One of the important issues in developing quantum technology is noise as quantum states are extremely sensitive to it. We propose a physical protocol which introduces reverse dynamics, in order to precisely control an open quantum system against noise. The reverse dynamics is realised by applying a well-controlled Hamiltonian and jump-operators. The control parameters for the Hamiltonian and jump operators are formulated by the Petz recovery map in continuous-time, from which we reverse the noisy quantum dynamics. The time-dependent jump operators can be implemented by considering strongly decaying ancillary qubits which interact with the system in a controlled manner. As a specific application, we demonstrate that our protocol efficiently suppresses only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.
One of the important issues in developing quantum technology is noise as quantum states are extremely sensitive to it. We propose a physical protocol which introduces reverse dynamics, in order to precisely control an open quantum system against noise. The reverse dynamics is realised by applying a well-controlled Hamiltonian and jump-operators. The control parameters for the Hamiltonian and jump operators are formulated by the Petz recovery map in continuous-time, from which we reverse the noisy quantum dynamics. The time-dependent jump operators can be implemented by considering strongly decaying ancillary qubits which interact with the system in a controlled manner. As a specific application, we demonstrate that our protocol efficiently suppresses only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.
An important issue in developing quantum technology is that quantum states are so sensitive to noise. We propose a protocol that introduces reverse dynamics, in order to precisely control quantum systems against noise described by the Lindblad master equation. The reverse dynamics can be obtained by constructing the Petz recovery map in continuous time. By providing the exact form of the Hamiltonian and jump operators for the reverse dynamics, we explore the potential of utilizing the near-optimal recovery of the Petz map in controlling noisy quantum dynamics. While time-dependent dissipation engineering enables us to fully recover a single quantum trajectory, we also design a time-independent recovery protocol to protect encoded quantum information against decoherence. Our protocol can efficiently suppress only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.
The quantum information lost in open evolutions cannot be fully recovered, but partial recovery is possible. The Petz recovery map guarantees almost optimal recovery, notably if the chosen reference state is close to the real one. This map has been widely used in theoretical studies, but has been the object of only a handful of experimental realisations, typically under a single fixed noise model. In this work, we describe and implement the Petz recovery map for a versatile class of qubit channels with tunable decoherence and dissipation. The setup we realize is also the first experimental example of ``tabletop reversibility'': for a good range of choices of the reference state, the Petz recovery map can be implemented with the same devices as the forward dissipative evolution, whose effect it is partially undoing. Our results demonstrate that the Petz recovery map can be resource-efficiently realized without requiring complex ancillary resources, providing a feasible pathway for mitigating information loss in quantum systems.
In this dissertation we are interested in the dynamics of open quantum systems in the context of quantum information. First, we investigate the dynamics of one qubit at the regime where an inverse evolution is not well defined. This limit is widely used and explored in this work, called as the limit of non-bijectivity. We demonstrate how to compute a completely positive inverse evolution, based on the theory of recovery maps, here to be the Petz recovery map. The analyzed evolutions are the typical decoherence processes: dephasing, depolarizing and amplitude damping channels in the regime of non-bijectivity. To measure how efficient the Petz can be recovering a random quantum state, we use the fidelity function as the figure of merit. Also, we quantify how non-invertible a dynamics is compared to another. As an application for this formalism, in the second part of this work we show how we can explore recovery maps in the context of non-Markovian evolutions, in order to minimize memory effects. We demonstrate that recovering maps can be useful under certain constraints to simulate a non-Markovian evolution by an “almost” Markovian one. We demonstrate that there exists a strong dependence between the success of this strategy and the initial correlations between system and environment.
We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing, and amplitude damping. We illustrate how well a physically implementable recovery map simulates an inverse evolution. We extend this idea to explore the use of recovery maps as an approximation of inverse maps, and apply it in the context of non-Markovian dynamics. We show how this strategy attenuates non-Markovian effects, such as the backflow of information.
The Petz recovery map is a central construct in quantum information theory, providing an explicit, channel-aware prescription for reversing the effects of noise. Unlike standard quantum operations, the Petz map is intrinsically dependent on a chosen reference state, which makes its physical implementation and experimental validation particularly challenging. Here, we report an experimental realization of Petz recovery maps on a nuclear magnetic resonance (NMR) quantum processor using the duality quantum computing (DQC) algorithm. We investigate two paradigmatic single-qubit noise models: amplitude damping and phase damping, and construct corresponding families of Petz recovery maps for varying reference states. By systematically tuning the reference state, we experimentally demonstrate the state-adapted nature of Petz recovery, observing both enhanced recovery when the reference state is well matched and fidelity degradation for mismatched choices. Our experimental results show close quantitative agreement with theoretical predictions, providing direct evidence that the Petz recovery map constitutes a physically realizable, reference-state-dependent recovery channel rather than a purely formal inverse of noise. This work bridges the gap between the abstract information-theoretic formulation of Petz recovery and its implementation on a realistic quantum platform, and establishes an experimental benchmark for testing noise-adapted recovery strategies on near-term quantum devices.
Analogue quantum simulators offer a promising route to explore quantum many-body dynamics beyond classical reach in the near term. However, their vulnerability to noise limits the accuracy of simulations. Here, we establish a new framework for mitigating noise in analogue quantum simulation, operating in a time-continuous manner. To our knowledge, this is the first protocol that is fully analogue and that achieves exact noise cancellation. Our method requires a small number of ancillary qubits, whose interaction with the system−combined with classical post-processing of joint measurement data−is tailored to cancel the effect of noise. Furthermore, the protocol is Hamiltonian-independent, robust to realistic ancilla noise, and avoids any discretization, preserving the continuous-time nature of the system's dynamics. This work opens a new direction for achieving high-fidelity analogue quantum simulation in the presence of noise.