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

Journal Article · Fri Jul 21 04:00:00 EDT 2023 · TBD

OSTI ID:1998927

Job, Joshua ^[1]

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1. Lockheed, Sunnyvale; Fermilab

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

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• DOE Contract Number: AC02-07CH11359
• OSTI ID: 1998927
• Report Number(s): FERMILAB-PUB-23-456-V; arXiv:2307.11900; oai:inspirehep.net:2679883
• Journal Information: TBD, Journal Name: TBD
• Country of Publication: United States
• Language: English