Adaptive ansatz based on low-rank state preparation

Abstract

Quantum State Preparation Algorithms consist of defining a sequence or unitary operations to load a specific target state on a quantum computer. We can use those algorithms in appli- cations such as quantum machine learning. However, some state preparation algorithms have exponential circuit complexity with the number of qubits on the system. That is the case of amplitude encoding algorithms, which is an encoding type for loading normalized data into the probability amplitudes of the state. To circumvent this overhead in circuits’ complexity, works explore specific properties of quantum states to optimize the circuit’s complexity, such as sparsity or symmetry. Other works explore simplifying the quantum circuit to load an ap- proximate quantum state. It is the case of Quantum Generative Adversarial Networks, which use a specific circuit architecture comprised of alternating blocks of single-qubit rotations and two-qubit entangling controlled gates. But when trained to load random distributions on, we observed the performance deteriorates as the number of qubits increases in terms of relative entropy. In this work, we propose different architectures for the Quantum Generative mod- els based on the state preparation algorithm known as Low-Rank. Through experiments for loading the log-normal distribution, we show error reductions in quantum state initialization.