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This paper introduces a novel approach for simulating peaked quantum circuits by utilizing a sparse and truncated state vector that captures only the most significant amplitudes. By leveraging vectorized operations and hardware acceleration, the authors demonstrate that their method can efficiently predict the most probable output bit strings while significantly reducing computational overhead compared to traditional dense representations. The results indicate that this simulation technique maintains accuracy while enabling classical computers to handle quantum circuit simulations more effectively.
Sparse state vector simulations can drastically cut down computational costs while accurately predicting outputs of peaked quantum circuits.
In a class of quantum circuits known as peaked circuits, the goal is to predict the most probable bit string at the output of the circuit. Since these circuits are designed to have a sharp peak in their output distribution, in principle it should be possible to simulate them using a truncated state vector with a limited number of terms, or a fraction of the total probability mass. This approximate simulation can be carried out on a classical computer with a sparse representation that stores only the nonzero amplitudes of the state vector, in contrast to the dense representations that are common in most quantum simulators. For efficiency, all operations on the state vector should be vectorized to the furthest possible extent and, if available, hardware acceleration can also be used. This work describes how these requirements were met in an open-source implementation, and discusses its performance and limitations.
