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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a function which connects the parameter of a previously publishedshort sequence of selective number-dependent arbitrary phase (SNAP) anddisplacement gates acting on a qudit encoded into the Fock states of asuperconducting cavity,$V_k(\alpha)=D(\alpha)R_\pi(k)D(-2\alpha)R_\pi(k)D(\alpha)$ to the angle of theGivens rotation $G(\theta)$ on levels $|k\rangle,|k+1\rangle$ that sequenceapproximates, namely $\alpha=\Phi(\theta) = \frac{\theta}{4\sqrt{k+1}}$.Previous publications left the determination of an appropriate $\alpha$ tonumerical optimization at compile time. The map $\Phi$ gives us the ability tocompile directly any $d$-dimensional unitary into a sequence of SNAP anddisplacement gates in $O(d^3)$ complex floating point operations with lowconstant prefactor, avoiding the need for numerical optimization. Numericalstudies demonstrate that the infidelity of the generated gate sequence $V_k$per Givens rotation $G$ scales as approximately $O(\theta^6)$. We findnumerically that the error on compiled circuits can be made arbitrarily smallby breaking each rotation into $m$ $\theta/m$ rotations, with the full $d\timesd$ unitary infidelity scaling as approximately $O(m^{-4})$. This represents asignificant reduction in the computational effort to compile qudit unitarieseither to SNAP and displacement gates or to generate them via direct low-levelpulse optimization via optimal control.

Efficient, direct compilation of SU(N) operations into SNAP & Displacement gates