quantum-computing

Faster Quantum Simulation Of Markovian Open Quantum Systems Via Randomisation

I.J. David, I. Sinayskiy, and F. Petruccione

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A team led by researchers David, Sinayskiy, and Petruccione has developed non-probabilistic randomised algorithms for simulating Markovian open quantum systems, introducing first and second-order randomised Trotter-Suzuki formulas and the QDRIFT channel. These methods preserve the physicality of quantum evolution while improving scalability and precision. By deriving error bounds and step count limits, the team bypassed the mixing lemma used in Hamiltonian simulations. Implemented via Classical Sampling, the randomised approaches demonstrate lower gate complexity than deterministic Trotter-Suzuki product formulas, enabling faster and more accurate quantum simulations of complex open systems.

Why it matters

This advance extends randomisation from Hamiltonian to open quantum system simulations, offering a scalable path to model real-world chemistry and materials without sacrificing physical validity or computational efficiency.

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AbstractWhen simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum systems, this has been achieved using first and second-order Trotter-Suzuki product formulas or probabilistic algorithms. In this work, we introduce novel non-probabilistic algorithms for simulating Markovian open quantum systems using randomisation. Our methods, including first and second-order randomised Trotter-Suzuki formulas and the QDRIFT channel, not only maintain the physicality of the system's evolution but also enhance the scalability and precision of quantum simulations. We derive error bounds and step count limits for these techniques, bypassing the need for the mixing lemma typically employed in Hamiltonian simulation proofs. Furthermore, we implement these randomised algorithms using Classical Sampling (CS), demonstrating their gate complexity advantages over deterministic TS product formulas. This work systematically extends powerful randomisation techniques from Hamiltonian simulation to the general setting of Markovian open quantum systems, highlighting their potential to enable faster and more accurate simulations.Featured image: Gate complexity of the developed randomised methods for simulating Markovian open quantum systems, plotted against the number of generator terms M and compared with deterministic Trotter–Suzuki.Popular summarySimulating quantum systems that interact with their surrounding environments—known as open quantum systems—is essential for modelling real-world chemistry, materials, and physics. Quantum computers are uniquely suited for this task because they process information using the same underlying physics as the systems themselves, bypassing the exponential memory limits that hamper traditional supercomputers. Yet, developing accurate quantum simulation methods for these complex environmental interactions without violating fundamental physical laws remains a major hurdle. Existing approaches present trade-offs: standard product formulas cannot scale to higher accuracies without breaking physical validity, while alternative methods either carry a non-zero probability of failure or rely on complex subroutines with heavy computational overhead. To address this, we introduced a new class of randomised algorithms—including randomised Trotter-Suzuki formulas and the QDRIFT channel—specifically tailored for open quantum systems. Instead of applying quantum operations in a deterministic, fixed sequence, our methods introduce controlled randomness to select which operations to perform at each time step. This approach guarantees that the simulated system remains physically valid throughout its evolution while dramatically reducing the number of quantum operations required. By deriving error bounds and step count limits for our techniques, we showed that applying randomisation to open quantum systems unlocks significantly faster, more scalable, and more precise simulations.► BibTeX data@article{David2026fasterquantum, doi = {10.22331/q-2026-09-03-2204}, url = {https://doi.org/10.22331/q-2026-09-03-2204}, title = {Faster {Q}uantum {S}imulation {O}f {M}arkovian {O}pen {Q}uantum {S}ystems {V}ia {R}andomisation}, author = {David, I.J. and Sinayskiy, I. and Petruccione, F.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2204}, month = sep, year = {2026} }► References [1] Richard P Feynman. ``Simulating physics with computers''. International Journal of Theoretical Physics 21, 467–488 (1982). https://doi.org/10.1007/BF02650179 [2] Yuri Manin. ``Computable and uncomputable''. Sovetskoye Radio. Moscow (1980). [3] Seth Lloyd. ``Universal quantum simulators''. Science 273, 1073–1078 (1996). https://doi.org/10.1126/science.273.5278.1073 [4] Dominic W Berry, Graeme Ahokas, Richard Cleve, and Barry C Sanders. ``Efficient quantum algorithms for simulating sparse Hamiltonians''. Communications in Mathematical Physics 270, 359–371 (2007). https://doi.org/10.1007/s00220-006-0150-x [5] Masuo Suzuki. ``Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations''. Physics Letters A 146, 319–323 (1990). https://doi.org/10.1016/0375-9601(90)90962-N [6] Masuo Suzuki. ``General theory of fractal path integrals with applications to many-body theories and statistical physics''. Journal of Mathematical Physics 32, 400–407 (1991). https://doi.org/10.1063/1.529425 [7] Andrew M Childs, Dmitri Maslov, Yunseong Nam, Neil J Ross, and Yuan Su. ``Toward the first quantum simulation with quantum speedup''. 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Physical Review Letters 120, 030402 (2018). https://doi.org/10.1103/PhysRevLett.120.030402 [40] Ryan Sweke, Mikel Sanz, Ilya Sinayskiy, Francesco Petruccione, and Enrique Solano. ``Digital quantum simulation of many-body non-Markovian dynamics''. Physical Review A 94, 022317 (2016). https://doi.org/10.1103/PhysRevA.94.022317 [41] Peter L Walters and Fei Wang. ``Path integral quantum algorithm for simulating non-Markovian quantum dynamics in open quantum systems''.

Physical Review Research 6, 013135 (2024). https://doi.org/10.1103/PhysRevResearch.6.013135Cited byCould not fetch Crossref cited-by data during last attempt 2026-09-03 11:15:21: Could not fetch cited-by data for 10.22331/q-2026-09-03-2204 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-09-03 11:15:22: 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. AbstractWhen simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum systems, this has been achieved using first and second-order Trotter-Suzuki product formulas or probabilistic algorithms. In this work, we introduce novel non-probabilistic algorithms for simulating Markovian open quantum systems using randomisation. Our methods, including first and second-order randomised Trotter-Suzuki formulas and the QDRIFT channel, not only maintain the physicality of the system's evolution but also enhance the scalability and precision of quantum simulations. We derive error bounds and step count limits for these techniques, bypassing the need for the mixing lemma typically employed in Hamiltonian simulation proofs. Furthermore, we implement these randomised algorithms using Classical Sampling (CS), demonstrating their gate complexity advantages over deterministic TS product formulas. This work systematically extends powerful randomisation techniques from Hamiltonian simulation to the general setting of Markovian open quantum systems, highlighting their potential to enable faster and more accurate simulations.Featured image: Gate complexity of the developed randomised methods for simulating Markovian open quantum systems, plotted against the number of generator terms M and compared with deterministic Trotter–Suzuki.Popular summarySimulating quantum systems that interact with their surrounding environments—known as open quantum systems—is essential for modelling real-world chemistry, materials, and physics. Quantum computers are uniquely suited for this task because they process information using the same underlying physics as the systems themselves, bypassing the exponential memory limits that hamper traditional supercomputers. Yet, developing accurate quantum simulation methods for these complex environmental interactions without violating fundamental physical laws remains a major hurdle. Existing approaches present trade-offs: standard product formulas cannot scale to higher accuracies without breaking physical validity, while alternative methods either carry a non-zero probability of failure or rely on complex subroutines with heavy computational overhead. To address this, we introduced a new class of randomised algorithms—including randomised Trotter-Suzuki formulas and the QDRIFT channel—specifically tailored for open quantum systems. Instead of applying quantum operations in a deterministic, fixed sequence, our methods introduce controlled randomness to select which operations to perform at each time step. This approach guarantees that the simulated system remains physically valid throughout its evolution while dramatically reducing the number of quantum operations required. By deriving error bounds and step count limits for our techniques, we showed that applying randomisation to open quantum systems unlocks significantly faster, more scalable, and more precise simulations.► BibTeX data@article{David2026fasterquantum, doi = {10.22331/q-2026-09-03-2204}, url = {https://doi.org/10.22331/q-2026-09-03-2204}, title = {Faster {Q}uantum {S}imulation {O}f {M}arkovian {O}pen {Q}uantum {S}ystems {V}ia {R}andomisation}, author = {David, I.J. and Sinayskiy, I. and Petruccione, F.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2204}, month = sep, year = {2026} }► References [1] Richard P Feynman. ``Simulating physics with computers''. International Journal of Theoretical Physics 21, 467–488 (1982). https://doi.org/10.1007/BF02650179 [2] Yuri Manin. ``Computable and uncomputable''. Sovetskoye Radio. Moscow (1980). [3] Seth Lloyd. ``Universal quantum simulators''. Science 273, 1073–1078 (1996). https://doi.org/10.1126/science.273.5278.1073 [4] Dominic W Berry, Graeme Ahokas, Richard Cleve, and Barry C Sanders. ``Efficient quantum algorithms for simulating sparse Hamiltonians''. Communications in Mathematical Physics 270, 359–371 (2007). https://doi.org/10.1007/s00220-006-0150-x [5] Masuo Suzuki. ``Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations''. Physics Letters A 146, 319–323 (1990). https://doi.org/10.1016/0375-9601(90)90962-N [6] Masuo Suzuki. ``General theory of fractal path integrals with applications to many-body theories and statistical physics''. Journal of Mathematical Physics 32, 400–407 (1991). https://doi.org/10.1063/1.529425 [7] Andrew M Childs, Dmitri Maslov, Yunseong Nam, Neil J Ross, and Yuan Su. ``Toward the first quantum simulation with quantum speedup''. Proceedings of the National Academy of Sciences 115, 9456–9461 (2018). https://doi.org/10.1073/pnas.1801723115 [8] Andrew M Childs, Yuan Su, Minh C Tran, Nathan Wiebe, and Shuchen Zhu. ``Theory of Trotter error with commutator scaling''. Physical Review X 11, 011020 (2021). https://doi.org/10.1103/PhysRevX.11.011020 [9] Earl Campbell. ``Random compiler for fast Hamiltonian simulation''.

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Faster Quantum Simulation Of Markovian Open Quantum Systems Via Randomisation

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