Digital Simulation of Projective Non-Abelian Anyons with 68 Superconducting Qubits

Abstract

Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather than merely a phase factor, in a space spanned by topologically degenerate wavefunctions. They are the building blocks of topological quantum computing. However, experimental observation of non-Abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto, in spite of various theoretical proposals. Here, we report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics with up to 68 programmable superconducting qubits arranged on a two-dimensional lattice. By implementing the ground states of the toric-code model with twists through quantum circuits, we demonstrate that twists exchange electric and magnetic charges and behave as a particular type of non-Abelian anyons—the Ising anyons. In particular, we show experimentally that these twists follow the fusion rules and non-Abelian braiding statistics of the Ising type, and can be explored to encode topological logical qubits. Furthermore, we demonstrate how to implement both single- and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical qubits. Our results demonstrate a versatile quantum digital approach for simulating non-Abelian anyons, offering a new lens into the study of such peculiar quasiparticles.

Simulation of Projective Non-Abelian Anyons for Quantum Computation

“…[4] The approaches used in Refs. [3,4] are similar. Additionally, the logic three-qubit entangled state encoded by six anyons has been prepared by the Google team using the braiding method for 25 superconducting qubits.…”

“…Notably, a collaboration team of superconducting quantum computation, from Zhejiang University of Haohua Wang and Chao Song experimental group and Tsinghua University of Dongling Deng theoretical group, has simulated a series of building blocks for topological quantum computation based on anyons. [3] They used, individually, 68 and 30 qubits located on the square lattices of two superconducting processors to perform the experiments, where the use of 30 qubits was generally for verification.…”

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

“…Quantum computation leverages quantum effects to store and process data, which could lead to a revolution in computational chemistry. − With the advent of noisy intermediate scale quantum (NISQ) computing, devices with tens of error-prone qubits are increasingly becoming available for use to researchers and the public. − Since such devices are not capable of running large-depth structured quantum algorithms, the question of how to best utilize them to solve chemistry problems is of deep scientific and commercial significance. In recent years, following pioneering proposals such as the variational quantum eigensolver (VQE), research has focused on variational algorithms based on parametrized quantum circuits (PQC). − In the long term, the quantum phase estimation (QPE) algorithm offers a promising route to evaluating the energy of molecular systems, as it may potentially provide an exponential advantage over classical full configuration interaction (FCI) treatment. , However, compared with VQE, the circuit depths required to run QPE are typically far too deep to run on near-term quantum devices, making VQE the approach of choice in the NISQ era.…”

Optical-Microwave Entanglement Paves the Way for Distributed Quantum Computation

“…However, this number is still several orders of magnitude away from the requirement of quantum error correction, which is essential for general-purpose quantum computers. [4][5][6][7][8] To overcome this hurdle, networking small-size quantum processors that are cooled individually, i.e., distributed quantum computation, becomes an important avenue to a large-scale quantum computer. However, the superconducting qubits work in the microwave regime.…”