A tree tensor network approach to simulating Shor's algorithm

Abstract

Simulating quantum systems constructively furthers our understanding of qualitative and quantitative features which may be analytically intractable. In this letter, we directly simulate and explore the entanglement structure present in a paradigmatic example of quantum information: Shor's wavefunction. The methodology employed is a dynamical tensor network which is initially constructed as a tree tensor network, inspired by the modular exponentiation quantum circuit, and later efficiently mapped to a matrix product state. Utilizing the Schmidt number as a local entanglement metric, our construction explicitly captures the wavefunction's non-local entanglement structure and an entanglement scaling relation is discovered. Specifically, we see that entanglement across a bipartition grows exponentially in the number of qubits before saturating at a critical scale which is proportional to the modular periodicity.

4+ pages, 4 figures, reference added

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Cited by in corpus (12)

• Quantum Machine Learning for Chemistry and Physics
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Validating Quantum-Classical Programming Models with Tensor Network Simulations
• Optimising Matrix Product State Simulations of Shor's Algorithm
• Automatic structural optimization of tree tensor networks
• Large-Scale Simulation of Shor's Quantum Factoring Algorithm
• Simulating quantum circuits using tree tensor networks
• Tensor networks for quantum computing
• Benchmarking treewidth as a practical component of tensor-network--based quantum simulation
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• Gauge-Fixing Quantum Density Operators At Scale
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm