On the probabilistic quantum error correction
arXiv:2206.05232 · doi:10.1109/TIT.2023.3254054
Abstract
Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the error-correcting procedure for general noise. We generalized the Knill-Laflamme conditions for probabilistically correctable errors. We show that for some noise channels, we should encode the information into a mixed state to maximize the probability of successful error correction. Finally, we investigate an advantage of the probabilistic error-correcting procedure over the deterministic one. Reducing the probability of successful error correction allows for correcting errors generated by a broader class of noise channels. Significantly, if the errors are caused by a unitary interaction with an auxiliary qubit system, we can probabilistically restore a qubit state by using only one additional physical qubit.
arXiv comment28 pages, 2 figures
References in corpus (29)
- Quantum Computing in the NISQ era and beyond
- Entanglement of a Pair of Quantum Bits
- Good Quantum Error-Correcting Codes Exist
- Multiple Particle Interference and Quantum Error Correction
- A Theory of Quantum Error-Correcting Codes
- Stabilizer Codes and Quantum Error Correction
- On quantum Renyi entropies: a new generalization and some properties
- Correcting Quantum Errors with Entanglement
- Probabilistic cloning and identification of linearly independent quantum states
- Sparse Graph Codes for Quantum Error-Correction
- A Unified and Generalized Approach to Quantum Error Correction
- Protecting quantum states from decoherence of finite temperature using weak measurement
- Protecting qutrit-qutrit entanglement by weak measurement and reversal
- Catalytic quantum error correction
- Random Quantum Operations
- Quantum Error Correcting Codes From The Compression Formalism
- Optimal probabilistic storage and retrieval of unitary channels
- Environment-Assisted Quantum State Restoration Via Weak Measurement
- Generating random quantum channels
- Quantum Codes of Maximal Distance and Highly Entangled Subspaces
- Quantum Error Correction beyond the Bounded Distance Decoding Limit
- Topological Quantum Error Correction with Optimal Encoding Rate
- Almost all quantum channels are equidistant
- On the mixed-unitary rank of quantum channels
- Quantum error correction with degenerate codes for correlated noise
- From quantum feedback to probabilistic error correction: Manipulation of quantum beats in cavity QED
- Multiple-shot and unambiguous discrimination of von Neumann measurements
- Probabilities of failure for quantum error correction
- Probabilistic quantum error correction