well-connected zone with all-to-all connectivity. The architecture is relevant to both ion trap and solid-state systems. We establish that fault tolerance can be achieved either by a surface code alone, or via an additional concatenated four-qubit gauge code. We find that the fault tolerance threshold is 0.12%, a feasible error rate with today’s technology, using 15-qubit segments, while larger segments are superior. For 35 or more qubits per segment one can achieve computation on a meaningful scale with today’s state-of-the-art fidelities without the use of the upper concatenation layer, thus minimising the overall device size. A quantum computer with components arranged on a line instead of more complex architectures could actually work, and be experiment-friendly. Ying Li and Simon Benjamin from University of Oxford propose a structure composed of many subunits arranged in 1D, each of them being a small set of qubits with all-to-all connections, and proved that, given the current performances of ion traps or solid-state systems, it could reach operativity already with around 15 qubits per subunit. This architecture would be much easier to realise than the ones currently being sought after, since it would get rid of the necessity to access the qubits from the z-direction, allowing the whole circuit (inclusive of controls) to be built on a 2D surface.