Quantum stabilizer codes embedding qubits into qudits

Abstract

We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to protect the qubit against both amplitude and phase errors. The performance of such code is evaluated on Weyl channels by means of the entanglement fidelity as function of the error probability. A comparison with standard block codes, like five and seven qubit stabilizer codes, shows its superiority.PACS numbers: quantum error correction (03.67.Pp); decoherence (03.65. Yz)

Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla

“…By encoding information in multi-level (qudit) systems, the number of units and operations required to implement an algorithm [25][26][27][28] could be signicantly reduced, compared to the conventional, two-level encoding. For instance, the extra levels of the qudit can be used to encode qubits with embedded quantum-error correction, a fundamental step to make the quantum hardware resistant to environmental noise [29][30][31][32][33][34] and still far from being realized even by the most advanced technologies. [35][36][37][38][39][40] Other examples are provided by the Toffoli gate, 41 the Deutsch, 42 Grover, 43 Quantum Fourier Transform, or Quantum Phase Estimation algorithms, which can be implemented much faster and using fewer operations on a qudit than on multiple qubits.…”

Cavity State Manipulation Using Photon-Number Selective Phase Gates

“…Several proposals exist to use this larger Hilbert space for redundant encoding to allow quantum error correction. Some of these are very similar to multi-qubit based codes [4,5] and others are based on superpositions of coherent states [6,7], or so-called cat-codes.…”

A Simple Comparative Analysis of Exact and Approximate Quantum Error Correction

“…However, we believe its consideration is suitable for our purposes, since we wish to essentially stress the similarities and differences between exact and approximate error correction schemes avoiding unnecessary complications. The exact error correction analysis for more realistic and truly quantum error models along the lines presented here could be found in previous works of one of the Authors [22][23][24].…”