Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator
arXiv:2203.16836 · doi:10.1109/CDC51059.2022.9992722
Abstract
Based on the stabilizer formalism underlying Quantum Error Correction (QEC), the design of an original Lindblad master equation for the density operator of a quantum harmonic oscillator is proposed. This Lindblad dynamics stabilizes exactly the finite-energy grid states introduced in 2001 by Gottesman, Kitaev and Preskill for quantum computation. Stabilization results from an exponential Lyapunov function with an explicit lower-bound on the convergence rate. Numerical simulations indicate the potential interest of such autonomous QEC in presence of non-negligible photon-losses.
arXiv commentSubmitted, 15 pages, 1 figures
References in corpus (14)
- Surface codes: Towards practical large-scale quantum computation
- Encoding a qubit in an oscillator
- Dynamically protected cat-qubits: a new paradigm for universal quantum computation
- Observation of quantum state collapse and revival due to the single-photon Kerr effect
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Symmetries and conserved quantities in Lindblad master equations
- Quantum error correction of a qubit encoded in grid states of an oscillator
- New class of quantum error-correcting codes for a bosonic mode
- Exponential suppression of bit-flips in a qubit encoded in an oscillator
- Repetition Cat Qubits for Fault-Tolerant Quantum Computation
- Towards Scalable Bosonic Quantum Error Correction
- Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
- Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
- Consensus in non-commutative spaces