Methodology of Resonant Equiangular Composite Quantum Gates

By Guang Hao Low, Theodore J. Yoder, Isaac L. Chuang. 2016

166 citations recorded by the source corpus.

The creation of composite quantum gates that implement quantum response functions $\hat{U}(\theta)$ dependent on some parameter of interest $\theta$ is often more of an art than a science. Through inspired design, a sequence of $L$ primitive gates also depending on $\theta$ can engineer a highly nontrivial $\hat{U}(\theta)$ that enables myriad precision metrology, spectroscopy, and control techniques. However, discovering new, useful examples of $\hat{U}(\theta)$ requires great intuition to perceive the possibilities, and often brute-force to find optimal implementations. We present a systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by $\theta$ act on a single spin. We fully characterize the realizable family of $\hat{U}(\theta)$, provide an efficient algorithm that decomposes a choice of $\hat{U}(\theta)$ into its shortest sequence of gates, and show how to efficiently choose an achievable $\hat{U}(\theta)$ that for fixed $L$, is an optimal approximation to objective functions on its quadratures. A strong connection is forged with \emph{classical} discrete-time signal processing, allowing us to swiftly construct, as examples, compensated gates with optimal bandwidth that implement arbitrary single spin rotations with sub-wavelength spatial selectivity.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/92c920802c9b70a81326871c0a3008515e8e583e

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Citations in the corpus

Toward the first quantum simulation with quantum speedup (2017, methodology): “, φM that realize this expansion can be computed by an efficient classical procedure (see Lemmas 1 and 3 of [53]).”
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics (2018, methodology): “(Flexible) Quantum Signal Processing [44] [43] [41] [42] Quantum Singular Value Transf.”
Hamiltonian Simulation by Qubitization (2016, methodology): “Furthermore, a table of select phases ~ φ computed using the algorithm in [37] can be found in Table 3.”
Grand Unification of Quantum Algorithms (2021, methodology): “This QSP convention is expressive enough for all of the polynomials considered in this paper and is used in [7, 12].”