# A Quantum Algorithm to Efficiently Sample from Interfering Binary Trees

## TL;DR

This paper introduces a quantum algorithm that efficiently samples from complex probability distributions involving interference, using a binary tree process, and explores classical simulation approaches for such quantum processes.

## Contribution

It presents a novel polynomial-time quantum algorithm for sampling from interfering binary tree distributions and relates it to a classical two-qubit measurement scheme.

## Key findings

- Quantum algorithm efficiently samples from interference-involved distributions.
- Classical simulation reduces to a two-qubit measurement process.
- Naive Markov Chain fails to produce correct distributions.

## Abstract

Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by a binary tree, we construct an explicit quantum algorithm that runs in polynomial time to sample from the process once. The corresponding naive Markov Chain algorithm does not produce the correct probability distribution and an explicit classical calculation of the full distribution requires exponentially many operations. However, the problem can be reduced to a system of two qubits with repeated measurements, shedding light on a quantum-inspired efficient classical algorithm.