# Context aware quantum simulation of a matrix stored in quantum memory

## TL;DR

This paper introduces a quantum circuit design for efficiently simulating block diagonal matrices stored in quantum memory, with applications in molecular Hamiltonian simulations and variational algorithms.

## Contribution

It presents a novel context-aware quantum circuit for matrix simulation that requires linear gates and adapts to data, extending to real matrices and improving quantum simulation techniques.

## Key findings

- Circuit requires O(n) quantum gates
- Success probability depends on matrix size, being 1/poly(n) for poly(n) matrices
- Applicable to variational quantum eigensolvers and molecular Hamiltonian simulations

## Abstract

In this paper a storage method and a context-aware circuit simulation idea are presented for the sum of block diagonal matrices. Using the design technique for a generalized circuit for the Hamiltonian dynamics through the truncated series, we generalize the idea to (0-1) matrices and discuss the generalization for the real matrices. The presented circuit requires $O(n)$ number of quantum gates and yields the correct output with the success probability depending on the number of elements: for matrices with $poly(n)$, the success probability is $1/poly(n)$. Since the operations on the circuit are controlled by the data itself, the circuit can be considered as a context aware computing gadget. In addition, it can be used in variational quantum eigensolver and in the simulation of molecular Hamiltonians.