Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2402.16944 · Physical review. B./Physical review. B

Probing anyonic statistics via Mach-Zehnder interferometry in quantum computers

Shiyu Zhou, Yi Teng, Claudio Chamon, Claudio Castelnovo, Armin Rahmani

Published Feb 9, 2026• 1 citation
arXivHTMLPDF

Abstract

We introduce a synthetic Mach-Zehnder interferometer for digitized quantum computing devices to probe fractional exchange statistics of anyonic excitations that appear in quantum spin liquids. Employing an IonQ quantum computer, we apply this scheme to the toric ladder, a quasi-one-dimensional reduction of the toric code. We observe interference patterns resulting from the movement of `electric' excitations in the presence and absence of `magnetic' ones. We model the noise in IonQ via depolarizing Lindbladian dynamics, and find quantitative agreement with the measurements obtained from the quantum device. The synthetic Mach-Zehnder interferometer can thus also serve as an effective means to probe the coherence length and time scales of multi-qubit noisy quantum devices.

DOI
10.1103/mv95-hd77

Related papers

Anyonic analogue of optical Mach-Zehnder interferometer

Navketan Batra, Zezhu Wei, Smitha Vishveshwara +1 more

Anyonic interferometry is a direct probe of fractional statistics. We propose an interferometry geometry that parallels an optical Mach-Zehnder interferometer and offers several advantages over existing interferometry schemes. In contrast to the currently studied electronic Mach-Zehnder interferometer, our setup has no drain inside the device so that the trapped topological charge is time-independent. In contrast to electronic Fabry-Pérot interferometry, anyons cannot go around the device more than once. Thus, the interference signal has a straightforward interpretation in terms of anyonic statistical phases. The proposed geometry suppresses the undesirable effects of bulk-edge coupling. Moreover, the setup allows for simple exact solutions for the electric current and noise for an arbitrary quasiparticle tunneling strength in a broad range of conditions. The structure of the solutions is similar to that for non-interacting electrons but reflects fractional charge and statistics. We present results for electric current and noise in Jain states and address thermal interferometry at zero voltage bias.

arXiv:2507.14115•Physical review. B./Physical review. B•Sep 15, 2025•0 citations

Thermal Interferometry of Anyons in Spin Liquids

Zezhu Wei, V. F. Mitrović, Dima E. Feldman

Aharonov-Bohm interferometry is the most direct probe of anyonic statistics in the quantum Hall effect. The technique involves oscillations of the electric current as a function of the magnetic field and is not applicable to Kitaev spin liquids and other systems without charged quasiparticles. Here, we establish a novel protocol, involving heat transport, for revealing fractional statistics even in the absence of charged excitations, as is the case in quantum spin liquids. Specifically, we demonstrate that heat transport in Kitaev spin liquids through two distinct interferometer's geometries, Fabry-Perot and Mach-Zehnder, exhibit drastically different behaviors. Therefore, we propose the use of heat transport interferometry as a probe of anyonic statistics in charge insulators.

arXiv:2105.06873•Physical Review Letters•Oct 11, 2021•15 citations

Anyonic Molecules in Atomic Fractional Quantum Hall Liquids: A Quantitative Probe of Fractional Charge and Anyonic Statistics

A. Muñoz de las Heras, E. Macaluso, Iacopo Carusotto

We study the quantum dynamics of massive impurities embedded in a strongly interacting two-dimensional atomic gas driven into the fractional quantum Hall (FQH) regime under the effect of a synthetic magnetic field. For suitable values of the atom-impurity interaction strength, each impurity can capture one or more quasi-hole excitations of the FQH liquid, forming a bound molecular state with novel physical properties. An effective Hamiltonian for such anyonic molecules is derived within the Born-Oppenheimer approximation, which provides renormalized values for their effective mass, charge and statistics by combining the finite mass of the impurity with the fractional charge and statistics of the quasi-holes. The renormalized mass and charge of a single molecule can be extracted from the cyclotron orbit that it describes as a free particle in a magnetic field. The anyonic statistics introduces a statistical phase between the direct and exchange scattering channels of a pair of indistinguishable colliding molecules, and can be measured from the angular position of the interference fringes in the differential scattering cross section. Implementations of such schemes beyond cold atomic gases are highlighted, in particular in photonic systems.

arXiv:2004.02477•Physical Review X•Dec 22, 2020•26 citations

Probing fractional statistics in quantum simulators of spin liquid Hamiltonians

Shiyu Zhou, Maria Zelenayova, Oliver Hart +2 more

Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of \mathbb{Z}_2 ℤ 2 topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the “quantumness” of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.

arXiv:2211.09784•SciPost Physics•Nov 14, 2023•5 citations

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

Jingjing Niu, Yishan Li, Lushuang Zhang +18 more

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.

Physical Review Letters•Jan 8, 2024•9 citations

Simulation of anyonic statistics and its topological path independence using a seven-qubit quantum simulator

Annie Jihyun Park, Emma McKay, Dawei Lu +1 more

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.

New Journal of Physics•Apr 28, 2016•28 citations
We introduce a synthetic Mach-Zehnder interferometer for digitized quantum computing devices to probe fractional exchange statistics of anyonic excitations that appear in quantum spin liquids. Employing an IonQ quantum computer, we apply this scheme to the toric ladder, a quasi-one-dimensional reduction of the toric code. We observe interference patterns resulting from the movement of electric' excitations in the presence and absence of magnetic' ones. We model the noise in IonQ via depolarizing Lindbladian dynamics, and find quantitative agreement with the measurements obtained from the quantum device. The synthetic Mach-Zehnder interferometer can thus also serve as an effective means to probe the coherence length and time scales of multi-qubit noisy quantum devices.
Anyonic interferometry is a direct probe of fractional statistics. We propose an interferometry geometry that parallels an optical Mach-Zehnder interferometer and offers several advantages over existing interferometry schemes. In contrast to the currently studied electronic Mach-Zehnder interferometer, our setup has no drain inside the device so that the trapped topological charge is time-independent. In contrast to electronic Fabry-Pérot interferometry, anyons cannot go around the device more than once. Thus, the interference signal has a straightforward interpretation in terms of anyonic statistical phases. The proposed geometry suppresses the undesirable effects of bulk-edge coupling. Moreover, the setup allows for simple exact solutions for the electric current and noise for an arbitrary quasiparticle tunneling strength in a broad range of conditions. The structure of the solutions is similar to that for non-interacting electrons but reflects fractional charge and statistics. We present results for electric current and noise in Jain states and address thermal interferometry at zero voltage bias.
Aharonov-Bohm interferometry is the most direct probe of anyonic statistics in the quantum Hall effect. The technique involves oscillations of the electric current as a function of the magnetic field and is not applicable to Kitaev spin liquids and other systems without charged quasiparticles. Here, we establish a novel protocol, involving heat transport, for revealing fractional statistics even in the absence of charged excitations, as is the case in quantum spin liquids. Specifically, we demonstrate that heat transport in Kitaev spin liquids through two distinct interferometer's geometries, Fabry-Perot and Mach-Zehnder, exhibit drastically different behaviors. Therefore, we propose the use of heat transport interferometry as a probe of anyonic statistics in charge insulators.
We study the quantum dynamics of massive impurities embedded in a strongly interacting two-dimensional atomic gas driven into the fractional quantum Hall (FQH) regime under the effect of a synthetic magnetic field. For suitable values of the atom-impurity interaction strength, each impurity can capture one or more quasi-hole excitations of the FQH liquid, forming a bound molecular state with novel physical properties. An effective Hamiltonian for such anyonic molecules is derived within the Born-Oppenheimer approximation, which provides renormalized values for their effective mass, charge and statistics by combining the finite mass of the impurity with the fractional charge and statistics of the quasi-holes. The renormalized mass and charge of a single molecule can be extracted from the cyclotron orbit that it describes as a free particle in a magnetic field. The anyonic statistics introduces a statistical phase between the direct and exchange scattering channels of a pair of indistinguishable colliding molecules, and can be measured from the angular position of the interference fringes in the differential scattering cross section. Implementations of such schemes beyond cold atomic gases are highlighted, in particular in photonic systems.
Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of \mathbb{Z}_2 ℤ 2 topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the “quantumness” of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.
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.