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Source code for "Engineering non-Gaussian bosonic gates through quantum signal processing"

Pak-Tik Fong, Hoi-Kwan Lau

Published Sep 4, 2026• 1 citation
Publisher

Abstract

This repository contains the Wolfram Mathematica source code associated with the article “Engineering non-Gaussian bosonic gates through quantum signal processing” by Pak-Tik Fong and Hoi-Kwan Lau. The notebooks implement numerical calculations and simulations for engineering non-Gaussian bosonic operations using quantum signal processing (QSP). They include the construction of QSP rotation sequences for mod-kk gates and noiseless linear amplification (NLA) under dispersive coupling. Specifically, the code compares QSP-based implementations with conventional multitone-driving schemes for dispersive- and Jaynes-Cummings-coupled qumode-qubit systems, including the simulations used to generate Figs. 2, 5(a), and 5(b) of the paper. The notebooks were developed using Wolfram Mathematica 12.0.

DOI
10.5281/zenodo.22262706

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This repository contains the Wolfram Mathematica source code associated with the article “Engineering non-Gaussian bosonic gates through quantum signal processing” by Pak-Tik Fong and Hoi-Kwan Lau. The notebooks implement numerical calculations and simulations for engineering non-Gaussian bosonic operations using quantum signal processing (QSP). They include the construction of QSP rotation sequences for mod-kk gates and noiseless linear amplification (NLA) under dispersive coupling. Specifically, the code compares QSP-based implementations with conventional multitone-driving schemes for dispersive- and Jaynes-Cummings-coupled qumode-qubit systems, including the simulations used to generate Figs. 2, 5(a), and 5(b) of the paper. The notebooks were developed using Wolfram Mathematica 12.0.
Non-Gaussian operations are essential for most bosonic quantum technologies. Yet, realizable non-Gaussian gates are rather limited in type and generally suffer from accuracy-duration trade-offs. In this work, we propose to use quantum signal processing (QSP) techniques to engineer non-Gaussian gates on hybrid qumode-qubit systems. For systems with dispersive coupling, our scheme can generate a new non-Gaussian gate that produces a phase shift depending on the modulus of the boson number. This gate reproduces the selective number-dependent arbitrary phase (SNAP) gates under certain parameter choices, but with higher accuracy within a short, fixed and excitation-independent interaction time. The gate unlocks new applications, for example, in entangling logical qudits and deterministically generating multi-component cat states. Additionally, our versatile QSP formalism can be extended to systems with other interactions, and also engineer non-unitary operations, such as noiseless linear amplification and generalized-parity measurement.
Quantum signal processing (QSP) transforms a unitary parametrized by a classical variable θ into one governed by a polynomial function f ( θ ) . Though quantum mechanics is linear, such highly nonlinear transformations arise naturally from the curvature of the qubit Bloch sphere. This capability underpins many quantum algorithms and enables robust control by decreasing sensitivity to errors in a control parameter, or quantum sensing by increasing sensitivity to variations one seeks to measure. Here, we extend QSP from classical, commuting control parameters to noncommuting quantum operators. We call this new multivariate class . Rather than treating the noncommutativity of quantum control variables as a complication, non-Abelian QSP exploits their richer commutator algebra as a resource for efficient control. A natural setting is hybrid oscillator-qubit systems realized in superconducting and trapped-ion processors, where the control variables can be the noncommuting position and momentum of a quantum harmonic oscillator. We introduce the Gaussian-controlled rotation (GCR), a canonical instance of non-Abelian QSP that cancels the Gaussian quantum-fluctuation error of an oscillator-controlled qubit rotation, matching the robustness of classical composite pulses with a much shorter circuit and an order-of-magnitude lower error. GCR enables fully analytical circuits for preparing squeezed, cat, GKP, and Fock states with performance comparable to state-of-the-art numerically optimized protocols. Building on this primitive, we develop an analytical framework for universal control of GKP bosonic codes, in which logical readout doubles as piecewise gate teleportation, yielding the first high-fidelity, error-mitigated single- and two-qubit logical gates for finite-energy GKP that surpass prior schemes even in the noiseless regime. The same framework supplies midcircuit error detection and extends in closed form to arbitrary lattices, qudits, and multimode codes relevant to the superconducting-circuit experiments now demonstrating beyond-break-even GKP memory. We further apply these ideas to close a key gap in oscillator-assisted quantum phase estimation. Together, these results show that the non-Abelian structure of quantum control operators can provide a practical resource for robust and efficient quantum control, establishing non-Abelian QSP as both a new theoretical framework and an experimentally accessible control paradigm.
Realizing coherent quantum computation requires precise and robust manipulation of quantum systems through quantum control protocols. Most quantum control techniques rely on heuristic methods for designing the driving pulses that steer the system towards a target state. Such methods are often based on brute-force optimization and offer limited understanding of the solution landscape. In contrast, quantum algorithms offer a rich body of analytical methods with rigorous error guarantees for implementing unitary and non-unitary transformations, which suggests a promising direction for developing new approaches to quantum control. Among various such algorithms, quantum signal processing (QSP) has emerged as a powerful framework for quantum algorithm design, implementation, and optimization. However, its potential for quantum control remains largely unexplored. In this work, we establish QSP-Control, an analytical framework for quantum control of qubit-oscillator dynamics. We focus on dispersively coupled qubit-oscillator systems and employ the QSP formalism to mitigate unwanted nonlinear effects arising from cross-Kerr interactions. In addition, we develop constructions for precise manipulation of Fock states by designing Fock-state-selective operators, based on structural parallels between the Jaynes-Cummings interaction and QSP. These findings demonstrate how several practically relevant problems in quantum control can be mapped to forms amenable to QSP, offering both a systematic design framework and an interpretable perspective on quantum control.