Avoiding Numerical Dead Zones to Prevent Quantum Computers Getting Stuck

Quantum hardware has made a lot of progress and there are many superconductor implementations in the noisy intermediate scale quantum (NISQ) systems. Promising application-oriented approaches are hybrid quantum-classical algorithms that rely on optimization of a parameterized quantum circuit. These system work in spite of errors and noise.

Researchers showed analytically and numerically that for a wide class of random quantum circuits, there are numerical deadzones. You would want to avoid initializing values that would start in with those values because then the quantum system would get stuck and would not reach a correct solution.

One approach to avoid these landscapes in the quantum setting is to use structured initial guesses, such as those adopted in quantum simulation. Another possibility is to use pre-training segment by segment, which was an early success in the classical setting.

Arxiv – an Initialization Strategy for Addressing Barren Plateaus in Parametrized Quantum Circuits

They propose a strategy which allows for efficient training of parametrized quantum circuits. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the final circuit is a sequence of shallow unitary blocks that each evaluates to the identity. Initializing in this way limits the effective depth of the circuits used to calculate the first parameter update so that they cannot be stuck in a barren plateau at the start of training. We show empirically that circuits initialized using this strategy can be trained using a gradient-based method.

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