Low Rank Approximation in Simulations of Quantum Algorithms

Understand

Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large.

• However, some quantum algorithms and the corresponding quantum circuits can be simulated efficiently on a classical computer if the input quantum state is a low-rank tensor and all intermediate states of the quantum algorithm can be represented or approximated by low-rank tensors.
• In this paper, we examine the possibility of simulating a few quantum algorithms by using low-rank canonical polyadic (CP) decomposition to represent the input and all intermediate states of these algorithms.
• Two rank reduction algorithms are used to enable efficient simulation.