Retrodictive Quantum Computing

TL;DR

This paper introduces retrodictive quantum computing, a novel approach that uses future information to improve problem-solving efficiency, demonstrated on several key quantum algorithms.

Contribution

It presents a new retrodictive paradigm for quantum computation and shows how to implement it at scale using symbolic computation tools.

Findings

Retrodictive quantum computing can efficiently solve key quantum algorithms.

Classical methods can exploit retrodictive quantum insights.

The approach challenges traditional predictive reasoning in quantum computing.

Abstract

Quantum models of computation are widely believed to be more powerful than classical ones. Efforts center on proving that, for a given problem, quantum algorithms are more resource efficient than any classical one. All this, however, assumes a standard predictive paradigm of reasoning where, given initial conditions, the future holds the answer. How about bringing information from the future to the present and exploit it to one's advantage? This is a radical new approach for reasoning, so-called Retrodictive Computation, that benefits from the specific form of the computed functions. We demonstrate how to use tools of symbolic computation to realize retrodictive quantum computing at scale and exploit it to efficiently, and classically, solve instances of the quantum Deutsch-Jozsa, Bernstein-Vazirani, Simon, Grover, and Shor's algorithms.