A Multilayer Network Approach to Quantum Computing

TL;DR

This paper introduces a multilayer network model called Quantum Multiverse Network (QuMvN) that reformulates quantum computation, enabling classical simulation of quantum circuits and providing insights into quantum speedups.

Contribution

The paper presents the QuMvN model, a novel multilayer network approach to quantum computing, and demonstrates its effectiveness in simulating complex quantum algorithms like Shor's Algorithm.

Findings

Successfully simulated Shor's Algorithm with 70 qubits on a commodity cloud server.

QuMvN enables classical simulation of certain quantum circuits more efficiently.

Discussed the role of layers and randomized algorithms in quantum speedups.

Abstract

The circuit model of quantum computation is reformulated as a multilayer network theory [3] called a Quantum Multiverse Network (QuMvN). The QuMvN formulation allows us to interpret the quantum wave function as a combination of ergodic Markov Chains where each Markov Chain occupies a different layer in the QuMvN structure. Layers of a QuMvN are separable components of the corresponding wave function. Single qubit measurement is defined as a state transition of the Markov Chain that emits either a $0$ or $1$ making each layer of the QuMvN a Discrete Information Source. A message is equivalent to a possible measurement outcome and the message length is the number of qubits. Therefore, the quantum wave function can be treated as a combination of multiple discrete information sources analogous to what Shannon called a "mixed" information source [18]. We show the QuMvN model has significant advantages in the classical simulation of some quantum circuits by implementing quantum gates as edge transformations on the QuMvNs. We implement a quantum virtual machine capable of simulating quantum circuits using the QuMvN model and use our implementation to classically simulate Shor's Algorithm [19]. We present results from multiple simulations of Shor's Algorithm culminating in a $70$ qubit simulation of Shor's Algorithm on a commodity cloud server with $96$ CPUS and $624$GB of RAM. Lastly, the source of quantum speedups is discussed in the context of layers in the QuMvN framework and how randomized algorithms can push the quantum supremacy boundary.