[ENTRY] Simulation of anyons within the toric code model (based on "Realizing topologically ordered states on a quantum processor" paper)

[Randl]

Team Name:

Barren plateau inhabitants

Project Description:

Quantum computing, an idea proposed by Richard Feynman in his famous Caltech lecture, is a powerful possible future tool for solving various optimization and physical problems previously inaccessible to classical computers. The cornerstone of building of a reliable quantum computer is implementation of fault-tolerant computation procedure, which is not susceptible to external noise and allows performing long computations. Such fault-tolerant computing can be implemented, as shown by Kitaev, within braiding the so-called anyons, new exotic particles with non-trivial mutual statistics. The latter is the defining feature of anyons and means that the system wave function in 2 dimensions picks up a non-zero phase (or even changes to a different state) when moving one anyon around the other. This non-trivial phase is topologically protected and guarantees high degree of resistivity to noise. Later on, Kitaev proposed the lattice spin model, Toric code, in paper "Fault-tolerant quantum computation by anyons", in which those anyons are realized. Ironically, those anyons within this Toric code model were simulated by Google on a noisy superconducting computer. In this project, we aimed at reproduction of the results of this work.

Namely, using Qiskit, we (i) create the circuit preparing the Toric code model ground state, (ii) using the Kitaev-Preskil cut formula, measure topological entanglement entropy and (iii) measure, within braiding, mutual exchange statistics between the e- and m-anyons realized in this model.

Our project is based on the paper "Realizing topologically ordered states on a quantum processor" by Satzinger et al, published in Science. The paper studies a topologically ordered state (toric code) by simulating it on a quantum computing. In particular, preparation of ground state, measurement of topological entropy, braiding statistics and logical qubit implementation are demonstrated.

In our project, we implement large part of the paper's experiments in Qiskit: GS preparation for matching boundary condition, second Rényi entropy and topological entropy evaluation and mutual/exchange statistics of quasiparticles. The simulation version can be run on a laptop (31+1 qubit) and is potentially ready to be run on a real-life quantum computer supporting Qiskit.

Presentation:

The jupyter notebook with main results is available in the repo

Source code:

https://github.com/Randl/qhack_toric_code

Which challenges/prizes would you like to submit your project for?

• IBM Qiskit Challenge
• Google Quantum AI Research Challenge
• Simulation Challenge

[isaacdevlugt]

Thank you for your submission! There's still time to populate your submission with code, presentation material, etc. Please make any final adjustments before the deadline tonight at 17h00 EST!

Good luck!

[Randl]

@isaacdevlugt The timer on a website shows 7 more hours. Am I understanding correctly that this is unrelated timer, and the deadline for the hackathon submissions is now? Are we prohibited to update submission after the deadline?