arXiv subjects

Peniel Bertrand Tsemo

Publications and source records attributed to Peniel Bertrand Tsemo.

3 recordsLinked to original sources

arXiv2026

Quantum linear solvers for quantum chemistry: prospects of exponential quantum advantage

Quantum linear solvers (QLSs) can offer the potential for exponential quantum advantage in solving quantum chemical problems, but its assessment hinges on determining the condition number ($κ$) scaling, which itself is computationally challenging. While a recent work applied the Harrow-Hassidim-Lloyd (HHL) algorithm to single-reference linearized coupled cluster equations (SRLCC), the validity of the HHL-SRLCC framework is restricted to weakly correlated regimes. A general treatment requires a formulation that can access strongly correlated regions. We thus begin by extending the QLS-SRLCC framework to its multi-reference form, which is based on the internally contracted multi-reference LCC method (QLS-icMRLCC). We then analyze $κ$ scaling using three complementary diagnostics that range from explicit computations to use of indirect structural indicators: (i) direct calculations of $κ$, (ii) scaling of the ratio of maximum to minimum diagonal entries of an A matrix, and (iii) structural analyses of the A matrices based on a recently proposed conjecture, which we adapt to the QLS-LCC problem. The three approaches yield consistent predictions, indicating a polylogarithmic $κ$ scaling in system size. This finding, when combined with our arguments on sub-linear scaling of sparsity, supports the prospects of exponential advantage using QLSs for the LCC problem. Finally, numerical calculations on potential energy curves of model systems containing up to four atoms recover the ground state energies with errors relative to benchmark classical methods not exceeding 0.009$\%$.

quant-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

Enhancing the Harrow-Hassidim-Lloyd (HHL) algorithm in systems with large condition numbers

Although the Harrow-Hassidim-Lloyd (HHL) algorithm offers an exponential speedup in system size for treating linear equations of the form $A\vec{x}=\vec{b}$ on quantum computers when compared to their traditional counterparts, it faces a challenge related to the condition number ($\mathcalκ$) scaling of the $A$ matrix. In this work, we address the issue by introducing the post-selection-improved HHL (Psi-HHL) framework that operates on a simple yet effective premise: subtracting mixed and wrong signals to extract correct signals while providing the benefit of optimal scaling in the condition number of $A$ (denoted as $\mathcalκ$) for large $\mathcalκ$ scenarios. This approach, which leads to minimal increase in circuit depth, has the important practical implication of having to use substantially fewer shots relative to the traditional HHL algorithm. The term `signal' refers to a feature of $|x\rangle$. We design circuits for overlap and expectation value estimation in the Psi-HHL framework. We demonstrate performance of Psi-HHL via numerical simulations. We carry out two sets of computations, where we go up to 26-qubit calculations, to demonstrate the ability of Psi-HHL to handle situations involving large $\mathcalκ$ matrices via: (a) a set of toy matrices, for which we go up to size $64 \times 64$ and $\mathcalκ$ values of up to $\approx$ 1 million, and (b) application to quantum chemistry, where we consider matrices up to size $256 \times 256$ that reach $\mathcalκ$ of about 393. The molecular systems that we consider are Li$_{\mathrm{2}}$, KH, RbH, and CsH.

physics.atom-ph↗