arXiv subjects

Hendry M. Lim

Publications and source records attributed to Hendry M. Lim.

6 recordsLinked to original sources

arXiv2026

SymQuPS: Symbolic Quantum Phase Space Algebra in Python

We present \texttt{SymQuPS}, a SymPy-based algebra system in Python mainly aimed toward the phase space representation of quantum mechanics within the Cahill-Glauber formalism (including the Glauber-Sudarshan $P$, Wigner, and Husimi $Q$ representations). By extension, the package serves as an algebraic venue for canonical quantization. A key feature is the phase space representation of an arbitrary Lindblad master equation, which gives the phase space equation of motion of the quantum system. We describe the core functionalities of the package, consisting of $s$-ordered operators, the star products, and the phase space representation. Some examples of use are given to illustrate the application of the package, and the package's performance in typical use cases is discussed.

quant-ph↗

arXiv2026

Normal-ordered equivalent of the Weyl ordering of $\hat{q}^j \hat{p}^k$

The problem of quantizing a bivariate dynamical system can be reduced to evaluating the ordering of $\hat{q}^j \hat{p}^k$. Here, we consider the Weyl ordering of $\hat{q}^j \hat{p}^k$ that is then expressed in term of the annihilation $\hat{a}$ and creation $\hat{a}^\dagger$ operator. The explicit formula for the normal-ordered equivalent (all $\hat{a}^\dagger$'s preceeding all $\hat{a}$'s) of the resulting expression is then given, and some relations are discussed.

math-ph↗

arXiv2025

Canonical quantization of a product within the Cahill-Glauber correspondence

The (canonical) quantization of a product of two phase-space functions can be expressed as a commutative mapping between the quantizations of its factors. In this note, we discuss such a mapping within the Cahill-Glauber $s$-parameterized correspondence framework, providing a heuristic (hence less mathematically rigorous, but arguably more easily understood) derivation for the bidifferential form. The term "hatted star product" is coined by virtue of the structural similarity to the star product in phase space, a special case of which is the celebrated Moyal star product.

quant-ph↗

arXiv2025

pyBoLaNO: A Python symbolic package for normal ordering involving bosonic ladder operators

We present pyBoLaNO, a Python symbolic package based on SymPy to quickly normal-order (Wick-order) any polynomial in bosonic ladder operators. By extension, this package offers the normal ordering of commutators of any two polynomials in bosonic ladder operators and the evaluation of the normal-ordered expectation value evolution in the Lindblad master equation framework for open quantum systems. The package also supports multipartite descriptions and multiprocessing. We describe the package's workflow, show examples of use, and discuss its computational performance. All codes and examples are available on our GitHub repository.

quant-ph↗

arXiv2024

Efficiency of optimal control for noisy spin qubits in diamond

Decoherence is a major challenge for quantum technologies. A way to mitigate its negative impact is by employing quantum optimal control. The decoherence dynamics varies significantly based on the characteristics of the surrounding environment of qubits, consequently affecting the outcome of the control optimization. In this work, we investigate the dependence of the shape of a spin inversion control pulse on the correlation time of the environment noise. Furthermore, we analyze the effects of constraints and optimization options on the optimization outcome and identify a set of strategies that improve the optimization performance. Finally, we present an experimental realization of the numerically-optimized pulses validating the optimization feasibility. Our work serves as a generic yet essential guide to implementing optimal control in the presence of realistic noise, e.g., in nitrogen-vacancy centers in diamond.

quant-ph↗

arXiv2024

Transient dynamics of the quantum Stuart-Landau oscillator

We investigate the transient dynamics of the quantum Stuart-Landau oscillator, a paradigmatic quantum system exhibiting a quantum limit cycle and synchronization. From the energy dynamics, we determine a condition for the classical regime of transient dynamics and the limit cycle. Additionally, we formulate a guess function that fits the classical-regime steady-state Wigner function. The equation of motion for the Wigner function is derived and compared to the Kramers-Moyal equation for stochastic processes. We then characterize the classical-like behavior as the system evolves from a coherent state, noting the slow decay of neighboring-level coherence. We also study the evolution of the Wigner negativity as an indicator of nonclassicality, showing its temporary increase for some specific cases. To quantify the evolution speed, we examined the system's Lindbladian spectra, particularly the Liouvillian gap. Finally, we record the time it takes to reach the steady state for some Fock, thermal, and coherent states. The parameter dependence of the steady-state time may differ from the Liouvillian gap, and the limit-cycle attraction is significantly slower for coherent states compared to Fock or thermal states. For the diagonal states, there are \revision{fast convergence regimes} for which the steady-state time is locally minimized. This study provides a deeper insight into the transient behavior of self-sustained quantum systems.

quant-ph↗