Quantum Advantage for Integral Transforms

Quantum computers promise to revolutionize some of the most computationally challenging tasks by executing calculations faster than classical computers. Integral transforms, such as convolution, Laplace transform, or path integration in quantum mechanics, are indispensable operations of scientific and technological progress. They are used from solving integro-differential equations to system modeling and signal processing. With the rapidly growing amount of collected information and the development of more complex systems, faster computations of integral transforms could dramatically expand analysis, design and execution capabilities. Here we show that the use of quantum processors can reduce the time complexity of integral transform evaluations from quadratic to quasi-linear. We present an experimental demonstration of the quantum-enhanced strategy for matched filtering. We implemented the qubit-based matched filtering algorithm on noisy superconducting qubits to carry out the first quantum-based gravitational-wave data analysis. We obtained a signal-to-noise ratio with this analysis for a binary black hole merger similar to that achievable with classical computation, providing evidence for the utility of qubits for practically relevant tasks. The presented algorithm is generally applicable to any integral transform with any number of integrands in any dimensions.