Fully optimised variational simulation of a dynamical quantum phase transition on a trapped-ion quantum computer
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AbstractWe time-evolve a translationally invariant quantum state on the Quantinuum H1-1 trapped-ion quantum processor, studying the dynamical quantum phase transition of the transverse field Ising model. This physics requires a delicate cancellation of phases in the many-body wavefunction and presents a tough challenge for current quantum devices. We follow the dynamics using a quantum circuit matrix product state ansatz, optimised for the time-evolution using a fidelity cost function. Sampling costs are mitigated by using the measured values of this circuit as stochastic corrections to a simple classical extrapolation of the ansatz parameters. Our results demonstrate the feasibility of variational quantum time-evolution and reveal a hitherto hidden simplicity of the evolution of the transverse-field Ising model through the dynamical quantum phase transition.Featured image: Quantum circuitry used on the Quantinuum H1-1 device to simulate a dynamical quantum phase transitionPopular summaryQuantum computers hold remarkable promise for simulating complex quantum systems, a promise that is just beginning to be realised. This paper reports the dynamical simulation of a problem that poses a particular challenge for quantum computers; the dynamical quantum phase transition in the transverse field Ising model. Revealing this phenomenon requires a detailed and accurate balancing of features in the quantum wavefunction. This is managed here for the first time. The work uses the tensor network approach; a method originally developed to simulate quantum systems on classical computers. Crucially classical tensor network algorithms can be translated to run on quantum computers allowing us to identify where the advantage lies in running on quantum hardware. Technical advances in the work include a method to dramatically reduce the sampling complexity – roughly the number of times that one has to ask a quantum computer a question in order to get an answer to a desired accuracy, and an important way in which the advantage of using a quantum computer can be lost in real world application.► BibTeX data@article{Gover2026fullyoptimised, doi = {10.22331/q-2026-05-20-2109}, url = {https://doi.org/10.22331/q-2026-05-20-2109}, title = {Fully optimised variational simulation of a dynamical quantum phase transition on a trapped-ion quantum computer}, author = {Gover, Lesley and Wimalaweera, Vinul and Azad, Fariha and DeCross, Matthew and Foss-Feig, Michael and Green, Andrew G.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2109}, month = may, year = {2026} }► References [1] Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957). URL https://doi.org/10.1103/PhysRev.108.1175. https://doi.org/10.1103/PhysRev.108.1175 [2] K., K., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Phys. Rev. Lett. 45, 494–497 (1980). URL https://doi.org/10.1103/PhysRevLett.45.494. https://doi.org/10.1103/PhysRevLett.45.494 [3] Savary, L. & Balents, L. Quantum spin liquids: A review. Rep. Prog. Phys. 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. https://doi.org/10.1088/0034-4885/80/1/016502 [4] White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863–2866 (1992). URL https://doi.org/10.1103/PhysRevLett.69.2863. https://doi.org/10.1103/PhysRevLett.69.2863 [5] Östlund, S. & Rommer, S. Thermodynamic limit of density matrix renormalization. Phys. Rev. Lett. 75, 3537–3540 (1995). URL https://doi.org/10.1103/PhysRevLett.75.3537. https://doi.org/10.1103/PhysRevLett.75.3537 [6] Perez-Garcia, D., Verstraete, F., Wolf, M. M. & Cirac, J. I. Matrix product state representations. Quantum Info. Comput. 7, 401–430 (2007). URL https://doi.org/10.26421/QIC7.5-6-1. https://doi.org/10.26421/QIC7.5-6-1 [7] Schollwöck, U. The density-matrix renormalization group in the age of matrix product states. Ann. Phys. (NY) 326, 96 – 192 (2011). URL https://doi.org/10.1016/j.aop.2010.09.012. January 2011 Special Issue. https://doi.org/10.1016/j.aop.2010.09.012 [8] Cerezo, M. et al.
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Could not fetch ADS cited-by data during last attempt 2026-05-20 10:07:05: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe time-evolve a translationally invariant quantum state on the Quantinuum H1-1 trapped-ion quantum processor, studying the dynamical quantum phase transition of the transverse field Ising model. This physics requires a delicate cancellation of phases in the many-body wavefunction and presents a tough challenge for current quantum devices. We follow the dynamics using a quantum circuit matrix product state ansatz, optimised for the time-evolution using a fidelity cost function. Sampling costs are mitigated by using the measured values of this circuit as stochastic corrections to a simple classical extrapolation of the ansatz parameters. Our results demonstrate the feasibility of variational quantum time-evolution and reveal a hitherto hidden simplicity of the evolution of the transverse-field Ising model through the dynamical quantum phase transition.Featured image: Quantum circuitry used on the Quantinuum H1-1 device to simulate a dynamical quantum phase transitionPopular summaryQuantum computers hold remarkable promise for simulating complex quantum systems, a promise that is just beginning to be realised. This paper reports the dynamical simulation of a problem that poses a particular challenge for quantum computers; the dynamical quantum phase transition in the transverse field Ising model. Revealing this phenomenon requires a detailed and accurate balancing of features in the quantum wavefunction. This is managed here for the first time. The work uses the tensor network approach; a method originally developed to simulate quantum systems on classical computers. Crucially classical tensor network algorithms can be translated to run on quantum computers allowing us to identify where the advantage lies in running on quantum hardware. Technical advances in the work include a method to dramatically reduce the sampling complexity – roughly the number of times that one has to ask a quantum computer a question in order to get an answer to a desired accuracy, and an important way in which the advantage of using a quantum computer can be lost in real world application.► BibTeX data@article{Gover2026fullyoptimised, doi = {10.22331/q-2026-05-20-2109}, url = {https://doi.org/10.22331/q-2026-05-20-2109}, title = {Fully optimised variational simulation of a dynamical quantum phase transition on a trapped-ion quantum computer}, author = {Gover, Lesley and Wimalaweera, Vinul and Azad, Fariha and DeCross, Matthew and Foss-Feig, Michael and Green, Andrew G.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2109}, month = may, year = {2026} }► References [1] Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957). URL https://doi.org/10.1103/PhysRev.108.1175. https://doi.org/10.1103/PhysRev.108.1175 [2] K., K., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Phys. Rev. Lett. 45, 494–497 (1980). URL https://doi.org/10.1103/PhysRevLett.45.494. https://doi.org/10.1103/PhysRevLett.45.494 [3] Savary, L. & Balents, L. Quantum spin liquids: A review. Rep. Prog. Phys. 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. https://doi.org/10.1088/0034-4885/80/1/016502 [4] White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863–2866 (1992). URL https://doi.org/10.1103/PhysRevLett.69.2863. https://doi.org/10.1103/PhysRevLett.69.2863 [5] Östlund, S. & Rommer, S. Thermodynamic limit of density matrix renormalization. Phys. Rev. Lett. 75, 3537–3540 (1995). 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Variational Quantum Algorithms.
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