arXiv subjects

Koushik Paul

Publications and source records attributed to Koushik Paul.

17 recordsLinked to original sources

arXiv2026

Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics

Trotter errors in digitized quantum dynamics arise from approximating time-ordered evolution under noncommuting Hamiltonian terms with a product formula. In the adiabatic regime, such errors are known to exhibit long-time self-healing [Phys. Rev. Lett. \textbf{131}, 060602 (2023)], where discretization effects are effectively suppressed. Here we show that self-healing persists at finite evolution times once nonadiabatic errors induced by finite-speed ramps are compensated. Using counterdiabatic driving to cancel diabatic transitions and isolate discretization effects, we study both noninteracting and interacting spin models and characterize the finite-time scaling with the Trotter steps and the total evolution time. In the instantaneous eigenbasis of the driven Hamiltonian, the leading digital error maps to an effective harmonic perturbation whose dominant Fourier component yields an analytic upper bound on the finite-time Trotter error and reveals the phase-cancellation mechanism underlying self-healing. Our results establish finite-time self-healing as a generic feature of digitized counterdiabatic protocols, clarify its mechanism beyond the long-time adiabatic limit, and provide practical guidance for high-fidelity state preparation on gate-based quantum processors.

quant-ph↗

arXiv2025

Computing Young's Natural Representations for Generalized Symmetric Groups

We provide an algorithmic framework for the computation of explicit representing matrices for all irreducible representations of a generalized symmetric group $\Grin_n$, i.e., a wreath product of cyclic group of order $r$ with the symmetric group $\Symm_n$. The basic building block for this framework is the Specht matrix, a matrix with entries $0$ and $\pm1$, defined in terms of pairs of certain words. Combinatorial objects like Young diagrams and Young tableaus arise naturally from this setup. In the case $r = 1$, we recover Young's natural representations of the symmetric group. For general $r$, a suitable notion of pairs of $r$-words is used to extend the construction to generalized symmetric groups. Separately, for $r = 2$, where $\Grin_n$ is the Weyl group of type $B_n$, a different construction is based on a notion of pairs of biwords.

math.RT↗

arXiv2025

Demonstration of Hardware Efficient Photonic Variational Quantum Algorithm

Quantum computing has brought a paradigm change in computer science, where non-classical technologies have promised to outperform their classical counterpart. Such an advantage was only demonstrated for tasks without practical applications, still out of reach for the state-of-art quantum technologies. In this context, a promising strategy to find practical use of quantum computers is to exploit hybrid quantum-classical models, where a quantum device estimates a hard-to-compute quantity, while a classical optimizer trains the parameters of the model. In this work, we demonstrate that single photons and linear optical networks are sufficient for implementing Variational Quantum Algorithms, when the problem specification, or ansatz, is tailored to this specific platform. We show this by a proof-of-principle demonstration of a variational approach to tackle an instance of a factorization task, whose solution is encoded in the ground state of a suitable Hamiltonian. This work which combines Variational Quantum Algorithms with hardware efficient ansatzes for linear-optics networks showcases a promising pathway towards practical applications for photonic quantum platforms.

quant-ph↗

arXiv2024

Symmetry-enhanced Counterdiabatic Quantum Algorithm for Qudits

Qubit-based variational quantum algorithms have undergone rapid development in recent years but still face several challenges. In this context, we propose a symmetry-enhanced digitized counterdiabatic quantum algorithm utilizing qudits instead of qubits. This approach offers three types of compression as compared to with respect to conventional variational circuits. First, compression in the circuit depth is achieved by counterdiabatic protocols. Second, information about the problem is compressed by replacing qubits with qudits, allowing for a more efficient representation of the problem. Lastly, the number of parameters is reduced by employing the symmetries of the system. We illustrate this approach by tackling a graph-based optimization problem Max-3-Cut and a highly-entangled state preparation, the qutrit W state. As our numerical results show, we achieve a better convergence with a lower circuit depth and less measurement overhead in all the cases considered. This work leads to a better design of shallow variational quantum circuits, improving the feasibility of their implementation on near-term qudit devices

quant-ph↗

arXiv2024

Lyapunov Controlled Counterdiabatic Quantum Optimization

We introduce a quantum algorithm integrating counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to tackle combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces the dependence on extensive higher-order CD terms and classical optimization techniques, rendering it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum computing.

quant-ph↗

arXiv2024

Benchmarking hybrid digitized-counterdiabatic quantum optimization

Hybrid digitized-counterdiabatic quantum computing (DCQC) is a promising approach for leveraging the capabilities of near-term quantum computers, utilizing parameterized quantum circuits designed with counterdiabatic protocols. However, the classical aspect of this approach has received limited attention. In this study, we systematically analyze the convergence behavior and solution quality of various classical optimizers when used in conjunction with the digitized-counterdiabatic approach. We demonstrate the effectiveness of this hybrid algorithm by comparing its performance to the traditional QAOA on systems containing up to 28 qubits. Furthermore, we employ principal component analysis to investigate the cost landscape and explore the crucial influence of parameterization on the performance of the counterdiabatic ansatz. Our findings indicate that fewer iterations are required when local cost landscape minima are present, and the SPSA-based BFGS optimizer emerges as a standout choice for the hybrid DCQC paradigm.

quant-ph↗

arXiv2023

Shortcuts to Adiabatic Soliton Compression in Active Nonlinear Kerr Media

We implement variational shortcuts to adiabaticity for optical pulse compression in an active nonlinear Kerr medium with distributed amplification and spatially varying dispersion and nonlinearity. Starting with the hyperbolic secant ansatz, we employ a variational approximation to systematically derive dynamical equations, establishing analytical relationships linking the amplitude, width, and chirp of the pulse. Through the inverse engineering approach, we manipulate the distributed gain/loss, nonlinearity and dispersion profiles to efficiently compress the optical pulse over a reduced distance with high fidelity. In addition, we explore the dynamical stability of the system to illustrate the advantage of our protocol over conventional adiabatic approaches. Finally, we analyze the impact of tailored higher-order dispersion on soliton self-compression and derive physical constraints on the final soliton width for the complementary case of soliton expansion. The broader implications of our findings extend beyond optical systems, encompassing areas such as cold-atom and magnetic systems highlighting the versatility and relevance of our approach in various physical contexts.

physics.optics↗

arXiv2023

Photonic counterdiabatic quantum optimization algorithm

We propose a hybrid quantum-classical approximate optimization algorithm for photonic quantum computing, specifically tailored for addressing continuous-variable optimization problems. Inspired by counterdiabatic protocols, our algorithm significantly reduces the required quantum operations for optimization as compared to adiabatic protocols. This reduction enables us to tackle non-convex continuous optimization and countably infinite integer programming within the near-term era of quantum computing. Through comprehensive benchmarking, we demonstrate that our approach outperforms existing state-of-the-art hybrid adiabatic quantum algorithms in terms of convergence and implementability. Remarkably, our algorithm offers a practical and accessible experimental realization, bypassing the need for high-order operations and overcoming experimental constraints. We conduct proof-of-principle experiments on an eight-mode nanophotonic quantum chip, successfully showcasing the feasibility and potential impact of the algorithm.

quant-ph↗

arXiv2022

Efficient broadband frequency conversion via shortcut to adiabaticity

The method of adiabatic frequency conversion, in analogy with the two level atomic system, has been put forward recently and verified experimentally to achieve robust frequency mixing processes such as sum and difference frequency generation. Here we present a comparative study of efficient frequency mixing using various techniques of shortcuts to adiabaticity (STA) such as counter-diabatic driving and invariant-based inverse engineering. We show that, it is possible to perform sum frequency generation by properly designing the poling structure of a periodically poled crystal and the coupling between the input lights and the crystal. The required crystal length for frequency conversion is significantly decreases beyond the adiabatic limit. Our approach significantly improves the robustness of the process against the variation in temperature as well as the signal frequency. By introducing a single parameter control technique with constant coupling and combining with the inverse engineering, perturbation theory and optimal control, we show that the phase mismatch can be further optimized with respect to the fluctuations of input wavelength and crystal temperature that results into a novel experimentally realizable mixing scheme.

quant-ph↗

arXiv2021

Digitized Adiabatic Quantum Factorization

Quantum integer factorization is a potential quantum computing solution that may revolutionize cryptography. Nevertheless, a scalable and efficient quantum algorithm for noisy intermediate-scale quantum computers looks far-fetched. We propose an alternative factorization method, within the digitized-adiabatic quantum computing paradigm, by digitizing an adiabatic quantum factorization algorithm enhanced by shortcuts to adiabaticity techniques. We find that this fast factorization algorithm is suitable for available gate-based quantum computers. We test our quantum algorithm in an IBM quantum computer with up to six qubits, surpassing the performance of the more commonly used factorization algorithms on the long way towards quantum advantage.

quant-ph↗

arXiv2020

Shortcuts to Adiabaticity in Digitized Adiabatic Quantum Computing

Shortcuts to adiabaticity are well-known methods for controlling the quantum dynamics beyond the adiabatic criteria, where counter-diabatic (CD) driving provides a promising means to speed up quantum many-body systems. In this work, we show the applicability of CD driving to enhance the digitized adiabatic quantum computing paradigm in terms of fidelity and total simulation time. We study the state evolution of an Ising spin chain using the digitized version of the standard CD driving and its variants derived from the variational approach. We apply this technique in the preparation of Bell and Greenberger-Horne-Zeilinger states with high fidelity using a very shallow quantum circuit. We implement this proposal in the IBM quantum computer, proving its usefulness for the speed up of adiabatic quantum computing in noisy intermediate-scale quantum devices.

quant-ph↗

arXiv2020

Smooth bang-bang shortcuts to adiabaticity for atomic transport in a moving harmonic trap

Bang-bang control is often used to implement a minimal-time shortcut to adiabaticity for efficient transport of atoms in a moving harmonic trap. However, drastic changes of the on-off controller, leading to high transport-mode excitation and energy consumption, become infeasible under realistic experimental conditions. To circumvent these problems, we propose smooth bang-bang protocols with near-minimal time, by setting the physical constraints on the relative displacement, speed, and acceleration between the mass center of the atom and the trap center. We adopt Pontryagin's maximum principle to obtain the analytical solutions of smooth bang-bang protocol for near-time-minimal control. More importantly, it is found that the energy excitation and sloshing amplitude are significantly reduced at the expense of operation time. We also present a multiple shooting method for the self-consistent numerical analysis. Finally, this method is applied to other tasks, e.g., energy minimization, where obtaining smooth analytical form is complicated.

quant-ph↗

arXiv2017

Nonlinear compression of temporal solitons in an optical waveguide via inverse engineering

We propose a novel method based on the so-called shortcut to adiabatic passage techniques to achieve fast compression of temporal solitons in a nonlinear waveguide. We demonstrate that soliton compression could be achieved, in principle, at an arbitrarily small distance by inverse engineering the pulse width and the nonlinearity of the medium. The proposed scheme could possibly be exploited for various short-distance communication protocols and may be even in nonlinear guided wave-optics devices and generation of ultrashort soliton pulses.

physics.optics↗

arXiv2017

Transitionless quantum driving based wireless power transfer

Shortcut to adiabaticity (STA) techniques have the potential to drive a system beyond the adiabatic limits. Here, we present a robust and efficient method for wireless power transfer (WPT) between two coils based on the so-called transitionless quantum driving (TQD) algorithm. We show that it is possible to transfer power between the coils significantly fast compared to its adiabatic counterpart. The scheme is fairly robust against the variations in the coupling strength and the coupling distance between the coils. Also, the scheme is found to be reasonably immune to intrinsic losses in the coils.

quant-ph↗

arXiv2016

High-Fidelity Entangled Bell States via Shortcuts to Adiabaticity

We present a couple of protocols based on shortcut to adiabaticity techniques for rapid generation of robust entangled Bell states in a system of two two-state systems. Our protocols rely on the so-called transitionless quantum driving (TQD) algorithm and Lewis-Riesenfeld invariant (LRI) method. Both TQD and LRI methods result in high fidelity in population transfer.Our study shows that it is possible to prepare an entangled state in infinitely short time without losing robustness and efficiency.

quant-ph↗

arXiv2016

Efficient shortcut techniques in evanescently coupled waveguides

Shortcut to Adiabatic Passage (SHAPE) technique, in the context of coherent control of atomic systems has gained considerable attention in last few years. It is primarily because of its ability to manipulate population among the quantum states infinitely fast compared to the adiabatic processes. Two methods in this regard have been explored rigorously, namely the transitionless quantum driving and the Lewis-Reisenfeld invariant approach. We have applied these two methods to realize SHAPE in adiabatic waveguide coupler. Waveguide couplers are integral components of photonic circuits, primarily used as switching devices. Our study shows that with appropriate engineering of the coupling coefficient and propagation constants of the coupler it is possible to achieve efficient and complete power switching. We also observed that the coupler length could be reduced significantly without affecting the coupling efficiency of the system.

physics.optics↗

arXiv2015

Shortcut to Adiabatic Passage in a Waveguide Coupler with Allen-Eberly scheme

We propose a directional coupler exploiting the framework of adiabatic passage for two level atomic systems with configuration dependent Allen-Eberly scheme. Recently developed shortcut to adiabatic passage method (STA), which uses transitionless quantum driving algorithm, is applied to the coupler. The study shows that it is possible to reduce the device length significantly using STA, keeping the efficiency of power transfer100%.Shortcut approach shows much superiority in terms of robustness and fidelity in power switching compared to the adiabatic one.

quant-ph↗