Trade-offs on number and phase shift resilience in bosonic quantum codes
arXiv:2008.12576 · doi:10.1109/TIT.2021.3102873
Abstract
Quantum codes typically rely on large numbers of degrees of freedom to achieve low error rates. However each additional degree of freedom introduces a new set of error mechanisms. Hence minimizing the degrees of freedom that a quantum code utilizes is helpful. One quantum error correction solution is to encode quantum information into one or more bosonic modes. We revisit rotation-invariant bosonic codes, which are supported on Fock states that are gapped by an integer apart, and the gap imparts number shift resilience to these codes. Intuitively, since phase operators and number shift operators do not commute, one expects a trade-off between resilience to number-shift and rotation errors. Here, we obtain results pertaining to the non-existence of approximate quantum error correcting -gapped single-mode bosonic codes with respect to Gaussian dephasing errors. We show that by using arbitrarily many modes, -gapped multi-mode codes can yield good approximate quantum error correction codes for any finite magnitude of Gaussian dephasing and amplitude damping errors.
arXiv commentfinal version
References in corpus (30)
- Encoding a qubit in an oscillator
- New class of quantum error-correcting codes for a bosonic mode
- An improved bound on distillable entanglement
- Performance and structure of single-mode bosonic codes
- Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
- Reversing quantum dynamics with near-optimal quantum and classical fidelity
- Approximate quantum error correction can lead to better codes
- Bosonic Quantum Codes for Amplitude Damping
- Quantum computing with rotation-symmetric bosonic codes
- Towards Scalable Bosonic Quantum Error Correction
- General conditions for approximate quantum error correction and near-optimal recovery channels
- The structure of degradable quantum channels
- Finite blocklength converse bounds for quantum channels
- Permutation-invariant quantum codes
- The quantum capacity with symmetric side channels
- Quantum error correction against photon loss using NOON states
- Quantum Coding with Finite Resources
- Strong converse rates for quantum communication
- Energy-constrained diamond norms and their use in quantum information theory
- Energy-constrained private and quantum capacities of quantum channels
- Protecting an optical qubit against photon loss
- Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
- Enhanced noise resilience of the surface-GKP code via designed bias
- Approximate quantum error correction, random codes, and quantum channel capacity
- Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on the maximum overlap problem using directional iterates
- Permutation-invariant qudit codes from polynomials
- Permutation-invariant constant-excitation quantum codes for amplitude damping
- Causal limit on quantum communication
- Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security
- Linear programming bounds for quantum amplitude damping codes
Cited by in corpus (4)
- Quantum capacity and codes for the bosonic loss-dephasing channel
- Clifford operations and homological codes for rotors and oscillators
- Explicit error-correction scheme and code distance for bosonic codes with rotational symmetry
- Estimating the performance boundary of Gottesman-Kitaev-Preskill codes and number-phase codes