Overhead-constrained circuit knitting for variational quantum dynamics

Gian Gentinetta, Friederike Metz, and Giuseppe Carleo

Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

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Simulating the dynamics of large quantum systems is a formidable yet vital pursuit for obtaining a deeper understanding of quantum mechanical phenomena. While quantum computers hold great promise for speeding up such simulations, their practical application remains hindered by limited scale and pervasive noise. In this work, we propose an approach that addresses these challenges by employing circuit knitting to partition a large quantum system into smaller subsystems that can each be simulated on a separate device. The evolution of the system is governed by the projected variational quantum dynamics (PVQD) algorithm, supplemented with constraints on the parameters of the variational quantum circuit, ensuring that the sampling overhead imposed by the circuit knitting scheme remains controllable. We test our method on quantum spin systems with multiple weakly entangled blocks each consisting of strongly correlated spins, where we are able to accurately simulate the dynamics while keeping the sampling overhead manageable. Further, we show that the same method can be used to reduce the circuit depth by cutting long-ranged gates.

In this work, we simulate the real-time dynamics of quantum many-body systems composed of multiple weakly-correlated subsystems by distributing the subsystems onto several quantum devices. This is achieved with a technique known as circuit knitting that decomposes a global quantum channel into locally realisable channels through a quasi-probability distribution. At the cost of an overhead in the number of measurements, this allows to classically reconstruct the entanglement between the different subsystems. In general, the sampling overhead scales exponentially in the simulation time due to the entanglement between subsystems growing over time.

As the main contribution of our work, we modify a variational quantum time evolution algorithm (PVQD) by constraining the variational parameters to a subspace where the required sampling overhead remains below a manageable threshold. We show that through this constrained optimisation algorithm, we achieve high fidelities in the time evolution of quantum spin systems for realistic thresholds. The accuracy of the simulation can be controlled by tuning this new hyperparameter, allowing for optimal results given a fixed budget of total quantum resources.

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Cited by

[1] Travis L. Scholten, Carl J. Williams, Dustin Moody, Michele Mosca, William Hurley, William J. Zeng, Matthias Troyer, and Jay M. Gambetta, "Assessing the Benefits and Risks of Quantum Computers", arXiv:2401.16317, (2024).

[2] Julien Gacon, "Scalable Quantum Algorithms for Noisy Quantum Computers", arXiv:2403.00940, (2024).

[3] Mingrui Jing, Chengkai Zhu, and Xin Wang, "Circuit Knitting Faces Exponential Sampling Overhead Scaling Bounded by Entanglement Cost", arXiv:2404.03619, (2024).

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