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:2303.17187 · Physical review. B./Physical review. B

Efficient variational quantum circuit structure for correlated topological phases

Rong-Yang Sun, Tomonori Shirakawa, Seiji Yunoki

Published Aug 11, 2023• 7 citations
arXivHTMLPDF

Abstract

We propose an efficient circuit structure of variational quantum circuit Ans\"atze used for the variational quantum eigensolver (VQE) algorithm in calculating gapped topological phases on the currently feasible noisy intermediate-scale quantum computers. An efficient circuit Ansatz should include two layers: the initialization layer and the variational layer. In the initialization layer, a fixed-depth circuit state with a compatible entanglement structure to the target topological phase is constructed. The circuit state is further adjusted subsequently to capture the details of the local correlations, which is dictated with the Hamiltonian, in the parametrized variational layer. Based on this strategy, we design a circuit Ansatz to investigate the symmetry-protected topological Haldane phase in a nonexactly solvable alternating spin-$\frac{1}{2}$ Heisenberg chain by VQE calculations. Main characterizations of the Haldane phase, including the long-ranged string order, the fourfold nearly degenerate ground states associated with four different localized edge-mode patterns for the system with open boundaries, and the twofold degeneracy of the entanglement spectrum, are all observed for the optimized shallow circuit state with only one-depth variational layer both in numerical simulations and on real quantum computers. We further demonstrate that the computational capacity (i.e., expressibility) of this quantum circuit Ansatz is determined not by the system size but only by the intrinsic correlation length of the system, thus implying that the scalable VQE calculation is possible.

DOI
10.1103/physrevb.108.075127

Related papers

Scalable Quantum Simulation for Topological Phases on NISQ Devices

Rong-Yang Sun, Tomonori Shirakawa, Seiji Yunoki

Topological quantum phases emerge from correlated quantum many-body systems containing novel features such as nontrivial entanglement structure and mutual statistics. However, the co-emerged exponential computational complexity strongly hampers the research of these systems using classical computers. Present booming quantum computing techniques offer a new way to investigate these challenging systems: the quantum simulation approach. Combining current available noise intermediate-scale quantum (NISQ) devices with variational quantum eigensolver (VQE) algorithm to solve quantum many-body problems has attracted extensive attention. Although the NISQ devices have up to hundreds of qubits, treating a quantum many-body problem with a similar size on these devices is still impossible. One fundamental reason for this is the lack of scalability in current quantum algorithms (i.e., the required quantum resources for realizing a quantum algorithm increase much faster than the increase of the problem size). In this poster, we introduce how to realize scalable VQE calculation in the topological quantum phases by designing problem-specified scalable parameterized quantum circuits (PQC). We construct a PQC with a two-layer structure to capture both the basic entanglement structure of the target topological phase and finite correlations governed by the details of the many-body Hamiltonian. Utilizing such a PQC, we numerically simulate both symmetry-protected topological (SPT) Haldane phase and trivial dimmer phase in the non-exactly solvable alternating Heisenberg chain using the VQE algorithm. Furthermore, we realize these optimized circuits on real quantum computers provided by IBM Quantum and observe the main characterizations of the SPT Haldane phase.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•3 citations

Symmetry-Preserving Variational Quantum Simulation of the Heisenberg Spin Chain on Noisy Quantum Hardware

Rudraksh Sharma

Variational quantum algorithms are among the most promising approaches for simulating interacting quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. However, the practical success of variational quantum eigensolvers (VQE) critically depends on the structure of the chosen variational ansatz. In this work, we investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed, symmetry-preserving variational circuits. We benchmark variational results against exact diagonalization and noiseless simulations, and subsequently validate the approach on real IQM Garnet quantum hardware. Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior when compared to hardware-efficient ansatz under identical resource constraints. These findings highlight the importance of problem specific ansatz construction for reliable quantum simulations in the NISQ era.

quant-pharXiv:2512.23009•Dec 30, 2025•0 citations

Variational preparation and characterization of chiral spin liquids in quantum circuits

Zi-Yang Zhang, Donghoon Kim, Ji-Yao Chen

Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with non-chiral topological order have been theoretically investigated and experimentally implemented, the realization and characterization of chiral topological phases have remained less explored. Here we show that chiral topological phases in spin systems, i.e., chiral spin liquids, can be prepared in quantum circuits using the variational quantum eigensolver (VQE) framework. On top of the VQE ground state, signatures of the chiral topological order are revealed using the recently proposed tangent space excitation ansatz for quantum circuits. We show that, both topological ground state degeneracy and the chiral edge mode can be faithfully captured by this approach. We demonstrate our approach using the Kitaev honeycomb model, finding excellent agreement of low-energy excitation spectrum on quantum circuits with exact solution in all topological sectors. Further applying this approach to a non-exactly solvable chiral spin liquid model on square lattice, the results suggest this approach works well even when the topological sectors are not exactly known.

cond-mat.str-elCross-listedarXiv:2602.14769•Physical review. B./Physical review. B•Feb 17, 2026•0 citations

Preparing 100-qubit symmetry-protected topological order on a digital quantum computer

George Pennington, Kevin C. Smith, James R. Garrison +3 more

Symmetry-protected topological (SPT) phases extend the Landau paradigm of quantum matter by admitting distinct symmetry-preserving phases that lack any local order parameter. Demonstrating these phases at scale on programmable quantum processors is a key milestone in using quantum hardware to probe emergent many-body phenomena, yet it is impeded by the circuit depth normally required to capture non-trivial entanglement. Here we use a tensor network based approximate quantum compiling (AQC) protocol to construct shallow quantum circuits (18-39 CNOT depth), which prepare 100-site ground states of the spin-1/2 bond-alternating Heisenberg chain in both SPT phases, to 97.9-99.0% fidelity. Upon executing the circuits on IBM quantum hardware, the resulting states exhibit all defining signatures of SPT order including non-local string order for strings of up to length 20, characteristic degeneracies in the entanglement spectrum and clear evidence of symmetry-protected edge modes. The simultaneous observation of these independent diagnostics establishes current quantum computers as versatile platforms for large-scale studies of symmetry-protected quantum matter. More broadly, our results establish a practical foundation for probing non-equilibrium quench dynamics of such systems in regimes that challenge classical computational methods.

quant-pharXiv:2603.06325•npj Quantum Information•Mar 9, 2026•0 citations

Variational preparation and characterization of chiral spin liquids in quantum circuits

Zi-Yang Zhang, Dong-Hoon Kim, Ji-Yao Chen

Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with non-chiral topological order have been theoretically investigated and experimentally implemented, the realization and characterization of chiral topological phases have remained less explored. Here we show that chiral topological phases in spin systems, i.e., chiral spin liquids, can be prepared in quantum circuits using the variational quantum eigensolver (VQE) framework. On top of the VQE ground state, signatures of the chiral topological order are revealed using the recently proposed tangent space excitation ansatz for quantum circuits. We show that, both topological ground state degeneracy and the chiral edge mode can be faithfully captured by this approach.We demonstrate our approach using the Kitaev honeycomb model, finding excellent agreement of low-energy excitation spectrum on quantum circuits with exact solution in all topological sectors. Further applying this approach to a non-exactly solvable chiral spin liquid model on square lattice, the results suggest this approach works well even when the topological sectors are not exactly known.

•Mar 11, 2026•1 citation

Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers

Chae-Yeun Park

A variational quantum eigensolver (VQE) solves the ground state problem of a given Hamiltonian by finding the parameters of a quantum circuit Ansatz that minimizes the Hamiltonian expectation value. Among possible quantum circuit Ansätze, the Hamiltonian variational Ansatz (HVA) is widely studied for quantum many-body problems as the Ansatz with sufficiently large depth is theoretically guaranteed to express the ground state. However, since the HVA shares the same symmetry with the Hamiltonian, it is not necessarily good at finding symmetry-broken ground states that prevail in nature. In this paper, we systematically explore the limitations of the HVA for solving symmetry-broken systems and propose an alternative quantum circuit Ansatz with symmetry-breaking layers. With extensive numerical simulations, we show that the proposed Ansatz finds the ground state in depth significantly shorter than the bare HVA when the target Hamiltonian has symmetry-broken ground states.

arXiv:2106.02509•APL Quantum•Feb 23, 2024•11 citations
We propose an efficient circuit structure of variational quantum circuit Ans"atze used for the variational quantum eigensolver (VQE) algorithm in calculating gapped topological phases on the currently feasible noisy intermediate-scale quantum computers. An efficient circuit Ansatz should include two layers: the initialization layer and the variational layer. In the initialization layer, a fixed-depth circuit state with a compatible entanglement structure to the target topological phase is constructed. The circuit state is further adjusted subsequently to capture the details of the local correlations, which is dictated with the Hamiltonian, in the parametrized variational layer. Based on this strategy, we design a circuit Ansatz to investigate the symmetry-protected topological Haldane phase in a nonexactly solvable alternating spin-12\frac{1}{2}21​ Heisenberg chain by VQE calculations. Main characterizations of the Haldane phase, including the long-ranged string order, the fourfold nearly degenerate ground states associated with four different localized edge-mode patterns for the system with open boundaries, and the twofold degeneracy of the entanglement spectrum, are all observed for the optimized shallow circuit state with only one-depth variational layer both in numerical simulations and on real quantum computers. We further demonstrate that the computational capacity (i.e., expressibility) of this quantum circuit Ansatz is determined not by the system size but only by the intrinsic correlation length of the system, thus implying that the scalable VQE calculation is possible.
Topological quantum phases emerge from correlated quantum many-body systems containing novel features such as nontrivial entanglement structure and mutual statistics. However, the co-emerged exponential computational complexity strongly hampers the research of these systems using classical computers. Present booming quantum computing techniques offer a new way to investigate these challenging systems: the quantum simulation approach. Combining current available noise intermediate-scale quantum (NISQ) devices with variational quantum eigensolver (VQE) algorithm to solve quantum many-body problems has attracted extensive attention. Although the NISQ devices have up to hundreds of qubits, treating a quantum many-body problem with a similar size on these devices is still impossible. One fundamental reason for this is the lack of scalability in current quantum algorithms (i.e., the required quantum resources for realizing a quantum algorithm increase much faster than the increase of the problem size). In this poster, we introduce how to realize scalable VQE calculation in the topological quantum phases by designing problem-specified scalable parameterized quantum circuits (PQC). We construct a PQC with a two-layer structure to capture both the basic entanglement structure of the target topological phase and finite correlations governed by the details of the many-body Hamiltonian. Utilizing such a PQC, we numerically simulate both symmetry-protected topological (SPT) Haldane phase and trivial dimmer phase in the non-exactly solvable alternating Heisenberg chain using the VQE algorithm. Furthermore, we realize these optimized circuits on real quantum computers provided by IBM Quantum and observe the main characterizations of the SPT Haldane phase.
Variational quantum algorithms are among the most promising approaches for simulating interacting quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. However, the practical success of variational quantum eigensolvers (VQE) critically depends on the structure of the chosen variational ansatz. In this work, we investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed, symmetry-preserving variational circuits. We benchmark variational results against exact diagonalization and noiseless simulations, and subsequently validate the approach on real IQM Garnet quantum hardware. Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior when compared to hardware-efficient ansatz under identical resource constraints. These findings highlight the importance of problem specific ansatz construction for reliable quantum simulations in the NISQ era.
Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with non-chiral topological order have been theoretically investigated and experimentally implemented, the realization and characterization of chiral topological phases have remained less explored. Here we show that chiral topological phases in spin systems, i.e., chiral spin liquids, can be prepared in quantum circuits using the variational quantum eigensolver (VQE) framework. On top of the VQE ground state, signatures of the chiral topological order are revealed using the recently proposed tangent space excitation ansatz for quantum circuits. We show that, both topological ground state degeneracy and the chiral edge mode can be faithfully captured by this approach. We demonstrate our approach using the Kitaev honeycomb model, finding excellent agreement of low-energy excitation spectrum on quantum circuits with exact solution in all topological sectors. Further applying this approach to a non-exactly solvable chiral spin liquid model on square lattice, the results suggest this approach works well even when the topological sectors are not exactly known.
Symmetry-protected topological (SPT) phases extend the Landau paradigm of quantum matter by admitting distinct symmetry-preserving phases that lack any local order parameter. Demonstrating these phases at scale on programmable quantum processors is a key milestone in using quantum hardware to probe emergent many-body phenomena, yet it is impeded by the circuit depth normally required to capture non-trivial entanglement. Here we use a tensor network based approximate quantum compiling (AQC) protocol to construct shallow quantum circuits (18-39 CNOT depth), which prepare 100-site ground states of the spin-1/2 bond-alternating Heisenberg chain in both SPT phases, to 97.9-99.0% fidelity. Upon executing the circuits on IBM quantum hardware, the resulting states exhibit all defining signatures of SPT order including non-local string order for strings of up to length 20, characteristic degeneracies in the entanglement spectrum and clear evidence of symmetry-protected edge modes. The simultaneous observation of these independent diagnostics establishes current quantum computers as versatile platforms for large-scale studies of symmetry-protected quantum matter. More broadly, our results establish a practical foundation for probing non-equilibrium quench dynamics of such systems in regimes that challenge classical computational methods.
Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with non-chiral topological order have been theoretically investigated and experimentally implemented, the realization and characterization of chiral topological phases have remained less explored. Here we show that chiral topological phases in spin systems, i.e., chiral spin liquids, can be prepared in quantum circuits using the variational quantum eigensolver (VQE) framework. On top of the VQE ground state, signatures of the chiral topological order are revealed using the recently proposed tangent space excitation ansatz for quantum circuits. We show that, both topological ground state degeneracy and the chiral edge mode can be faithfully captured by this approach.We demonstrate our approach using the Kitaev honeycomb model, finding excellent agreement of low-energy excitation spectrum on quantum circuits with exact solution in all topological sectors. Further applying this approach to a non-exactly solvable chiral spin liquid model on square lattice, the results suggest this approach works well even when the topological sectors are not exactly known.
A variational quantum eigensolver (VQE) solves the ground state problem of a given Hamiltonian by finding the parameters of a quantum circuit Ansatz that minimizes the Hamiltonian expectation value. Among possible quantum circuit Ansätze, the Hamiltonian variational Ansatz (HVA) is widely studied for quantum many-body problems as the Ansatz with sufficiently large depth is theoretically guaranteed to express the ground state. However, since the HVA shares the same symmetry with the Hamiltonian, it is not necessarily good at finding symmetry-broken ground states that prevail in nature. In this paper, we systematically explore the limitations of the HVA for solving symmetry-broken systems and propose an alternative quantum circuit Ansatz with symmetry-breaking layers. With extensive numerical simulations, we show that the proposed Ansatz finds the ground state in depth significantly shorter than the bare HVA when the target Hamiltonian has symmetry-broken ground states.