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Paper 1

Interface between topological and superconducting qubits.

Jiang L, Kane CL, Preskill J.

Year

2011

Journal

Phys Rev Lett

DOI

10.1103/physrevlett.106.130504

arXiv

-

No abstract.

Open paper

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.

Open paper