Tensor quantum programming

Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. In this article, we propose a novel approach called Tensor Quantum Programming, which leverages tensor networks (TNs) for hybrid quantum computing. Our key insight is that the primary challenge of algorithms based on TNs lies in their high ranks (bond dimensions). Quantum computing offers a potential solution to this challenge, as an ideal quantum computer can represent tensors with arbitrarily high ranks in contrast to classical counterparts, which indicates the way towards quantum advantage. While tensor-based vector-encoding and state-readout are known procedures, the matrix-encoding required for performing matrix-vector multiplications directly on quantum devices is much less studied. We introduce an algorithm that encodes matrix product operators into quantum circuits with a depth that scales linearly with the number of qubits. We demonstrate the algorithm’s performance for matrices commonly encountered in differential equations, optimization problems, and quantum chemistry, for systems involving up to 50 qubits.