arXiv subjects

Mikel Garcia de Andoin

Publications and source records attributed to Mikel Garcia de Andoin.

6 recordsLinked to original sources

arXiv2026

Digital-Analog Quantum Computing with Qudits

Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to $d$-level systems by conjugating an analog Hamiltonian block with single-qudit gates drawn from the Weyl-Heisenberg basis, which provides a natural set of operations for qudit architectures. More specifically, we propose a protocol to simulate arbitrary two-body Hamiltonians with at most $O(d^4 n^2)$ analog blocks. The power of this approach is illustrated by the simulation of many-body qudit spin Hamiltonians including magnetic quadrupolar terms.

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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

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arXiv2024

Mitigating noise in digital and digital-analog quantum computation

Noisy Intermediate-Scale Quantum (NISQ) devices lack error correction, limiting scalability for quantum algorithms. In this context, digital-analog quantum computing (DAQC) offers a more resilient alternative quantum computing paradigm that outperforms digital quantum computation by combining the flexibility of single-qubit gates with the robustness of analog simulations. This work explores the impact of noise on both digital and DAQC paradigms and demonstrates DAQC's effectiveness in error mitigation. We compare the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single and two-qubit noise sources in superconducting processors. DAQC consistently surpasses digital approaches in fidelity, particularly as processor size increases. Moreover, zero-noise extrapolation further enhances DAQC by mitigating decoherence and intrinsic errors, achieving fidelities above 0.95 for 8 qubits, and reducing computation errors to the order of $10^{-3}$. These results establish DAQC as a viable alternative for quantum computing in the NISQ era.

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arXiv2023

Digital-analog quantum simulation of fermionic models

Simulating quantum many-body systems is a highly demanding task since the required resources grow exponentially with the dimension of the system. In the case of fermionic systems, this is even harder since nonlocal interactions emerge due to the antisymmetric character of the fermionic wave function. Here, we introduce a digital-analog quantum algorithm to simulate a wide class of fermionic Hamiltonians including the paradigmatic one-dimensional Fermi-Hubbard model. These digital-analog methods allow quantum algorithms to run beyond digital versions via an efficient use of coherence time. Furthermore, we exemplify our techniques with a low-connected architecture for realistic digital-analog implementations of specific fermionic models.

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arXiv2022

Hybrid Quantum-Classical Heuristic for the Bin Packing Problem

Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum resources. Up to now, many problems of different nature have been addressed through the perspective of this revolutionary computation paradigm, but there are still many open questions. In this work, a hybrid classical-quantum approach is presented for dealing with the one-dimensional Bin Packing Problem (1dBPP). The algorithm comprises two modules, each one designed for being executed in different computational ecosystems. First, a quantum subroutine seeks a set of feasible bin configurations of the problem at hand. Secondly, a classical computation subroutine builds complete solutions to the problem from the subsets given by the quantum subroutine. Being a hybrid solver, we have called our method H-BPP. To test our algorithm, we have built 18 different 1dBPP instances as a benchmarking set, in which we analyse the fitness, the number of solutions and the performance of the QC subroutine. Based on these figures of merit we verify that H-BPP is a valid technique to address the 1dBPP.

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arXiv2021

Implementable Hybrid Quantum Ant Colony Optimization Algorithm

We propose a new hybrid quantum algorithm based on the classical Ant Colony Optimization algorithm to produce approximate solutions for NP-hard problems, in particular optimization problems. First, we discuss some previously proposed Quantum Ant Colony Optimization algorithms, and based on them, we develop an improved algorithm that can be truly implemented on near-term quantum computers. Our iterative algorithm codifies only the information about the pheromones and the exploration parameter in the quantum state, while subrogating the calculation of the numerical result to a classical computer. A new guided exploration strategy is used in order to take advantage of the quantum computation power and generate new possible solutions as a superposition of states. This approach is specially useful to solve constrained optimization problems, where we can implement efficiently the exploration of new paths without having to check the correspondence of a path to a solution before the measurement of the state. As an example of a NP-hard problem, we choose to solve the Quadratic Assignment Problem. The benchmarks made by simulating the noiseless quantum circuit and the experiments made on IBM quantum computers show the validity of the algorithm.

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