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Accuracy Guarantees and Quantum Advantage in Analog Open Quantum Simulation with and without Noise

Vikram Kashyap1, Georgios Styliaris2,3, Sara Mouradian1, J. Ignacio Cirac2,3, and Rahul Trivedi2,3,1,*

  • *Contact author: rahul.trivedi@mpq.mpg.de
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Phys. Rev. X 15, 021017 – Published 16 April, 2025

DOI: https://doi.org/10.1103/PhysRevX.15.021017

Abstract

Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically analyze noisy analog quantum simulation of geometrically local open quantum systems and provide evidence that this problem both is hard to simulate on classical computers and could be approximately solved on near-term quantum devices. First, given a noiseless quantum simulator, we show that the dynamics of local observables and the fixed-point expectation values of rapidly mixing local observables in geometrically local Lindbladians can be obtained to a precision of ϵ in time that is poly(ϵ−1) and uniform in system size. Furthermore, we establish that the quantum simulator would provide a superpolynomial advantage, in run-time scaling with respect to the target precision and either the evolution time (when simulating dynamics) or the Lindbladian’s decay rate (when simulating fixed points), over any classical algorithm for these problems, assuming BQP≠BPP. We then consider the presence of noise in the quantum simulator in the form of additional geometrically local Lindbladian terms. We show that the simulation tasks considered in this paper are stable to errors; i.e., they can be solved to a noise-limited, but system-size independent, precision. Finally, we establish that, assuming BQP≠BPP, there are stable geometrically local Lindbladian simulation problems such that, as the noise rate on the simulator is reduced, classical algorithms must take time superpolynomially longer in the inverse noise rate to attain the same precision as the analog quantum simulator.

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Popular Summary

Analog quantum simulators work by using a controllable experimental system to mimic the behavior of a theoretical model being studied. While quantum simulators are expected to be able to solve many-body problems in physics that cannot be solved on classical computers, until now it was not known if there exists a problem that is easy to implement on quantum simulators, is hard to solve on classical computers, and is robust to errors in the simulator for large systems. Using techniques from quantum optics, quantum information, and quantum complexity theory, we show that dissipative many-body dynamics satisfies all these constraints.

Specifically, we examine the computational difficulty of simulating open quantum systems, which evolve according to Lindbladian master equations. The key finding is that for geometrically local Lindbladians, these quantum simulators can approximate both dynamical and steady-state properties with system-size-independent precision. Moreover, even in the presence of noise, the quantum advantage persists, meaning that as the noise level decreases, classical algorithms would require exponentially more time to achieve the same accuracy.

Our work opens the possibility of using currently available quantum simulators to study physically relevant problems, while providing the theoretical underpinnings needed to confidently trust the simulation results in the presence of noise.

Article Text

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Phys. Rev. X 15, 021017– Published 16 April, 2025
  • Received 24 April 2024
  • Revised 8 November 2024
  • Accepted 14 February 2025
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