Approximate encoding of quantum states using shallow circuits

A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, thereby setting a strict barrier for exact state preparation on near-term quantum devices. In this talk, I will present an efficient method for creating an approximate encoding of a target state using a limited number of gates [1]. In the first part of the talk, I will focus on a classical implementation of the algorithm and demonstrate its performance by comparing the optimal and suboptimal circuits on real devices. Then, in the second part of the talk, I will consider a direct implementation of the proposed algorithm on a quantum computer and show how to overcome inherent barren plateaus by employing a local cost function rather than a global one. I will further examine how many shots are required to reach optimization convergence and show that the number of shots scales merely polynomially with the number of qubits. 

[1] arXiv: https://arxiv.org/pdf/2207.00028.pdf