Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.36431

Transverse momentum as the counter-diabatic generator in bent waveguide couplers

Yu-kai Lee·Shuo-Yen Tseng
View original source ↗Read source document ↗Export metadata ↓

Abstract

Bending the axis of a mode-evolution coupler suppresses the nonadiabatic coupling between its supermodes, and bent couplers of this kind were recently shown to realize the counter-diabatic (CD) protocol. Here we identify the operator responsible. Rigid lateral displacement of a waveguide structure is generated by the transverse momentum $\hat p_x$, whose diagonal matrix elements vanish in a real supermode basis and whose off-diagonal element is purely imaginary; in a two-mode system such an operator is proportional to $\sy$. The CD term of a two-waveguide coupler is itself proportional to $\sy$, while the detuning and the coupling, the two parameters set by the waveguide widths and spacing, lie in the $σ_z$--$σ_x$ plane and cannot produce it. The transverse momentum is therefore the CD generator of the bent coupler, by necessity rather than by design. Equating the term it supplies to the nonadiabatic coupling gives the axis slope in closed form as a ratio of two matrix elements of the unperturbed supermodes at a single cross section, which a commutator identity recasts in coupled-mode variables as $\dot{\xo}=\dotθ/(γ\dbeta^{2})$. The expression agrees with the numerical offset search to $0.3\%$ and requires no search. Beam propagation simulations confirm the design and compare it, for the first time, with the CD protocol realized by unitary transformation in a straight coupler built from the same reference structure. The two devices reach $0.994$ and $1.000$ supermode fidelity where the untreated coupler reaches $0.886$, and agree in bandwidth and fabrication tolerance, while their internal trajectories differ by exactly the frame transformation that relates them.

Explore related subjects

quant-phphysics.optics

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yu-kai Lee, Shuo-Yen Tseng. 2026-09-29. Transverse momentum as the counter-diabatic generator in bent waveguide couplers. https://arxiv.org/abs/2609.36431

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Preparation of Hamming-Weight-Preserving Quantum States with Log-Depth Quantum Circuits

Hamming-Weight-Preserving (HWP) states, $\vertψ_{\mathrm{H}}\rangle=\sum_{\mathrm{HW}(x)=k}α_x\vert x\rangle$, represent a fundamental class of quantum states on $n$ qubits with fixed excitation number $k$, playing a pivotal role in quantum simulation, machine learning, and optimization, with prominent examples including the Bethe eigenstates of integrable models and Configuration Interaction states. However, existing preparation methodologies typically rely on sequential architectures whose depth scales linearly with the subspace dimension, whereas practical deployment on realistic quantum hardware demands shallow circuits to mitigate decoherence. In this work, we present quantum circuits that achieve the information theoretic limit of depth logarithmic in the number of populated computational basis states while maintaining asymptotically optimal size. Specifically, for general HWP states, we provide a construction that matches the lower bounds of $Θ(\log \binom{n}{k})$ depth and $Θ(\binom{n}{k})$ size. Furthermore, we propose a resource efficient scheme utilizing only $O(\log k)$ ancillary qubits. For the $k=2$ case, where HWP states naturally admit a graph representation, we show that states whose support graphs are trees or grids admit ancilla free preparation with $Θ(\log n)$ depth and $Θ(m)$ size. Overall, our work provides logarithmic depth state preparation algorithms across various regimes while establishing a connection between quantum state synthesis and Krawtchouk polynomials.

quant-ph↗
arXiv2026

Matrix-product-state-assisted variational Gibbs-state preparation

Evaluating the von Neumann entropy is a central challenge in variational Gibbs-state preparation. We introduce and benchmark matrix-product-state (MPS) assistance for classically evaluating and optimizing the purification circuits without full-statevector storage, examining how circuit architecture affects both thermal-state accuracy and the computational resources required. Comparisons on four- and six-spin transverse-field Ising and XXZ chains reveal complementary strengths: a thermofield-double ansatz performs better at high temperature, whereas a contiguous hardware-efficient ansatz (HEA) performs better on cooling. We identify a layer-dependent entropy ceiling in the contiguous HEA and compare it with an interleaved architecture whose entropy capacity is set solely by the ancilla qubit count. MPS-based benchmarks on 10 x 1, 20 x 1, 3 x 3, and 4 x 4 transverse-field Ising systems show that the tested interleaved circuits generally lower the free-energy errors and improve thermal observables. However, greater entropy capacity and lower free energy do not guarantee improvement in every observable. The architectures also differ in classical cost: contiguous registers permit entropy evaluation at a single MPS bond, whereas the interleaved arrangement requires a dense entropy calculation that scales exponentially with the number of ancillas. These benchmarks connect the accuracy of MPS-assisted Gibbs-state preparation to circuit capacity, optimization, and the tractability of energy and entropy evaluation.

quant-ph↗
arXiv2026

A Unified Error Correction Code for Universal Quantum Computing with Identical Particles

We present a universal fault-tolerant quantum computing architecture based on identical particle qubits (IPQs), where we find that the first-order IPQ - bath interaction fundamentally differs from the conventional first-order qubit-bath interaction. This key distinction necessitates a redesign of existing strategies to fight decoherence. We propose that the simplest quantum error correction code can be realized directly within the physical qubit, provided that conventional correction and restoration are generalized beyond unitary operations to employ physically implementable reversal operations -- naturally placing logical and physical qubits on equal footing. We further demonstrate that dynamical decoupling (DD) remains effective within this unified framework, and that a decoherence-free subspace (DFS) -- like structure emerges. Unlike previous approximate treatments, our analytically solvable IPQ-Bath model enables rigorous testing of these strategies, with numerical simulations validating their effectiveness.

quant-ph↗