Third Law of Thermodynamics and the Scaling of Quantum Computers

Year: 2022

Authors: Buffoni L., Gherardini S., Zambrini Cruzeiro E., Omar Y.

Autors Affiliation: PQI – Portuguese Quantum Institute, 1049-001 Lisboa, Portugal. CNR-INO, Area Science Park, Basovizza, Trieste, I-34149, Italy. LENS, University of Florence, via G. Sansone 1, Sesto Fiorentino, I-50019, Italy. Instituto Superior Tycnico, Universidade de Lisboa, Lisboa, 1049-001, Portugal 4) Instituto Superior Tycnico, Universidade de Lisboa, Lisboa, 1049-001, Portugal; Centro de Fnsica e Engenharia de Materiais Avanzados (CeFEMA), Physics of Information and Quantum Technologies Group, Lisboa, 1049-001, Portugal.

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 Letter, 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.


Volume: 129 (15)      Pages from: 150602  to:

More Information: We gratefully thank Per Delsing, Thomas Monz, and Michele Campisi for pointing out useful references and fruitful discussions. We also acknowledge the access to advanced services provided by the IBM Quantum Researchers Program. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum team. E. Z. C. and Y. O. acknowledge the support from FCT-Fundacao para a Ciencia e a Tecnologia (Portugal), namely through project UIDB/50008/2020 and UIDB/04540/2020, as well as from projects TheBlinQC and QuantHEP supported by the EU H2020 QuantERA ERA-NET Cofund in Quantum Technologies and by FCT (QuantERA/0001/2017 and QuantERA/0001/2019, respectively), and from the EU H2020 Quantum Flagship project QMiCS (820505). S. G. acknowledges the Blanceflor Foundation for financial support through the project “The theRmodynamics behInd thE meaSuremenT postulate of quantum mEchanics (TRIESTE).”
KeyWords: Thermodynamics of computation, Quantum information theory, Quantum thermodynamics
DOI: 10.1103/PhysRevLett.129.150602