Third law of thermodynamics and the scaling of quantum computers

TL;DR

This paper explores how the third law of thermodynamics impacts the initialization of quantum computers, highlighting the challenge of finite effective temperatures on scalability and fidelity, supported by theoretical analysis and real quantum processor tests.

Contribution

It introduces a thermodynamic perspective to quantum computing scalability, emphasizing the impact of finite temperatures on initial state purity and fidelity constraints.

Findings

Finite effective temperature affects quantum state initialization.

Thermodynamic limits pose challenges to quantum computer scaling.

Experimental validation on real quantum hardware supports theoretical claims.

Abstract

The third law of thermodynamics, also known as the Nernst unattainability principle, puts a fundamental bound on how close a system, whether classical or quantum, can be cooled to a temperature near to absolute zero. On the other hand, a fundamental assumption of quantum computing is to start each computation from a register of qubits initialized in a pure state, i.e., at zero temperature. These conflicting aspects, at the interface between quantum computing and thermodynamics, are often overlooked or, at best, addressed only at a single-qubit level. In this work, we argue how the existence of a small, but finite, effective temperature, which makes the initial state a mixed state, poses a real challenge to the fidelity constraints required for the scaling of quantum computers. Our theoretical results, carried out for a generic quantum circuit with $N$-qubit input states, are validated by test runs performed on a real quantum processor.