Reducing computational complexity of quantum correlations

Quantum implicit computational complexity

We introduce a quantum lambda calculus inspired by Lafont’s Soft Linear Logic and capturing the polynomial quantum complexity classes EQP, BQP and ZQP. The calculus is based on the ‘‘classical control and quantum data’’ paradigm. This is the first example of a formal systemcapturing quantumcomplexity classes in the spirit of implicit computational complexity — it is machine-free and no explicit...

Quantum Computational Complexity

Computational complexity of the quantum separability problem

Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first systematic and comprehensive treatment of this (bipartite) quantum separability problem, focusing on its deterministic (as opposed to randomized) computationa...

Computational Complexity Measures of Multipartite Quantum Entanglement

We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions— approximability and distinguishability. Built upon the formal treatment of partial separability, we measure the complexity of an entangled quantum state by determining (i) how hard to approximate it from a fix...

Computational complexity of quantum optimal control landscapes

We study the Hamiltonian-independent contribution to the complexity of quantum optimal control problems. The optimization of controls that steer quantum systems to desired objectives can itself be considered a classical dynamical system that executes an analog computation. The systemindependent component of the equations of motion of this dynamical system can be integrated analytically for vari...