Abstract
Adversarial learning is one of the most successful approaches to modeling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential applications. In this work, we derive an adversarial algorithm for the problem of approximating an unknown quantum pure state. Although this could be done on universal quantum computers, the adversarial formulation enables us to execute the algorithm on near-term quantum computers. Two parametrized circuits are optimized in tandem: one tries to approximate the target state, the other tries to distinguish between target and approximated state. Supported by numerical simulations, we show that resilient backpropagation algorithms perform remarkably well in optimizing the two circuits. We use the bipartite entanglement entropy to design an efficient heuristic for the stopping criterion. Our approach may find application in quantum state tomography.
Highlights
In February 1988 Richard Feynman wrote on his blackboard: ‘What I cannot create, I do not understand’ [1]
The target state would come from an external channel and would be loaded in the quantum computer’s register with no significant overhead
We show that adversarial quantum circuit learning can be used to approximate entangled target states
Summary
In February 1988 Richard Feynman wrote on his blackboard: ‘What I cannot create, I do not understand’ [1]. Generative models are algorithms trained to approximate the joint probability distribution of a set of variables, given a dataset of observations. The quantum generalization is straightforward; Quantum generative models are algorithms trained to approximate the wave function of a set of qubits, given a dataset of quantum states. This process of approximately reconstructing a quantum state is already known to physicists under the name of quantum state tomography. Quantum mechanics could provide a new set of tools to machine learning practitioners for tackling classical tasks. Identifying classical datasets that can be modeled better via quantum correlations is an interesting open question in itself [9]
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