English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We analyze quantum computers which perform Shor's factoring algorithm, payingattention to asymptotic properties as the number L of qubits is increased.Using numerical simulations and a general theory of the stabilities ofmany-body quantum states, we show the following: Anomalously fluctuating states(AFSs), which have anomalously large fluctuations of additive operators, appearin various stages of the computation. For large L, they decohere at anomalouslygreat rates by weak noises that simulate noises in real systems. Decoherence ofsome of the AFSs is fatal to the results of the computation, whereasdecoherence of some of the other AFSs does not have strong influence on theresults of the computation. When such a crucial AFS decoheres, the probabilityof getting the correct computational result is reduced approximatelyproportional to L^2. The reduction thus becomes anomalously large withincreasing L, even when the coupling constant to the noise is rather small.Therefore, quantum computations should be improved in such a way that all AFSsappearing in the algorithms do not decohere at such great rates in the existingnoises.Comment: 11 figures. A few discussions were added in verion 2. Version 3 is  the SAME as version 2; only errors during the Web-upload were fixed. Version  4 is the publised version, in which several typos are fixed and the reference  list is update

Appearance and stability of anomalously fluctuating states in Shor’s factoring algorithm