# Simulating Large Quantum Circuits on a Small Quantum Computer

## TL;DR

This paper introduces a cluster-based simulation method enabling small quantum computers to simulate larger quantum systems or algorithms, with applications demonstrated on molecular energy estimation.

## Contribution

The authors propose a novel cluster simulation scheme that decomposes quantum circuits into manageable clusters, allowing small quantum devices to simulate larger systems efficiently.

## Key findings

- Simulation of large molecules using small quantum computers is feasible.
- Cluster parameters $K$ and $d$ effectively characterize circuit complexity.
- Experimental validation with BeH$_2$ molecule demonstrates practical applicability.

## Abstract

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters $K$ and $d$ of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most $d$ with at most $K$ qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any $(K,d)$-clustered quantum circuit on a $d$-qubit machine in time roughly $2^{O(K)}$, with further speedups possible when taking more fine-grained circuit structure into account. We show how our scheme can be used to simulate clustered quantum systems -- such as large molecules -- that can be partitioned into multiple significantly smaller clusters with weak interactions among them. By using a suitable clustered ansatz, we also experimentally demonstrate that a quantum variational eigensolver can still achieve the desired performance for estimating the energy of the BeH$_2$ molecule while running on a physical quantum device with half the number of required qubits.