Noise-adapted recovery circuits for quantum error correction
arXiv:2305.11093 · doi:10.1103/PhysRevResearch.6.043034
Abstract
Implementing quantum error correction (QEC) protocols is a challenging task in today's era of noisy intermediate-scale quantum devices. We present quantum circuits for a universal, noise-adapted recovery map, often referred to as the Petz map, which is known to achieve close-to-optimal fidelity for arbitrary codes and noise channels. While two of our circuit constructions draw upon algebraic techniques such as isometric extension and block encoding, the third approach breaks down the recovery map into a sequence of two-outcome POVMs. In each of the three cases we improve upon the resource requirements that currently exist in the literature. Apart from Petz recovery circuits, we also present circuits that can directly estimate the fidelity between the encoded state and the recovered state. As a concrete example of our circuit constructions, we implement Petz recovery circuits corresponding to the -qubit QEC code tailored to protect against amplitude-damping noise. The efficacy of our noise-adapted recovery circuits is then demonstrated through ideal and noisy simulations.
16 pages, 18 figures
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Cited by in corpus (8)
- Noise-adapted qudit codes for amplitude-damping noise
- Bosonic quantum error correction using squeezed Fock states
- Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
- Smallest quantum codes for amplitude damping noise
- Proper and improper mixed states serve as different prior beliefs for quantum state retrodiction
- Expedited Noise Spectroscopy of Transmon Qubits
- Explicit decoders using fixed-point amplitude amplification based on QSVT
- Realizing the Petz Recovery Map on an NMR Quantum Processor