Constant Time Adiabatic Preparation of the Laughlin State

The Laughlin wavefunction describes the quantum Hall state at filling factor 1/3 and is an example of a strongly correlated topological phase with anyonic excitations. Such systems are of importance in quantum computing because they are protected by a gap to excited states and thus are robust to local noise. We show that the Laughlin state can be adiabatically connected to a product state by tuning a geometric degree of freedom of the system [1]. Furthermore the gap along this pathway is a constant even in the thermodynamic limit indicating that the state can be prepared in constant time for arbitrary system size up to sub-polynomial factors. In particular, we design and optimize a digital quantum circuit that can be used to prepare the Laughlin state for 6 electrons on as few as 16 qubits, which is within the range of near-term quantum hardware [2]. Techniques like this will be essential for digital quantum computers to aid in the understanding and application of many-body topologically ordered states.
[1] S. Johri et al, New Journal of Physics 18 (2), 025011 (2016).
[2] T.E. O’Brien, B. Tarasinski, and L. DiCarlo, NPJ Quantum Information 3, 39 (2017).