Instantaneous Quantum Computation

TL;DR

This paper explores a theoretical model of instantaneous quantum computation, demonstrating its ability to sample complex distributions efficiently and with fewer qubits than traditional quantum algorithms like Shor's, and proposing interactive proof systems.

Contribution

It introduces a new quantum computation paradigm with minimal temporal structure, leveraging binary matroids to enable complex sampling and proof systems with fewer qubits.

Findings

Enables sampling from classically hard distributions

Supports simple interactive proof systems for quantum effects

Requires fewer qubits than Shor's Algorithm

Abstract

We examine theoretic architectures and an abstract model for a restricted class of quantum computation, called here instantaneous quantum computation because it allows for essentially no temporal structure within the quantum dynamics. Using the theory of binary matroids, we argue that the paradigm is rich enough to enable sampling from probability distributions that cannot, classically, be sampled from efficiently and accurately. This paradigm also admits simple interactive proof games that may convince a skeptic of the existence of truly quantum effects. Furthermore, these effects can be created using significantly fewer qubits than are required for running Shor's Algorithm.