# Freiburg 2019 – wissenschaftliches Programm

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# FM: Fall Meeting

## FM 21: Quantum Computation: Algorithms

### FM 21.6: Talk

### Montag, 23. September 2019, 17:45–18:00, 2006

**Improved variational quantum algorithms for optimization problems in a quantum computer** — •Panagiotis Barkoutsos^{1}, Giacomo Nannicini^{2}, Anton Robert^{1}, Ivano Tavernelli^{1}, and Stefan Woerner^{1} — ^{1}IBM Research - Zurich Research Lab — ^{2}IBM T.J. Watson Research Center

Recent advances in Noisy Intermediate-Scale Quantum (NISQ) computers allow us to find solutions for combinatorial optimization problems encoded in Hamiltonians via hybrid quantum/classical variational algorithms. Current approaches minimize the expectation of the problem Hamiltonian for a parameterized trial state generated in the quantum circuit. The expectation is obtained by sampling the full outcome of an ensemble of measurements of the corresponding matrix element, while the trial wavefunction parameters are optimized classically. This procedure is fully justified for quantum mechanical observables (i.e. molecular energy). However, in the case of the simulation of classical optimization problems, which yield diagonal Hamiltonians, we argue that it is more natural to aggregate the samples using a different aggregation function than the expected value. This is because our goal is simply to determine with good probability which basis state is the optimum. In this talk, we present results of the aforementioned scheme for a plethora of interesting optimization problems where we demonstrate faster convergence towards more accurate solutions.