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Paper 1

Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code

F. Setiawan, Campbell McLauchlan

Year

2024

Journal

arXiv preprint

DOI

arXiv:2411.04974

arXiv

2411.04974

We propose the X$^3$Z$^3$ Floquet code, a dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent stabiliser-product symmetry, which surprisingly exists in a code without constant stabilisers. Even if such a symmetry is allowed, we prove that general dynamical codes with two-qubit parity measurements cannot admit one-dimensional decoding graphs, a key feature responsible for the high performance of bias-tailored stabiliser codes. Despite this, our comprehensive simulations show that the symmetry of the X$^3$Z$^3$ Floquet code renders its performance under biased noise far better than several leading Floquet codes. To maintain high-performance implementation in hardware without native two-qubit parity measurements, we introduce ancilla-assisted bias-preserving parity measurement circuits. Our work establishes the X$^3$Z$^3$ code as a prime quantum error-correcting code, particularly for devices with reduced connectivity, such as the honeycomb and heavy-hexagonal architectures.

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Paper 2

Simulating Neutron Scattering on an Analog Quantum Processor

Nora Bauer, Victor Ale, Pontus Laurell, Serena Huang, Seth Watabe, David Alan Tennant, George Siopsis

Year

2024

Journal

arXiv preprint

DOI

arXiv:2410.03958

arXiv

2410.03958

Neutron scattering characterization of materials allows for the study of entanglement and microscopic structure, but is inefficient to simulate classically for comparison to theoretical models and predictions. However, quantum processors, notably analog quantum simulators, have the potential to offer an unprecedented, efficient method of Hamiltonian simulation by evolving a state in real time to compute phase transitions, dynamical properties, and entanglement witnesses. Here, we present a method for simulating neutron scattering on QuEra's Aquila processor by measuring the dynamic structure factor (DSF) for the prototypical example of the critical transverse field Ising chain, and propose a method for error mitigation. We provide numerical simulations and experimental results for the performance of the procedure on the hardware, up to a chain of length $L=25$. Additionally, the DSF result is used to compute the quantum Fisher information (QFI) density, where we confirm bipartite entanglement in the system experimentally.

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