Quantum computing with defects

Luke Gordon, Justin R. Weber, Joel Basile Varley +3 more

Mohammad H. Ansari

Alice Eriksson

Quantum computing has the potential to meet the increasing demand for computational power by solving some unique issues more efficiently than classical computers. To realize the full capabilities of quantum computing, a reliable physical implementation of quantum bits is essential. Point defects in semiconductors may offer a promising solution for this implementation. However, point defects, like most qubit implementations, would benefit from increased coherence times. For certain point defects, this improvement comes from clock transitions, where the transition frequency becomes locally independent of the magnetic field. This thesis consists of a thorough analysis of clock transitions in point defects. First, the clock transition of the bismuth vacancy (BiV) in CaO is reproduced. Then, an automatic workflow for finding clock transitions and converging computational parameters are built as an extension to the ADAQ (Automatic defect analysis andqualification) software. 10243 clock transitions were found in a set of 3704 defects, 143 of these are due to zero-field splitting, and the rest due to hyperfine interactions. Clock transitions that arise only from zero-field splitting have a clear correlation between separation and the 2nd derivative. Clock transitions that emerge from hyperfine interactions have no such clear trend, meaning that they need to be studied in more detail for individual defects.

Colleen Delaney, Zhenghan Wang

We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions of unitary modular tensor categories. The algebraic data of these categories afford projective unitary representations of the braid group. Elements in the image of such representations correspond to quantum gates arising from exchanging anyons and symmetry defects in topological phases of matter with symmetry. We provide some small examples that highlight features of practical interest for quantum computing. In particular, symmetry defects show the potential to generate non-abelian statistics from abelian topological phases and to be used as as a tool to enlarge the set of quantum gates accessible to an anyonic device.

Alexandru Paler, Austin G. Fowler, Robert Wille

The first large-scale practical quantum computer is within reach. Coming to grips with the strategy and challenges of preparing reliable executions of an arbitrary quantum computation is not difficult. In fact, defects are good.

Julien M. Drouet, Xanda C. Kolesnikow, Campbell K. McLauchlan +6 more

A solid-state quantum-computing architecture will require the fabrication of arrays of many coupled qubits. It is inevitable that this process will produce qubits and couplers with varying performance, with some components underperforming due to imperfect fabrication. Quantum error-correction requires high-performing components and hence these defects must be dealt with, either by adapting the code to exclude the defects, or by informing the decoder to accommodate defects in post-processing. Here we implement and compare strategies to operate distance-5 surface codes on a quantum processor consisting of a square-lattice array of 120 superconducting qubits. We demonstrate a dramatic reduction in the probability of a logical error in a memory experiment by excluding underperforming components, compared with both a standard approach of ignoring defects, and a defect-aware decoding approach. We observe up to 2.8X improvement in logical errors per round when excluding defects compared with the standard defect-ignorant approach (1.62% compared to 4.49%). In contrast, defect-aware decoding gives only modest gains. Defects are also expected to be particularly harmful for measurement-based logical operations. Using a stability experiment we show that excluding defects resurrects measurement-based logic gate performance, observing a 6.3% per-round suppression of failure rate when excluding defects, compared to zero suppression otherwise. Furthermore, we show a further substantial decrease in logical errors when using leakage post-selection in combination with our defect exclusion strategies, resulting in a distance-5 code outperforming the best distance-3 in one basis. Our experiments therefore give a proof-of-principle demonstration of the essential utility of defect exclusion methods in the scale-up of solid-state quantum computing approaches.