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Physical Review Letters

Demonstrating Path-Independent Anyonic Braiding on a Modular Superconducting Quantum Processor

Jingjing Niu, Yishan Li, Lushuang Zhang, Jiajian Zhang, Ji Chu, Jiaxing Huang, Wenhui Huang, Lifu Nie, Jiawei Qiu, Xuandong Sun, Ziyu Tao, Weiwei Wei, Jiawei Zhang, Yuxuan Zhou, Yuanzhen Chen, Ling Hu, Yang Liu, Song Liu, Youpeng Zhong, Dawei Lu, Dapeng Yu

Published Jan 8, 2024• 9 citations
Publisher

Abstract

Anyons, exotic quasiparticles in two-dimensional space exhibiting nontrivial exchange statistics, play a crucial role in universal topological quantum computing. One notable proposal to manifest the fractional statistics of anyons is the toric code model; however, scaling up its size through quantum simulation poses a serious challenge because of its highly entangled ground state. In this Letter, we demonstrate that a modular superconducting quantum processor enables hardware-pragmatic implementation of the toric code model. Through in-parallel control across separate modules, we generate a 10-qubit toric code ground state in four steps and realize six distinct braiding paths to benchmark the performance of anyonic statistics. The path independence of the anyonic braiding statistics is verified by correlation measurements in an efficient and scalable fashion. Our modular approach, serving as a hardware embodiment of the toric code model, offers a promising avenue toward scalable simulation of topological phases, paving the way for quantum simulation in a distributed fashion.

DOI
10.1103/physrevlett.132.020601

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Anyons, exotic quasiparticles in two-dimensional space exhibiting nontrivial exchange statistics, play a crucial role in universal topological quantum computing. One notable proposal to manifest the fractional statistics of anyons is the toric code model; however, scaling up its size through quantum simulation poses a serious challenge because of its highly entangled ground state. In this Letter, we demonstrate that a modular superconducting quantum processor enables hardware-pragmatic implementation of the toric code model. Through in-parallel control across separate modules, we generate a 10-qubit toric code ground state in four steps and realize six distinct braiding paths to benchmark the performance of anyonic statistics. The path independence of the anyonic braiding statistics is verified by correlation measurements in an efficient and scalable fashion. Our modular approach, serving as a hardware embodiment of the toric code model, offers a promising avenue toward scalable simulation of topological phases, paving the way for quantum simulation in a distributed fashion.
Anyons, quasiparticles living in two-dimensional spaces with exotic exchange statistics, can serve as the fundamental units for fault-tolerant quantum computation. However, experimentally demonstrating anyonic statistics is a challenge due to the technical limitations of current experimental platforms. Here, we take a state perpetration approach to mimic anyons in the toric code using a seven-qubit nuclear magnetic resonance quantum simulator. Anyons are created by dynamically preparing the ground and excited states of a seven-qubit planar version of the toric code, and are subsequently braided along two distinct, but topologically equivalent paths. We observe that the phase acquired by the anyons is independent of the path, and coincides with the ideal theoretical predictions when decoherence and implementation errors are taken into account. As the first demonstration of the topological path independence of anyons, our experiment helps to study and exploit the anyonic properties towards the goal of building a topological quantum computer.
Anyons are quasiparticles occurring in two dimensions, whose topological properties are believed to be robust against local perturbations and may hold promise for fault tolerant quantum computing. Here we present an experiment of demonstrating the path independent nature of anyonic braiding statistics with a superconducting quantum circuit, which represents a 7-qubit version of the toric code model. We dynamically create the ground state of the model, achieving a state fidelity of 0.688±0.015 as verified by quantum state tomography. Anyonic excitations and braiding operations are subsequently implemented with single-qubit rotations. The braiding robustness is witnessed by looping an anyonic excitation around another one along two distinct, but topologically equivalent paths: Both reveal the nontrivial π-phase shift, the hallmark of Abelian 1/2 anyons, with a phase accuracy of ∼99% in the Ramsey-type interference measurement.
Anyons are quasiparticles that obey fractional statistics, producing a phase intermediate to bosons and fermions under particle interchange. Anyons form the basis for topological quantum computation and error correction, where the topological aspect of anyonic braiding is one of the important features that gives rise to fault tolerance. A central model that exhibits anyons is Kitaev’s toric code, where the excited states involve anyons that exhibit topological behavior. Here, we experimentally create the ground state and anyonic excitations of a nine-qubit planar code using eight photons. Stabilizer measurements of the states of the planar code are performed to directly reveal the locations of the anyons in the system. We further perform braiding operations on the anyons, which gives rise to a topologically path-independent phase. Our work provides a platform for simulating the braiding operations with linear optics, opening up the possibility of further exploring the features of anyonic statistics.
Anyons, quasiparticles living in two-dimensional spaces with exotic exchange statistics, can serve as the fundamental units for fault-tolerant quantum computation. However, experimentally demonstrating anyonic statistics is a challenge due to the technical limitations of current experimental platforms. Here, we take a state perpetration approach to mimic anyons in the Kitaev lattice model using a 7-qubit nuclear magnetic resonance quantum simulator. Anyons are created by dynamically preparing the ground and excited states of the 7-qubit Kitaev lattice model, and are subsequently braided along two distinct, but topologically equivalent, paths. We observe that the phase acquired by the anyons is independent of the path, and coincides with the ideal theoretical predictions when decoherence and implementation errors are taken into account. As the first demonstration of the topological path independence of anyons, our experiment helps to study and exploit the anyonic properties towards the goal of building a topological quantum computer.
Topological quantum computation encodes quantum information in the internal fusion space of non-Abelian anyonic quasiparticles, whose braiding implements logical gates. This goes beyond Abelian topological order (TO) such as the toric code, as its anyons lack internal structure. However, the simplest non-Abelian generalizations of the toric code do not support universality via braiding alone. Here we demonstrate that such minimally non-Abelian TOs can be made universal by treating anyon fusion as a computational primitive. We prepare a 54-qubit TO wavefunction associated with the smallest non-Abelian group, S3S_3S3​, on Quantinuum's H2 quantum processor. This phase of matter exhibits cyclic anyon fusion rules, known to underpin universality, which we evidence by trapping a single non-Abelian anyon on the torus. We encode logical qutrits in the nonlocal fusion space of non-Abelian fluxes and, by combining an entangling braiding operation with anyon charge measurements, realize a universal topological gate set and read-out, which we further demonstrate by topologically preparing a magic state. This work establishes S3S_3S3​ TO as simple enough to be prepared efficiently, yet rich enough to enable universal topological quantum computation.
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, i.e., 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.