[Paper Review] A proposal to demonstrate non-abelian anyons on a NISQ device

Jovan Jovanović, Carolin Wille+2 more|arXiv (Cornell University)|Jun 22, 2023

Quantum Information and Cryptography30 references44 citations

TL;DR

The paper proposes a practical scheme to realize non-Abelian anyons in the quantum double D(D4) on a NISQ device, with circuit-depth reductions for ground-state preparation, anyon manipulation via simplified ribbon operators, partial charge measurements, and numerical simulations supporting feasibility.

ABSTRACT

In this work we present a proposal for realising non-Abelian anyons on a NISQ device. In particular we explore the feasibility of implementing the quantum double model $D(D_4)$. We propose techniques to drastically simplify the circuits for the manipulation and measurements of anyons. Numerical simulations with realistic noise models suggest that current NISQ technology is capable of probing signatures of non-Abelian anyons far beyond elemental properties such as the non-commutativity of braids. In particular, we conclude that experimentally measuring the full modular data of the model is feasible.

Motivation & Objective

• Identify a suitable non-Abelian topological phase amenable to NISQ implementation (D(D4)).
• Develop variably shallow quantum circuits for ground-state preparation and anyon manipulation suitable for NISQ devices.
• Design measurement protocols to extract non-Abelian signatures, including full modular data, with reduced quantum-resource requirements.
• Demonstrate feasibility of probing non-Abelian braiding and fusion on current noisy quantum hardware via simulations.

Proposed method

• Analyze Kitaev’s quantum double models and select D(D4) as the target phase due to its size and solvability.
• Prepare the ground state with a direct unitary circuit, avoiding feed-forward protocols to suit architectures with limited mid-circuit measurements.
• Implement ribbon operators for creating and moving anyons using ancilla qudits, exploiting structure (C, χ) of non-Abelian anyons to reduce circuit depth and avoid Toffoli gates.
• Use partial charge measurements by probing subgroup transformations to infer total topological charge without full group multiplicative circuits.
• Propose elemental protocols for anyon fusion, braiding, and interferometry, and validate them via numerical simulations with realistic noise models.

Experimental results

Research questions

• RQ1 Can D(D4) non-Abelian anyons be prepared and manipulated on a NISQ device with circuit depths compatible with current noise levels?
• RQ2 What circuit-depth reductions are achievable for ribbon-operator based creation/movement of non-Abelian anyons by leveraging the (C, χ) structure?
• RQ3 Is it possible to extract full modular data (S- and T-matrices) of D(D4) using feasible measurement schemes on NISQ hardware?
• RQ4 Does partial charge measurement suffice to unambiguously identify topological charge content in D(D4) with a limited number of subgroup probes?
• RQ5 How do the proposed protocols extend to related groups (e.g., D(Q8), S3) and what are the implications for universal quantum computation?

Key findings

• Current NISQ technology can probe non-Abelian anyon signatures beyond basic braiding properties in D(D4).
• Ground-state preparation can be achieved with low depth circuits in quasi-one-dimensional geometries (braiding ladder).
• Ribbon operators can be implemented with drastically reduced circuit depth by tailoring to the anyon type, avoiding Toffoli gates on qubit platforms.
• Partial charge measurements via subgroups can identify topological charge with a small set of measurements, avoiding full group multiplicativity.
• Elemental protocols for fusion, braiding, and interferometry are feasible and supported by numerical simulations with realistic noise.
• Extensions to S3 suggest native-qutrit devices may maintain depth advantages, while qubit-only devices face substantial depth increases.