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

Physical review. B./Physical review. B

Direct probe of topology and geometry of quantum states on the IBM Q quantum processor

Tianqi Chen, Hai-Tao Ding, Ruizhe Shen, Shi-Liang Zhu, Jiangbin Gong

Published Nov 1, 2024• 5 citations
Publisher

Abstract

The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Although they have been investigated on various experimental platforms, to date a direct probe of the topological and geometric properties on a universal quantum computer even for a minimum model is still in vain. In this work, we first show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly reconstructed from Pauli operator measurements on a quantum circuit. We then propose two algorithms suitable for IBM quantum computers to directly probe QGT. The first algorithm is a variational quantum algorithm particularly suitable for noisy intermediate-scale quantum era devices, whereas the second one is a pure quantum algorithm based on quantum imaginary time evolution. Explicit results obtained from IBM Q simulating a Chern insulator model are presented and analyzed. Our results indicate that transmon qubit-based universal quantum computers have the potential to directly simulate and investigate topological and geometric properties of a quantum system.

DOI
10.1103/physrevb.110.205402

Related papers

Direct Probe of Topology and Geometry of Quantum States on IBM Q

Tianqi Chen, Hai-Tao Ding, Shen, Ruizhe +2 more

The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric properties on a universal quantum computer even for a minimum model is still in vain. In this work, we first show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly re-constructed from Pauli operator measurements on a quantum circuit. We then propose two algorithms, suitable for IBM quantum computers, to directly probe QGT. The first algorithm is a variational quantum algorithm particularly suitable for Noisy Intermediate-Scale Quantum (NISQ)-era devices, whereas the second one is a pure quantum algorithm based on quantum imaginary time evolution. Explicit results obtained from IBM Q simulating a Chern insulator model are presented and analysed. Our results indicate that transmon qubit-based universal quantum computers have the potential to directly simulate and investigate topological and geometric properties of a quantum system.

arXiv:2403.14249•Mar 21, 2024•0 citations

Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit

Xinsheng Tan, Dan-Wei Zhang, Zhen Yang +12 more

A Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system. The work opens up a unique approach to explore the topology of quantum states with the QGT.

arXiv:1906.01462•Physical Review Letters•May 29, 2019•153 citations

Experimental measurement of the quantum geometric tensor using coupled qubits in diamond

Min Yu, Pengcheng Yang, Musang Gong +9 more

Abstract Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.

arXiv:1811.12840•National Science Review•Nov 21, 2019•133 citations

Digital Simulation of Topological Matter on Programmable Quantum Processors

Feng Mei, Qihao Guo, Ya-Fei Yu +3 more

Simulating the topological phases of matter in synthetic quantum simulators is a topic of considerable interest. Given the universality of digital quantum simulators, the prospect of digitally simulating exotic topological phases is greatly enhanced. However, it is still an open question how to realize the digital quantum simulation of topological phases of matter. Here, using common single- and two-qubit elementary quantum gates, we propose and demonstrate an approach to design topologically protected quantum circuits on the current generation of noisy quantum processors where spin-orbital coupling and related topological matter can be digitally simulated. In particular, a low-depth topological quantum circuit is performed on both the IBM and Rigetti quantum processors. In the experiments, we not only observe but also distinguish the 0 and π energy topological edge states by measuring the qubit excitation distribution at the output of the circuits.

arXiv:2003.06086•Physical Review Letters•Oct 15, 2020•39 citations

Quantum computing topological invariants of two-dimensional quantum matter

Marcel Niedermeier, Marc Nairn, Christian Flindt +1 more

Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials, and a variety of numerical approaches for this purpose have been developed. However, the complexity of quantum many-body Hamiltonians makes calculations of topological invariants challenging for interacting systems. Here, we present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. Both circuits combine a gate-based adiabatic time evolution over the discretized Brillouin zone with particular phase estimation techniques. The first algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. The second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits. Our results establish a method for computing topological invariants with quantum circuits, taking a step towards characterizing interacting topological quantum matter using quantum computers. Published by the American Physical Society 2024

arXiv:2404.06048•Physical Review Research•Dec 17, 2024•8 citations

Quantum Computing-Based Geometric Topology Analysis

Jincheng Zhang

This paper investigates the application of quantum computing to geometric topology, specifically focusing on the analysis of quantum topological phases. We explore how quantum entanglement, a fundamental property of quantum mechanics, can be leveraged to uncover the underlying geometric structure of these phases and ultimately reveal the laws governing them. The core mechanism involves simulating quantum states using quantum algorithms, which allows for the exploration of complex geometric relationships previously inaccessible through classical methods. We present preliminary results demonstrating the potential of this approach to identify key topological features and provide insights into the formation of quantum topological states. The investigation will highlight the benefits of quantum computing in tackling challenges in geometric topology and offers a new theoretical framework for understanding these phenomena.

•Aug 31, 2026•0 citations
The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Although they have been investigated on various experimental platforms, to date a direct probe of the topological and geometric properties on a universal quantum computer even for a minimum model is still in vain. In this work, we first show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly reconstructed from Pauli operator measurements on a quantum circuit. We then propose two algorithms suitable for IBM quantum computers to directly probe QGT. The first algorithm is a variational quantum algorithm particularly suitable for noisy intermediate-scale quantum era devices, whereas the second one is a pure quantum algorithm based on quantum imaginary time evolution. Explicit results obtained from IBM Q simulating a Chern insulator model are presented and analyzed. Our results indicate that transmon qubit-based universal quantum computers have the potential to directly simulate and investigate topological and geometric properties of a quantum system.
The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric properties on a universal quantum computer even for a minimum model is still in vain. In this work, we first show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly re-constructed from Pauli operator measurements on a quantum circuit. We then propose two algorithms, suitable for IBM quantum computers, to directly probe QGT. The first algorithm is a variational quantum algorithm particularly suitable for Noisy Intermediate-Scale Quantum (NISQ)-era devices, whereas the second one is a pure quantum algorithm based on quantum imaginary time evolution. Explicit results obtained from IBM Q simulating a Chern insulator model are presented and analysed. Our results indicate that transmon qubit-based universal quantum computers have the potential to directly simulate and investigate topological and geometric properties of a quantum system.
A Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system. The work opens up a unique approach to explore the topology of quantum states with the QGT.
Abstract Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.
Simulating the topological phases of matter in synthetic quantum simulators is a topic of considerable interest. Given the universality of digital quantum simulators, the prospect of digitally simulating exotic topological phases is greatly enhanced. However, it is still an open question how to realize the digital quantum simulation of topological phases of matter. Here, using common single- and two-qubit elementary quantum gates, we propose and demonstrate an approach to design topologically protected quantum circuits on the current generation of noisy quantum processors where spin-orbital coupling and related topological matter can be digitally simulated. In particular, a low-depth topological quantum circuit is performed on both the IBM and Rigetti quantum processors. In the experiments, we not only observe but also distinguish the 0 and π energy topological edge states by measuring the qubit excitation distribution at the output of the circuits.
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials, and a variety of numerical approaches for this purpose have been developed. However, the complexity of quantum many-body Hamiltonians makes calculations of topological invariants challenging for interacting systems. Here, we present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. Both circuits combine a gate-based adiabatic time evolution over the discretized Brillouin zone with particular phase estimation techniques. The first algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. The second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits. Our results establish a method for computing topological invariants with quantum circuits, taking a step towards characterizing interacting topological quantum matter using quantum computers. Published by the American Physical Society 2024
This paper investigates the application of quantum computing to geometric topology, specifically focusing on the analysis of quantum topological phases. We explore how quantum entanglement, a fundamental property of quantum mechanics, can be leveraged to uncover the underlying geometric structure of these phases and ultimately reveal the laws governing them. The core mechanism involves simulating quantum states using quantum algorithms, which allows for the exploration of complex geometric relationships previously inaccessible through classical methods. We present preliminary results demonstrating the potential of this approach to identify key topological features and provide insights into the formation of quantum topological states. The investigation will highlight the benefits of quantum computing in tackling challenges in geometric topology and offers a new theoretical framework for understanding these phenomena.