Abstract
Landauer’s principle asserts that any computation has an unavoidable energy cost that grows proportionally to its degree of logical irreversibility. But even a logically reversible operation, when run on a physical processor that operates on different energy levels, requires energy. Here we quantify this energy requirement, providing upper and lower bounds that coincide up to a constant factor. We derive these bounds from a general quantum resource-theoretic argument, which implies that the initial resource requirement for implementing a unitary operation within an error grows like times the amount of resource generated by the operation. Applying these results to quantum circuits, we find that their energy requirement can, by an appropriate design, be made independent of their time complexity.
- Received 15 November 2019
- Revised 14 January 2021
- Accepted 3 March 2021
DOI:https://doi.org/10.1103/PhysRevX.11.021014
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Processing information, be it by the brain or by a computer, requires energy. As is true for other devices, such as engines, the energy requirement of a computer can be reduced by a clever design. However, there exist fundamental limits: The laws of physics imply that even an optimal computer requires a certain minimal amount of energy to run. A well-known principle known as Landauer’s limit quantifies the amount of energy that must be dissipated by any irreversible computation. But even a fully reversible computation may require energy. Here, we determine a fundamental energy requirement for such reversible computations.
Our result consists of two complementary parts. First, we prove that a quantum computer will not be accurate unless provided with a certain minimum amount of energy, no matter how clever the design of the computer. Specifically, to ensure that the error in a computation remains below a given threshold, the laws of physics demand that we supply energy that scales inversely with the square root of that threshold. Second, we show that there indeed exists a design for a quantum computer that can work at that limit. In other words, that computer only consumes as much energy as the fundamental physical bound demands, but not more.
Significantly, we find that the energy invested to carry out the individual steps of a computation can be recycled after each step and used for the next one. This idea may serve as a design principle for future energy-efficient quantum computers.
