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Acta Physica Hungarica B) Quantum Electronics

Quantum Trajectory Method for Determining the Time Evolution Operator of Dissipative Quantum Systems

Петер Адам, A. Karpati, József Janszky

Published Apr 1, 2005• 1 citation
Publisher
DOI
10.1556/aph.23.2005.1-2.5

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We present a theory of non-Markovian quantum trajectories that describe the dynamics of a quantum system coupled to an environment of harmonic oscillators. When averaged over the noise, they reproduce the standard reduced density matrix without any approximation, in particular without Markov approximation. The time evolution of the environment can also be determined from these non-Markovian quantum trajectories. We present a simple example to demonstrate the power of our approach. As a remarkable feature of non-Markovian quantum trajectories, we show that for strong coupling to a dissipative environment with memory, the asymptotic state can be reached in a finite time. Further examples are described in the text.
Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the dynamics of open quantum systems governed by Lindbladians. We introduce a new approximation channel for short-time evolution, inspired by the quantum trajectory method, which underpins the efficiency of our algorithms. The first algorithm achieves a gate complexity independent of the number of jump operators, m , marking a significant improvement in efficiency. The second algorithm achieves near-optimal dependence on the evolution time t and precision ϵ and introduces only an additional O ~ ( m ) factor, which strictly improves upon state-of-the-art gate-based quantum algorithm that has an O ~ ( m 2 ) factor. The improvement stems from the integration of the new approximation channel with a novel structured linear combination of unitaries method. In both our algorithms, the reduction of dependence on m significantly enhances the efficiency of simulating practical dissipative processes characterized by a large number of jump operators.