arXiv subjects

Jordi Riu

Publications and source records attributed to Jordi Riu.

8 recordsLinked to original sources

arXiv2026

Reshaping quantum annealing landscapes with diagonal catalysts

Quantum annealing is often limited by population trapped in local minima many spin flips from the solution. We introduce a mathematical framework to understand the connection between energy and Hamming distance in optimization problems. Using this, we build ZZ-catalysts from ground-state patterns of small frustration-free subproblems that make configurations far from the solution less energetically competitive. On sparse problems they multiply the near-solution probability at short sweeps, with gains persisting on fully-connected models and tunable via subproblem choice.

quant-ph↗

arXiv2026

Do quantum linear solvers offer advantage for networks-based system of linear equations?

In this exploratory numerical study, we assess the suitability of Quantum Linear Solvers(QLSs)toward providing a quantum advantage for Networks-based Linear System Problems (NLSPs). NLSPs naturally arise from graphs, and are of importance as they are connected to real-world applications. The achievable advantage with a QLS for an NLSP depends on the interplay between the scaling of condition number and sparsity of matrices associated with the graph family. We analyze 50 graph families and identify that within the scope of our study, only 21 of them exhibit prospects for an exponential advantage with the Harrow-Hassidim-Lloyd (HHL) algorithm relative to an efficient classical solver. We call graph families that offer advantage with HHL as good graph families. We also compare the performance of the considered 50 graph families with 7 other QLSs. Furthermore, we report that some graph families graduate from offering no advantage with HHL to promising an exponential advantage with improved algorithms such as the Childs-Kothari-Somma algorithm. We also introduce a unified graph superfamily and show the existence of infinite good graph families in it. Since the runtime expressions for linear solvers involve condition number, which in itself is not easy to compute, ascertaining advantage prospects with quantum linear solvers itself is not an easy problem. Thus, we conjecture the conditions under which one may visually examine a graph family and guess the prospects for an advantage. Finally, we very briefly touch upon some practical issues that may arise even if the aforementioned graph theoretic requirements are satisfied, including quantum hardware challenges.

quant-ph↗

arXiv2025

Quantum annealing eigensolver as a NISQ era tool for probing strong correlation effects in quantum chemistry

The quantum-classical hybrid variational quantum eigensolver (VQE) algorithm is arguably the most popular noisy intermediate-scale quantum (NISQ) era approach to quantum chemistry. We consider the underexplored quantum annealing eigensolver (QAE) algorithm as a worthy alternative. We use a combination of numerical calculations for a system where strong correlation effects dominate, and conclusions drawn from our preliminary scaling analysis for QAE and VQE to make the case for QAE as a NISQ era contender to VQE for quantum chemistry. For the former, we pick the representative example of computing avoided crossings in the H4 molecule in a rectangular geometry, and demonstrate that we obtain results to within about 1.2% of the full configuration interaction value on the D-Wave Advantage system 4.1 hardware. We carry out analyses on the effect of the number of shots, anneal time, and the choice of Lagrange multiplier on our obtained results. Following our numerical results, we carry out a detailed yet preliminary analysis of the scaling behaviours of both the QAE and the VQE algorithms. We analyze the non-recurring and recurring costs involved in both the algorithms and arrive at their net scaling behaviours.

physics.chem-ph↗

arXiv2025

Trapped ion quantum hardware demonstration of energy calculations using a multireference unitary coupled cluster ansatz: application to the BeH2 insertion problem

In this study, we employ the variational quantum eigensolver algorithm with a multireference unitary coupled cluster ansatz to report the ground state energy of the BeH2 molecule in a geometry where strong correlation effects are significant. We consider the two most important determinants in the construction of the reference state for our ansatz. We remove redundancies in order to execute a redundancy-free calculation. In view of the currently available noisy quantum hardware, we carry out parameter optimization on a classical computer and measure the energy with optimized parameters on a quantum computer. Furthermore, in order to carry out our intended 12-qubit computation with error mitigation and post-selection on a noisy intermediate scale quantum era trapped ion hardware (the commercially available IonQ Forte-I), we perform a series of resource reduction techniques to a. decrease the number of two-qubit gates by 99.84% (from 12243 to 20 two-qubit gates) relative to the unoptimized circuit, and b. reduce the number of measurements via the idea of supercliques, while losing 2.69% in the obtained ground state energy relative to that computed classically for the same resource-optimized problem setting.

physics.chem-ph↗

arXiv2025

Reinforcement Learning Based Quantum Circuit Optimization via ZX-Calculus

We propose a novel Reinforcement Learning (RL) method for optimizing quantum circuits using graph-theoretic simplification rules of ZX-diagrams. The agent, trained using the Proximal Policy Optimization (PPO) algorithm, employs Graph Neural Networks to approximate the policy and value functions. We demonstrate the capacity of our approach by comparing it against the best performing ZX-Calculus-based algorithm for the problem in hand. After training on small Clifford+T circuits of 5-qubits and few tenths of gates, the agent consistently improves the state-of-the-art for this type of circuits, for at least up to 80-qubit and 2100 gates, whilst remaining competitive in terms of computational performance. Additionally, we illustrate the versatility of the agent by incorporating additional optimization routines on the workflow during training, improving the two-qubit gate count state-of-the-art on multiple structured quantum circuits for relevant applications of much larger dimension and different gate distributions than the circuits the agent trains on. This conveys the potential of tailoring the reward function to the specific characteristics of each application and hardware backend. Our approach is a valuable tool for the implementation of quantum algorithms in the near-term intermediate-scale range (NISQ).

quant-ph↗

arXiv2025

Relativistic VQE calculations of molecular electric dipole moments on trapped ion quantum hardware

The quantum-classical hybrid variational quantum eigensolver (VQE) algorithm is among the most actively studied topics in atomic and molecular calculations on quantum computers, yet few studies address properties other than energies or account for relativistic effects. This work presents high-precision 18-qubit relativistic VQE simulations for calculating the permanent electric dipole moments (PDMs) of BeH to RaH molecules on traditional computers, and 6- and 12-qubit PDM computations for SrH on IonQ quantum devices. To achieve high precision on current noisy intermediate scale era quantum hardware, we apply various resource reduction methods, including Reinforcement Learning and causal flow preserving ZX-Calculus routines, along with error mitigation and post-selection techniques. Our approach reduces the two-qubit gate count in our 12-qubit circuit by 99.71%, with only a 2.35% trade-off in precision for PDM when evaluated classically within a suitably chosen active space. On the current generation IonQ Forte-I hardware, the error in PDM is -1.17% relative to classical calculations and only 1.21% compared to the unoptimized circuit.

physics.atom-ph↗

arXiv2024

A coherent approach to quantum-classical optimization

Hybrid quantum-classical optimization techniques, which incorporate the pre-optimization of Variational Quantum Algorithms (VQAs) using Tensor Networks (TNs), have been shown to allow for the reduction of quantum computational resources. In the particular case of large optimization problems, commonly found in real-world use cases, this strategy is almost mandatory to reduce the otherwise unfathomable execution costs and improve the quality of the results. We identify the coherence entropy as a crucial metric in determining the suitability of quantum states as effective initialization candidates. Our findings are validated through extensive numerical tests for the Quantum Approximate Optimization Algorithm (QAOA), in which we find that the optimal initialization states are pure Gibbs states. Further, these results are explained with the inclusion of a simple and yet novel notion of expressivity adapted to classical optimization problems. Based on this finding, we propose a quantum-classical optimization protocol that significantly improves on previous approaches for such tasks, with specific focus on its effectiveness.

quant-ph↗

arXiv2019

Quantum Observables for continuous control of the Quantum Approximate Optimization Algorithm via Reinforcement Learning

We present a classical control mechanism for Quantum devices using Reinforcement Learning. Our strategy is applied to the Quantum Approximate Optimization Algorithm (QAOA) in order to optimize an objective function that encodes a solution to a hard combinatorial problem. This method provides optimal control of the Quantum device following a reformulation of QAOA as an environment where an autonomous classical agent interacts and performs actions to achieve higher rewards. This formulation allows a hybrid classical-Quantum device to train itself from previous executions using a continuous formulation of deep Q-learning to control the continuous degrees of freedom of QAOA. Our approach makes a selective use of Quantum measurements to complete the observations of the Quantum state available to the agent. We run tests of this approach on MAXCUT instances of size up to N = 21 obtaining optimal results. We show how this formulation can be used to transfer the knowledge from shorter training episodes to reach a regime of longer executions where QAOA delivers higher results.

quant-ph↗