Classical feature map surrogates and metrics for quantum control landscapes

Martino Calzavara, Tommaso Calarco, Felix Motzoi We derive and analyze three feature map representations of parametrized quantum dynamics, which generalize variational quantum circuits. These are (i) a Lie-Fourier partial sum, (ii) a Taylor expansion, and (iii) a finite-dimensional sinc kernel regression representation. The Lie-Fourier representation is shown to have a dense spectrum with discrete peaks, that reflects control Hamiltonian properties,…

Gradients, parallelism, and variance of quantum estimates

Francesco Preti, Michael Schilling, József Zsolt Bernád, Tommaso Calarco, Francisco Cárdenas-López, Felix Motzoi Computation of observables and their gradients on near-term quantum hardware is a central aspect of any quantum algorithm. In this work, we first review standard approaches to the estimation of observables with and without quantum amplitude estimation for both cost functions and gradients, discuss sampling problems, and…

Quantum Algorithm for the Advection-Diffusion Equation with Optimal Success Probability

Paul Over, Sergio Bengoechea, Peter Brearley, Sylvain Laizet, Thomas Rung. A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. After discretization, the explicit time-marching operator is separated into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation problem and is combined with the shift operator through…
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The QCFD (Quantum Computational Fluid Dynamics) project is funded under the European Union’s Horizon Programme (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10), Grant Agreement 101080085 QCFD.