Abstract
The computational cost of preparing a quantum state can be substantial 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 computation can diminish due to redundant state initialization. We present a framework based on quantum forking that bypasses this fundamental issue and expedites a family of tasks that require sampling from independent quantum processes. Quantum forking propagates an input state to multiple quantum trajectories in superposition, and a weighted power sum of individual results from each trajectories is obtained in one measurement via quantum interference. The significance of our work is demonstrated via applications to implementing non-unitary quantum channels, studying entanglement and benchmarking quantum control. A proof-of-principle experiment is implemented on the IBM and Rigetti quantum cloud platforms.
Highlights
Designing an efficient quantum algorithm to solve a computational task does not alone ensure a quantum advantage over a classical counterpart, but there must be an efficient procedure to prepare the desired initial quantum state
We developed quantum forking-based sampling as a tool to avoid redundant initial state preparations and significantly reduce the time complexity of weighted power summation, which has wide applications in quantum science
The qth power summation of d measurement outcomes with arbitrary weights can be carried out with the constant cost of initial state preparation, while requiring q(d − 1) ancilla qubits given in arbitrary states, a control qudit with dimension d, q-local measurement and 2q(d − 1) c-swap gates
Summary
Designing an efficient quantum algorithm to solve a computational task does not alone ensure a quantum advantage over a classical counterpart, but there must be an efficient procedure to prepare the desired initial quantum state. We present quantum forking-based sampling (QFS) to accelerate various tasks that require adding the results from independent quantum trajectories as a convex combination. With this framework, the number of state preparation routines and measurements required for performing a weighted power summation of measurement outcomes sampled from an arbitrary number of independent quantum processes remains constant, though this is at the cost of introducing a control qudit, ancilla qubits in arbitrary states, and a series of controlled swap gates.
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