Related papers: Real-Time Krylov Theory for Quantum Computing Algo…
We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given…
Predicting ground state energies of quantum many-body systems is one of the central computational challenges in quantum chemistry, physics, and materials science. Krylov subspace methods, such as Krylov Quantum Diagonalization and…
The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy intermediate-scale quantum (NISQ) devices. A particular application is to obtain ground…
The preparation of Hamiltonian eigenstates is essential for many applications in quantum computing; the efficiency with which this can be done is of key interest. A canonical approach exploits the quantum phase estimation (QPE) algorithm.…
Recent research has shown that wavefunction evolution in real- and imaginary-time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum…
We propose an extended version of the symmetry-adapted variational-quantum-eigensolver (VQE) and apply it to a two-component Fermi-Hubbard model on a bipartite lattice. In the extended symmetry-adapted VQE method, the Rayleigh quotient for…
Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE)…
Quantum chemistry applications on quantum computers currently rely heavily on the variational quantum eigensolver (VQE) algorithm. This hybrid quantum-classical algorithm aims at finding ground state solutions of molecular systems based on…
Simulating quantum imaginary-time evolution (QITE) is a major promise of quantum computation. However, the known algorithms are either probabilistic (repeat until success) with impractically small success probabilities or coherent (quantum…
Computing eigenvalues is a computationally intensive task central to numerous applications in the natural sciences. Toward this end, we investigate the quantum block Krylov subspace projector (QBKSP) algorithm - a multireference quantum…
Variational Quantum Imaginary Time Evolution (VQITE) is a leading technique for ground state preparation on quantum computers. A significant computational challenge of VQITE is the determination of the quantum geometric tensor. We show that…
The Krylov subspace method is a standard approach to approximate quantum evolution, allowing to treat systems with large Hilbert spaces. Although its application is general, and suitable for many-body systems, estimation of the committed…
We present an algorithm that uses block encoding on a quantum computer to exactly construct a Krylov space, which can be used as the basis for the Lanczos method to estimate extremal eigenvalues of Hamiltonians. While the classical Lanczos…
The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. We do not expect to be able to afford the overhead required for quantum error correction in…
The variational quantum eigensolver (VQE) is an algorithm for finding the ground states of a given Hamiltonian. Its application to binary-formulated combinatorial optimization (CO) has been widely studied in recent years. However, typical…
Quantum computing technology has the potential to revolutionize the simulation of materials and molecules in the near future. A primary challenge in achieving near-term quantum advantage is effectively mitigating the noise effects inherent…
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…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a…
Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…