Quantum circuit simulation of superchannels

Abstract

Quantum simulation is one of the central discipline to demonstrate the power of quantum computing. 
In recent years, the theoretical framework of quantum superchannels has been developed and applied widely as the extension of quantum channels. 
In this work, we study the quantum circuit simulation task of superchannels.
We develop a quantum superchannel simulation algorithm based on the convex decomposition into sum of extreme superchannels.
We demonstrate the algorithm by numerical simulation of qubit superchannels with high accuracy, making it applicable to current experimental platforms.
Our study stands as an expansion of the superchannel theory to the field of quantum simulation and algorithm, as well as an extension of quantum simulation from channels and open-system dynamics to superchannels and processes with manifest quantum memory effects.

Commutation simulator for open quantum dynamics

“…For this case of qubit amplitude damping, figure 2 demonstrates examples of relevant non-zero matrix elements of the Lindblad equation equation ( 21), for specific parameter choices and as functions of t and θ. In figure 2(a) we observe that the real part of equation (24) oscillates in time for θ ̸ = 0 and π. The static cases (θ = 0 , π) identify the eigenvectors |0⟩ and |1⟩ of H, whereas ω follows from the period of the oscillation in sin(ωt) (with ω = −2 and ϕ = 0 in this example).…”

“…This is because the simulation approach preserves a probabilistic interpretation for the system even for open systems, generating the generally irreversible evolution of the system probabilities from the diagonal elements of a density describing just the system of interest. The investigation of possible quantum advantage in such open system applications will be an interesting topic for future study, for example to investigate the quantum speed limit of simulating an open quantum system [22,23] and the study of quantum channels [24].…”

Experimental simulation of quantum superchannels

“…with K m v = ⟨m|V|0⟩, K ma w = ⟨m|W|a⟩, and t stands for transposition. Given an arbitrary superchannel, an algorithm has been developed recently for the task of circuit simulation of the superchannel [48]. The algorithm also explores the convexity of the set of superchannels.…”

“…Our algorithm A accepts an arbitrary target superchannel Ŝ as the input, in the form of its Choi state ω Ŝ ′ for instance, and uses an optimization scheme from a built-in package of MATLAB [48] to minimize the trace distance d(ω Ŝ , ω Ŝ ′ ). This trace distance represents simulation accuracy for…”

“…In this work, we implement quantum superchannels based on a recent simulation algorithm [48]. A central part of the algorithm is the decomposition into a convex sum of generalized extreme superchannels, which not only benefits practical simulation, but also is relevant for the study of information-theoretic features of channels and superchannels, e.g.…”