High-fidelity magic-state preparation with biased noise qubits in practice

Producing high-fidelity magic states with an error rate below 10e-12 is essential for achieving large-scale, fault-tolerant quantum computation, which encompasses the most promising applications of quantum computers. Indeed, algorithms such as Shor’s, as well as quantum chemistry and condensed-matter simulations, typically require billions of non-Clifford gates.

The standard approach to achieving such high fidelity involves using a second layer of distillation at the logical level using surface-code encoding on top of a first cultivation or distillation step.

Here, we adapt the standard approach to noise-biased qubits, and exploit hitherto overlooked synergies from the underlying architecture.

When targeting a logical error rate above 10e-8, circuit-level Monte Carlo simulations are still feasible. However, achieving logical error rates below 10e-12 makes such numerical simulations impractical.

In our scheme, we must rely on logical error models for each requisite quantum operations. These models are constructed by fitting tailored Ansatz on data from Monte Carlo simulations of quantum operations performed at smaller code distances. We provide concrete layouts and volume estimates for producing ultra-low-error magic states using a two-layer distillation protocol optimized for biased-noise qubits significantly reducing the overhead compared to state of the art surface code implementations.