arXiv subjects

Alejandro Gomez Cadavid

Publications and source records attributed to Alejandro Gomez Cadavid.

25 records · Page 2Linked to original sources

arXiv2024

Analog Counterdiabatic Quantum Computing

We propose analog counterdiabatic quantum computing (ACQC) to tackle combinatorial optimization problems on neutral-atom quantum processors. While these devices allow for the use of hundreds of qubits, adiabatic quantum computing struggles with non-adiabatic errors, which are inevitable due to the hardware's restricted coherence time. We design counterdiabatic protocols to circumvent those limitations via ACQC on analog quantum devices with ground-Rydberg qubits. To demonstrate the effectiveness of our paradigm, we experimentally apply it to the maximum independent set (MIS) problem with up to 100 qubits and show an enhancement in the approximation ratio with a short evolution time. We believe ACQC establishes a path toward quantum advantage for a variety of industry use cases.

quant-ph↗

arXiv2024

Bias-field digitized counterdiabatic quantum optimization

We introduce a method for solving combinatorial optimization problems on digital quantum computers, where we incorporate auxiliary counterdiabatic (CD) terms into the adiabatic Hamiltonian, while integrating bias terms derived from an iterative digitized counterdiabatic quantum algorithm. We call this protocol bias-field digitized counterdiabatic quantum optimization (BF-DCQO). Designed to effectively tackle large-scale combinatorial optimization problems, BF-DCQO demonstrates resilience against the limitations posed by the restricted coherence times of current quantum processors and shows clear enhancement even in the presence of noise. Additionally, our purely quantum approach eliminates the dependency on classical optimization required in hybrid classical-quantum schemes, thereby circumventing the trainability issues often associated with variational quantum algorithms. Through the analysis of an all-to-all connected general Ising spin-glass problem, we exhibit a polynomial scaling enhancement in ground state success probability compared to traditional DCQO and finite-time adiabatic quantum optimization methods. Furthermore, it achieves scaling improvements in ground state success probabilities, increasing by up to two orders of magnitude, and offers an average 1.3x better approximation ratio than the quantum approximate optimization algorithm for the problem sizes studied. We validate these findings through experimental implementations on both trapped-ion quantum computers and superconducting processors, tackling a maximum weighted independent set problem with 36 qubits and a spin-glass on a heavy-hex lattice with 100 qubits, respectively. These results mark a significant advancement in gate-based quantum computing, employing a fully quantum algorithmic approach.

quant-ph↗

arXiv2024

Digital-Analog Counterdiabatic Quantum Optimization with Trapped Ions

We introduce a hardware-specific, problem-dependent digital-analog quantum algorithm of a counterdiabatic quantum dynamics tailored for optimization problems. Specifically, we focus on trapped-ion architectures, taking advantage from global Mølmer-Sørensen gates as the analog interactions complemented by digital gates, both of which are available in the state-of-the-art technologies. We show an optimal configuration of analog blocks and digital steps leading to a substantial reduction in circuit depth compared to the purely digital approach. This implies that, using the proposed encoding, we can address larger optimization problem instances, requiring more qubits, while preserving the coherence time of current devices. Furthermore, we study the minimum gate fidelity required by the analog blocks to outperform the purely digital simulation, finding that it is below the best fidelity reported in the literature. To validate the performance of the digital-analog encoding, we tackle the maximum independent set problem, showing that it requires fewer resources compared to the digital case. This hybrid co-design approach paves the way towards quantum advantage for efficient solutions of quantum optimization problems.

quant-ph↗

arXiv2023

Physics-Informed Neural Networks for an optimal counterdiabatic quantum computation

We introduce a novel methodology that leverages the strength of Physics-Informed Neural Networks (PINNs) to address the counterdiabatic (CD) protocol in the optimization of quantum circuits comprised of systems with $N_{Q}$ qubits. The primary objective is to utilize physics-inspired deep learning techniques to accurately solve the time evolution of the different physical observables within the quantum system. To accomplish this objective, we embed the necessary physical information into an underlying neural network to effectively tackle the problem. In particular, we impose the hermiticity condition on all physical observables and make use of the principle of least action, guaranteeing the acquisition of the most appropriate counterdiabatic terms based on the underlying physics. The proposed approach offers a dependable alternative to address the CD driving problem, free from the constraints typically encountered in previous methodologies relying on classical numerical approximations. Our method provides a general framework to obtain optimal results from the physical observables relevant to the problem, including the external parameterization in time known as scheduling function, the gauge potential or operator involving the non-adiabatic terms, as well as the temporal evolution of the energy levels of the system, among others. The main applications of this methodology have been the $\mathrm{H_{2}}$ and $\mathrm{LiH}$ molecules, represented by a 2-qubit and 4-qubit systems employing the STO-3G basis. The presented results demonstrate the successful derivation of a desirable decomposition for the non-adiabatic terms, achieved through a linear combination utilizing Pauli operators. This attribute confers significant advantages to its practical implementation within quantum computing algorithms.

quant-ph↗

arXiv2023

Efficient DCQO Algorithm within the Impulse Regime for Portfolio Optimization

We propose a faster digital quantum algorithm for portfolio optimization using the digitized-counterdiabatic quantum optimization (DCQO) paradigm in the impulse regime, that is, where the counterdiabatic terms are dominant. Our approach notably reduces the circuit depth requirement of the algorithm and enhances the solution accuracy, making it suitable for current quantum processors. We apply this protocol to a real-case scenario of portfolio optimization with 20 assets, using purely quantum and hybrid classical-quantum paradigms. We experimentally demonstrate the advantages of our protocol using up to 20 qubits on an IonQ trapped-ion quantum computer. By benchmarking our method against the standard quantum approximate optimization algorithm and finite-time digitized-adiabatic algorithms, we obtain a significant reduction in the circuit depth by factors of 2.5 to 40, while minimizing the dependence on the classical optimization subroutine. Besides portfolio optimization, the proposed method is applicable to a large class of combinatorial optimization problems.

quant-ph↗

arXiv2023

A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules

We propose a hybrid quantum-classical algorithm for solving the time-independent Schrödinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix by inverting the Hamiltonian matrix expressed in the basis of square-integrable functions. The computational bottleneck of the classical algorithm -- symmetric matrix inversion -- is addressed here using the variational quantum linear solver (VQLS), a recently developed noisy intermediate-scale quantum (NISQ) algorithm for solving systems of linear equations. We apply our algorithm to single and multichannel quantum scattering problems, obtaining accurate vibrational relaxation probabilities in collinear atom-molecule collisions. We also show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules. Our results demonstrate that it is possible to calculate scattering cross sections and rates for complex molecular collisions on NISQ quantum processors, opening up the possibility of scalable digital quantum computation of gas-phase bimolecular collisions and reactions of relevance to astrochemistry and ultracold chemistry.

quant-ph↗

arXiv2020

About the Teaching of Plane Motion of Rigid Bodies

The study of the motion of a rigid body on a plane (RBP motion) is usually one of the most challenging topics that students face in introductory physics courses. In this paper, we discuss a couple of problems which are typically used in basic physics courses, in order to highlight some aspects related to RBP motion which are not usually well understood by physics students. The first problem is a pendulum composed of a rod and disk. The angular frequency of the pendulum is calculated in two situations: disk fixed to the rod and disk free to spin. A detailed explanation of the change in the angular frequency from one case to another is given. The second problem is a ladder which slides touching a frictionless surface. We use this problem to highlight the fact that the contact forces applied by the surface perform translational and rotational work despite that the total mechanical energy of the ladder is conserved.

physics.ed-ph↗