Accuracy guarantees and quantum advantage in analogue open quantum simulation with and without noise

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 analogue quantum simulation of geometrically local open quantum systems and provide evidence that this problem is both 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 $\epsilon$ in time that is $\text{poly}({\epsilon }^{-1})$ 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 $\ne$ BPP. We then consider the presence of noise in the quantum simulator in the form of additional geometrically-local Linbdladian 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 $\ne$ 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.

References in corpus (47)

• Quantum Simulation
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Logical quantum processor based on reconfigurable atom arrays
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Non-Hermitian Topology and Exceptional-Point Geometries
• Keldysh Field Theory for Driven Open Quantum Systems
• Tools for quantum simulation with ultracold atoms in optical lattices
• Exponential improvement in photon storage fidelities using subradiance and "selective radiance" in atomic arrays
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Real-time quantum error correction beyond break-even
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Dissipative Phase Transition in Central Spin Systems
• Quantum Simulation for High Energy Physics
• Simulation methods for open quantum many-body systems
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• The power of quantum systems on a line
• Experimental demonstration of topological error correction
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Universality of Dicke superradiance in arrays of quantum emitters
• Quantum memories based on engineered dissipation
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
• Quantum Simulating Nature's Fundamental Fields
• Quantum logarithmic Sobolev inequalities and rapid mixing
• The ${\chi }^2$-divergence and Mixing times of quantum Markov processes
• Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
• Experimental demonstration of continuous quantum error correction
• Quasi-locality and efficient simulation of Markovian quantum dynamics
• Dicke superradiance in ordered lattices: dimensionality matters
• Non-Equilibrium Universality in the Heating Dynamics of Interacting Luttinger Liquids
• Stability of local quantum dissipative systems
• Classification of phases for mixed states via fast dissipative evolution
• Simulating Open Quantum Systems Using Hamiltonian Simulations
• Rapid mixing implies exponential decay of correlations
• Quantum simulation of dissipative collective effects on noisy quantum computers
• Noise-assisted digital quantum simulation of open systems
• Error propagation in NISQ devices for solving classical optimization problems
• Superradiance and subradiance in inverted atomic arrays
• Rapid thermalization of spin chain commuting Hamiltonians
• Dissipative Universal Lindbladian Simulation
• Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
• Area law for fixed points of rapidly mixing dissipative quantum systems
• Rapid mixing and stability of quantum dissipative systems
• Integrability of open boundary driven quantum circuits
• Thermalization in Kitaev's quantum double models via Tensor Network techniques
• Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

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