arXiv subjects

K. Sugisaki

Publications and source records attributed to K. Sugisaki.

4 recordsLinked to original sources

arXiv2025

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

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↗

arXiv2023

Adapting the HHL algorithm to quantum many-body theory

Rapid progress in developing near- and long-term quantum algorithms for quantum chemistry has provided us with an impetus to move beyond traditional approaches and explore new ways to apply quantum computing to electronic structure calculations. In this work, we identify the connection between quantum many-body theory and a quantum linear solver, and implement the Harrow-Hassidim-Lloyd (HHL) algorithm to make precise predictions of correlation energies for light molecular systems via the (non-unitary) linearised coupled cluster theory. We alter the HHL algorithm to integrate two novel aspects- (a) we prescribe a novel scaling approach that allows one to scale any arbitrary symmetric positive definite matrix A, to solve for Ax = b and achieve x with reasonable precision, all the while without having to compute the eigenvalues of A, and (b) we devise techniques that reduce the depth of the overall circuit. In this context, we introduce the following variants of HHL for different eras of quantum computing- AdaptHHLite in its appropriate forms for noisy intermediate scale quantum (NISQ), late-NISQ, and the early fault-tolerant eras, as well as AdaptHHL for the fault-tolerant quantum computing era. We demonstrate the ability of the NISQ variant of AdaptHHLite to capture correlation energy precisely, while simultaneously being resource-lean, using simulation as well as the 11-qubit IonQ quantum hardware.

quant-ph↗

arXiv2023

Accurate Computation of Relativistic Excitation Energies Using Quantum Annealing

We report the first results for the computation of relativistic effects in quantum many-body systems using quantum annealers. An average accuracy of 98.9% in the fine structure splitting of boron-like ions with respect to experiments has been achieved using the Quantum Annealer Eigensolver (QAE) algorithm on the D-Wave Advantage hardware. We obtain these results in the framework of the many-electron Dirac theory. We implement QAE through our quantum annealing workflow that includes a novel qubit encoding scheme and a perturbation theory-based decomposition strategy.

quant-ph↗