Thermodynamic Limits of Quantum Search

TL;DR

This paper explores the fundamental thermodynamic limits of quantum search algorithms, establishing bounds on their efficiency and implications for cryptography, including key length requirements and the security of quantum cryptographic protocols.

Contribution

It introduces a thermodynamic framework for quantum search, deriving tight bounds and proposing an optimized quantum protocol that saturates these limits.

Findings

Quantum search has a fundamental work-runtime trade-off.

A specific quantum protocol outperforms existing implementations.

A secret key of 831 bits cannot be broken before cosmic events cease.

Abstract

Modern cryptography relies on keyed symmetric ciphers to ensure the secrecy and authenticity of high bandwidth data transfer. While the advent of quantum computers poses a challenge for public key cryptography, unbroken ciphers are considered safe against quantum attacks if their key is sufficiently long. However, concrete bounds on the required key length thus far remain elusive: Despite the well known asymptotic complexity of Grover's quantum search, the optimal algorithm to recover a secret key, no implementation-agnostic tight bounds were established. Here, we discuss the quantum thermodynamic limits of generic search algorithms, and find a work-runtime trade-off for autonomous computers with a fundamental lower bound. By devising an application-specific quantum protocol, which outperforms circuit and adiabatic implementations, and saturates this bound, we demonstrate that it is tight. Applying this limit, we find that a secret key of 831 bit length cannot be reconstructed deterministically in an expanding, dark-energy-dominated universe until star formation is expected to cease. Implications for post quantum cryptography, and quantum key distribution are discussed.