The sum-over-histories formulation of quantum computing

TL;DR

This paper introduces a sum-over-histories approach to quantum computing, offering a new perspective inspired by the path integral formalism, complementing traditional state vector models.

Contribution

It presents a novel formulation of quantum circuits based on path integrals, expanding the theoretical framework of quantum computing.

Findings

Demonstrates the application of the sum-over-histories approach to basic quantum problems

Provides a complementary perspective to the Schrödinger-based models

Explores potential advantages of the path integral formalism in quantum computation

Abstract

Since Deutsch (1985), quantum computers have been modeled exclusively in the language of state vectors and the Schroedinger equation. We present a complementary view of quantum circuits inspired by the path integral formalism of quantum mechanics, and examine its application to some simple textbook problems.