Related papers: Scalable Quantum Computation of Highly Excited Eig…
Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block encoded matrices, a central task that lies at the heart of most prominent…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Quantum-selected configuration interaction (QSCI) is an approach for quantum chemical calculations using current quantum computers. In conventional QSCI, Slater determinants used for the wave function expansion are sampled by iteratively…
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
Quantum simulators offer the potential to utilize the quantum nature of a physical system to study another physical system. In contrast to conventional simulation, which experiences an exponential increase in computational complexity,…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications…
Hamiltonian inverse engineering enables the design of protocols for specific quantum evolutions or target state preparation. Perfect state transfer (PST) and remote entanglement generation are notable examples, as they serve as key…
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…
Finding eigenstates of a given many-body Hamiltonian is a long-standing challenge due to the perceived computational complexity. Leveraging on the hardware of a quantum computer accommodating the exponential growth of the Hilbert space size…
Computing the excited states of a given Hamiltonian is computationally hard for large systems, but methods that do so using quantum computers scale tractably. This problem is equivalent to the PCA problem where we are interested in…