Distributed Computing Model: Classical vs. Quantum vs. Post-Quantum

Abstract

Computation refers to an algorithmic process of producing outputs from a given set of inputs. We consider a particular model of computation where the computing device is comprised of several components/ports placed at different spacetime locations -the inputs are distributed among different ports, whereas the output is to be assessed by some other port. Importantly, communications among the different ports are limited as the physical systems allowed to be transmitted among the different ports are constrained with information theoretic restrictions. Interestingly, this limited communication distributed computing prototype provides an efficient modus operandi to compare the computational strength of different mathematical models used to describe those physical systems. We come up with computing tasks where quantum theory outperforms its classical counterpart. More surprisingly, a broader class of operational theories with state or/and effect space structures more exotic than quantum theory turns out to be suboptimal in performing some distributed computing tasks. We characterize the computations that can be perfectly accomplished in quantum theory but not in other theories. The proposed computing model thus provides a new approach to single out quantum theory in the theory space and promises a novel perspective towards the axiomatic derivation of Hilbert space quantum mechanics.

Timelike correlations and quantum tensor product structure

“…For a detailed overview of this framework we refer to the works [9][10][11][12][13][14]. In the recent past several interesting results have been reported within this framework [25][26][27][28][29][30][31]. A GPT is specified by a list of system types and the composition rules specifying combination of several systems, where a system S is specified by identifying the three-tuple (Ω S , E S , T S ) of the state space, effect space, and the set of transformations.…”

Can Noise on Qubits Be Learned in Quantum Neural Network? A Case Study on QuantumFlow

“…Quantum computing has the pbertels2021quantumotential to provide exponential speedup over the classical computers [7,26,1,21,2], which is considered to be one of the best candidates for solving some of the complicated computational problems that cannot be solved by classical computing in a reasonable time [7,27,8]. We are now witnessing the rapid development in both quantum hardware and quantum algorithms: on the hardware side, the newly emerging quantum computers (such as IBM Q [10]) are developed with superconductor and can perform superposition and quantum entanglement on the physical quantum bits (qubits); on the other side, different quantum algorithms have been devised, such as Shor's algorithm for primary factorization [22] and the quantum approximate optimization algorithm (QAOA) for optimization problems [5].…”