omoya Hayata and Yuta Kikuchi at Keio University present a method that eliminates Trotter errors by taking the continuous-time limit, simplifying analysis and improving accuracy. The algorithm successfully estimates the ground-state energy of the $H_3^+$ molecular Hamiltonian and computes out-of-time-ordered correlators within the Sachdev, Ye, Kitaev model. Key validation of the protocol comes from numerical simulations and experiments performed on Quantinuum Reimei, a trapped-ion quantum computer, suggesting a pathway towards more efficient and reliable quantum simulations.\n\n
Continuous-time evolution delivers high-precision ground-state energy calculations and
\n\nGround-state energy estimation achieved 99.7% accuracy, a substantial improvement over the 5% accuracy of the initial Hartree-Fock state used as a benchmark. This represents a significant leap forward in the precision of quantum simulations, particularly for systems where even small errors can drastically alter the predicted outcomes. Previously unattainable precision resulted from the accumulation of errors inherent in traditional quantum simulation methods; the new stochastic time-evolution algorithm eliminates these inaccuracies by adopting the continuous-time limit, streamlining calculations and enabling more reliable results. Traditional methods often rely on discretising time evolution into a series of short steps, a technique known as Trotterisation. This introduces errors, termed Trotter errors, which accumulate as the simulation progresses. By transitioning to a continuous-time formulation, the researchers effectively bypass these errors, leading to a more accurate representation of the system’s dynamics. Scientists and Quantinuum successfully computed out-of-time-ordered correlators within the sparse Sachdev-Ye-Kitaev model, a challenging task in condensed matter physics. This computation was validated through experiments on Quantinuum Reimei, a trapped-ion quantum computer0.0.0.0.99.7 per cent accuracy in ground-state energy estimation represents a marked improvement from the 5 per cent accuracy of the initial Hartree-Fock state used for comparison.\n\nA new stochastic time-evolution algorithm drove this precision; it operates by adopting the continuous-time limit, effectively eliminating errors common in conventional quantum simulations and simplifying calculations. The algorithm successfully computed out-of-time-ordered correlators, a complex calculation within the sparse Sachdev-Ye-Kitaev model, a key area of condensed matter physics. The Sachdev-Ye-Kitaev model is particularly relevant to understanding the behaviour of strongly correlated electron systems and has implications for the development of novel materials. Quantinuum Reimei, a trapped-ion quantum computer with 20 all-to-all connected 171Yb+ qubits, facilitated validation through experiments. Trapped-ion systems are a leading platform for quantum computing due to their high fidelity and long coherence times. The team also employed a noise-mitigation technique tailored specifically to the algorithm’s requirements, though the current experimental demonstration is limited by sampling costs, as balancing noise suppression with statistical fluctuations remains a significant hurdle. Noise mitigation is crucial for extracting meaningful results from near-term quantum devices, which are susceptible to various sources of error. The trade-off between noise suppression and statistical fluctuations highlights the challenges of achieving both accuracy and efficiency in quantum simulations.\n\n
Mitigating time-evolution errors through probabilistic angle interpolation in quantum simulations
\n\nResearchers are pushing the boundaries of quantum simulation, seeking ways to model complex systems beyond the reach of classical computers. This is particularly important for areas like materials’ science, drug discovery, and fundamental physics, where understanding the quantum behaviour of matter is essential. The new algorithm offers a promising route by tackling a fundamental obstacle: errors that accumulate during calculations, specifically those arising from approximations in how time evolves within the simulation. Current experiments, however, reveal a significant limitation; memory noise, the tendency of qubits to lose information while idle or being moved, severely degrades performance on real quantum hardware like Quantinuum Reimei. This decoherence is a major challenge in building practical quantum computers and requires sophisticated error correction techniques.\n\nDespite disappointing results from Quantinuum’s Reimei computer, the algorithm establishes a valuable new approach to quantum simulation. By using a method called probabilistic angle interpolation, it tackles errors caused by approximations in time evolution, a persistent challenge in modelling complex quantum systems, simplifying calculations and reducing the impact of these errors. Probabilistic angle interpolation involves randomly sampling angles during the time evolution process, effectively averaging out some of the errors introduced by the discretisation. The algorithm was tested using Quantinuum’s Reimei computer, addressing errors from complex calculations; probabilistic angle interpolation simplifies processes and reduces inaccuracies. The choice of interpolation angle, denoted as delta, is a critical parameter that influences the algorithm’s performance, and further optimisation is needed to maximise its efficiency.\n\nExperiments revealed that memory noise, or loss of qubit information during operation, sharply hampered performance, despite improvements seen in emulator tests without this interference. This underscores the importance of developing robust error correction schemes to protect qubits from decoherence. The algorithm establishes a new approach to Hamiltonian simulation, circumventing limitations of conventional methods through a stochastic algorithm. Adopting a continuous-time limit eliminates inaccuracies stemming from Trotter errors, simplifying calculations and offering a clear trade-off between circuit complexity and required sampling. Demonstrations on both molecular energy estimation and modelling complex material interactions, specifically the Sachdev-Ye-Kitaev model, validate the algorithm’s flexible nature and performance on Quantinuum Reimei, a trapped-ion quantum computer. This advancement prompts further investigation into optimising parameters like the interpolation angle, delta, to enhance efficiency and accuracy for increasingly complex quantum systems. Future work could also explore the application of this algorithm to other challenging problems in quantum chemistry and condensed matter physics, potentially unlocking new insights into the behaviour of complex materials and molecules.\n\nThe research successfully demonstrated a new stochastic algorithm using probabilistic angle interpolation for simulating quantum systems. This method simplifies calculations and reduces errors inherent in modelling complex quantum phenomena, as validated through simulations and experiments on Quantinuum Reimei, a trapped-ion quantum computer. By eliminating Trotter errors and employing a noise-mitigation strategy, the algorithm accurately estimated the ground-state energy of the H₃⁺ molecular Hamiltonian and computed out-of-time-ordered correlators in the Sachdev, Ye, Kitaev model. The authors suggest future work will focus on optimising the algorithm’s parameters for improved performance with increasingly complex systems.\n\n
