The characterization of observables, expressed via Hermitian operators, is a crucial task in quantum mechanics. For this reason, an eigensolver is a fundamental algorithm for any quantum technology. In this work, we implement a semi-autonomous algorithm to obtain an approximation of the eigenvectors of an arbitrary Hermitian operator using the IBM quantum computer. To this end, we only use single-shot measurements and pseudo-random changes handled by a feedback loop, reducing the number of measures in the system. Due to the classical feedback loop, this algorithm can be cast into the reinforcement learning paradigm. Using this algorithm, for a single-qubit observable, we obtain both eigenvectors with fidelities over 0.97 with around 200 single-shot measurements. For two-qubits observables, we get fidelities over 0.91 with around 1500 single-shot measurements for the four eigenvectors, which is a comparatively low resource demand, suitable for current devices. This work is useful to the development of quantum devices able to decide with partial information, which helps to implement future technologies in quantum artificial intelligence.
We present an analog version of the quantum approximate optimization algorithm suitable for current quantum annealers. The central idea of this algorithm is to optimize the schedule function, which defines the adiabatic evolution. It is achieved by choosing a suitable parametrization of the schedule function based on interpolation methods for a fixed time, with the potencial to generate any function. This algorithm provides an approximate result of optimization problems that may be developed during the coherence time of current quantum annealers on their way towards quantum advantage.
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of stochastic algorithms. We follow a bioinspired evolutionary mutation method to introduce changes in the involved matrices. Our optimization is based on two figures of merit: learning speed and learning accuracy. This method provides high fidelities for the searched eigenvectors and faster convergence on the way to quantum advantage with current noisy intermediate-scaled quantum computers.
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