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

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

Analog quantum error correction

Quantum error-correction routines are developed for continuous quantum variables such as position and momentum. The result of such analog quantum error correction is the construction of composite continuous quantum variables that are largely immune to the effects of noise and decoherence.Comment: Ten pages, Te

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