Quantum catalysts enable efficient work extraction from complex systems
Computational Work Extraction: The Complexity of Catalysts
Computational Complexity
Summary
This paper studies how much useful energy, called ergotropy, can be taken out of quantum systems. It shows that while there is a lot of energy theoretically available, if you use simple and efficient methods, you can get almost no work out. However, if you allow the use of special helper qubits called catalysts that must return to their original state, you can efficiently extract the full energy. The authors connect this ability to solve certain computational problems and define a new concept called pseudoergotropy, similar to pseudorandomness in computing. They also prove these results hold both for quantum and classical systems.
What this means in practice
- •For quantum computing engineers: Identify how catalytic qubits can be used to efficiently extract work from complex quantum systems when designing quantum thermal machines.
- •For cryptography software developers: Use the connection between catalytic ergotropy and computational complexity to design protocols distinguishing classical and quantum behaviors.
A theory result. No direct application yet.
Authors
Atul Singh Arora, Shantanav Chakraborty, Alexandru Cojocaru, Sreyas Saminathan, Uttam Singh
Abstract
We prove maximal separations: $n$-qubit systems can have $Θ(n)$ ergotropy, while every efficient process extracts negligible work, even for Hamiltonians consisting of single-qubit terms. We establish an unconditional existential separation and give an explicit construction in the random oracle model. Assuming the existence of quantum-secure pseudorandom functions, this separation extends to the plain model. This work uncovers an important connection between ergotropy and the complexity of catalytic computation---computation where auxiliary qubits must be finally restored to their initial state. Relative to a random oracle, we establish relational and decision problems that: (i) can be solved efficiently with $λ$ catalysts; but (ii) cannot be solved by any algorithm with $cλ$ catalysts, for any $c<1$. We show this by proving query lower bounds for quantum-space bounded algorithms. As a consequence, for computational ergotropy, catalysts prove to be surprisingly powerful---there is a family of Hamiltonians and states for which catalysts enable efficient extraction of the full $Θ(n)$ ergotropy, while every efficient non-catalytic process extracts negligible work. Furthermore, catalysts also allow us to introduce and instantiate the notion of pseudoergotropy---analogous to pseudorandomness. On the other hand, we show catalysts do not change (information-theoretic) ergotropy. Finally, our work also sheds light on the classical aspect of the problem. First, most of our constructions rely on classical states and Hamiltonians and therefore imply analogous results for classical ergotropy. Second, we show that certain proof of quantumness protocols can be used to generically separate classical and quantum catalytic ergotropy.