Erroneous error correction

[FIRST PARAGRAPH] Libraries have been using computers for years now. Many librarians are not mystified by mega-byte-sized jargon and take MOP-buckets in their stride. Nonetheless those black boxes can still come up with a surprise or two. I know a library which has just installed a new issue system (it hardly matters which brand, since this is just a cautionary tale). This computer has been told to capitalise each word in the book-title (machines don’t have to write in CAPITALS now), which looked a little odd when it came to Richard Iii. It was also given a list of stop-words (The, A, Le, La … ) which are not searchable, frustrating anyone looking for titles like A B C of … or A E Houseman or books by Mr Das or Ms Lo. On one occasion the index ‘slipped’ overnight and to look up SMITH one actually had to enter TNJUI

Tracking Quantum Error Correction

To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large scale quantum computation with the GKP qubit [Phys. Rev. X. {\bf 8}, 021054 (2018)], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit level quantum error correction is partially substituted by the single-qubit level quantum error correction. In the proposed method, the analog quantum error correction is utilized to make the performances of the single-qubit level quantum error correction almost identical to those of the logical-qubit level quantum error correction in a practical noise level. The numerical results show that the proposed tracking quantum error correction reduces the number of qubits during a quantum error correction process by the reduction rate $\left\{{2(n-1)\times4^{l-1}-n+1}\right\}/({2n \times 4^{l-1}})$ for $n$-cycles of the quantum error correction process using the Knill's $C_{4}/C_{6}$ code with the concatenation level $l$. Hence, the proposed tracking quantum error correction has great advantage in reducing the required number of physical qubits, and will open a new way to bring up advantage of the GKP qubits in practical quantum computation

Automatic Quantum Error Correction

Criteria are given by which dissipative evolution can transfer populations and coherences between quantum subspaces, without a loss of coherence. This results in a form of quantum error correction that is implemented by the joint evolution of a system and a cold bath. It requires no external intervention and, in principal, no ancilla. An example of a system that protects a qubit against spin-flip errors is proposed. It consists of three spin 1/2 magnetic particles and three modes of a resonator. The qubit is the triple quantum coherence of the spins, and the photons act as ancilla.Comment: 16 pages 12 fig LaTex uses multicol, graphicx expanded version of letter submitted to Phys Rev Let

Catalytic quantum error correction

We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional stabilizer codes are equivalent to dual-containing symplectic codes. In contrast, EAQEC codes do not require the dual-containing condition, which greatly simplifies their construction. We show how any quaternary classical code can be made into a EAQEC code. In particular, efficient modern codes, like LDPC codes, which attain the Shannon capacity, can be made into EAQEC codes attaining the hashing bound. In a quantum computation setting, EAQEC codes give rise to catalytic quantum codes which maintain a region of inherited noiseless qubits. We also give an alternative construction of EAQEC codes by making classical entanglement assisted codes coherent.Comment: 30 pages, 10 figures. Notation change: [[n,k;c]] instead of [[n,k-c;c]