Reversing Lindblad Dynamics via Continuous Petz Recovery Map

Abstract

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.

6+16 pages

References in corpus (8)

• Surface codes: Towards practical large-scale quantum computation
• Self-cooling of a micro-mirror by radiation pressure
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Model for l/f Flux Noise in SQUIDs and Qubits
• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• Quantum memories based on engineered dissipation
• The structure of preserved information in quantum processes
• Universal two-qubit interactions, measurement and cooling for quantum simulation and computing

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• Noise-adapted recovery circuits for quantum error correction
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• Exponentially reduced circuit depths in Lindbladian simulation
• Unraveling-paired dynamical maps can recover the input of quantum channels
• Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
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• Autonomous Quantum Processing Unit: An Autonomous Thermal Computing Machine & its Physical Limitations
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
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• Stochastic Schrödinger Equations for Quantum Reverse Diffusion
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• Exact large deviations and emergent long-range correlations in sequential quantum East circuits
• Quantum Error Correction with Superpositions of Squeezed Fock States
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• Realizing the Petz Recovery Map on an NMR Quantum Processor