Quantum forking for fast weighted power summation

The computational cost of preparing an input quantum state can be significant depending on the structure of data to be encoded. Many quantum algorithms require repeated sampling to find the answer, mandating reconstruction of the same input state for every execution of an algorithm. Thus, the advantage of quantum information processing can diminish due to redundant state initialization. Here we present a framework based on quantum forking that bypasses such a fundamental issue and expedites a weighted power summation of measurement outcomes from independent quantum processes. Our approach uses quantum interference to add up expectation values measured from independent quantum trajectories created in superposition by quantum forking, while requiring only a single initial state preparation routine. As examples, we describe applications of the framework for entanglement witnesses and purity benchmarking. A proof-of-principle experiment is implemented on the IBM and Rigetti quantum cloud platforms.