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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

Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement

Joseph Andress, Alexander Engel, Yuan Shi, Scott Parker

Year

2024

Journal

arXiv preprint

DOI

arXiv:2410.03838

arXiv

2410.03838

We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a dynamical system to a Hamiltonian form, where the Hamiltonian matrix is a function of dynamical variables. To advance in time, we measure expectation values from the previous time step, and evaluate the Hamiltonian function classically, which introduces stochasticity into the dynamics. We then perform standard quantum Hamiltonian simulation over a short time, using the evaluated constant Hamiltonian matrix. This approach requires evolving an ensemble of quantum states, which are consumed each step to measure required observables. We apply this approach to the classic logistic and Lorenz systems, in both integrable and chaotic regimes. Out analysis shows that solutions' accuracy is influenced by both the stochastic sampling rate and the nature of the dynamical system.

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