Quantum-classical data conversion using tensor network optimization techniques

Converting classical information into a quantum circuit is a necessary step in harnessing the power of quantum computing. Present-day quantum computers, known as NISQ devices, exhibit high noise levels without error correction, imposing stringent constraints on qubit count and quantum gate usage. Consequently, it becomes imperative to design quantum circuits with reduced depth. Particularly, when employing amplitude encoding to transform classical-quantum information, conventional methods often require an exponential number of quantum gates relative to the number of qubits. This renders them unsuitable for today's NISQ devices.

In this context, we investigate a technique to construct an approximate improvement for amplitude encoding circuits, taking into account classical information stored in a floating-point number array. Our approach involves optimizing the matrix elements of a two-qubit unitary gate, akin to techniques used in tensor network methods. Subsequently, we analytically break down the resulting unitary matrix into a series of elementary unitary gates. Furthermore, building upon this fundamental optimization technique, we explore a method for selectively incorporating superior quantum gates.

We apply this methodology to the challenge of creating a circuit that approximates the ground state of a quantum spin model. As a result, we discover that more efficient circuits can be generated automatically, without the need for prior knowledge of the classical information.