99 research outputs found
Efficient, direct compilation of SU(N) operations into SNAP & Displacement gates
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,
to the angle of the
Givens rotation on levels that sequence
approximates, namely .
Previous publications left the determination of an appropriate to
numerical optimization at compile time. The map gives us the ability to
compile directly any -dimensional unitary into a sequence of SNAP and
displacement gates in 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
per Givens rotation scales as approximately . We find
numerically that the error on compiled circuits can be made arbitrarily small
by breaking each rotation into rotations, with the full unitary infidelity scaling as approximately . 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.Comment: 6 pages, 2 figure
Quantum adiabatic machine learning by zooming into a region of the energy surface
Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, an algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the receiver operating characteristic curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks
Norm properties of generalized derivations on norm ideals
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaWe investigate the norm properties of a generalized derivation on a norm ideal J of B(H), the
algebra of bounded linear operators on a Hilbert space H. Specifically, we extend the concept
of S-universality from the inner derivation to the generalized derivation context. Further, we
investigate the applications of the concept of S-universality.Maseno University, Kenya
- …