Related papers: The quantum super-Krylov method
Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground and excited-state energies of a quantum many-body system. While QKSD…
Quantum algorithms based on classical processing of individual samples have recently emerged as the most effective and robust methods to approximate ground-state wave functions of many-body quantum systems on pre-fault-tolerant and…
We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov…
Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD…
Quantum Krylov subspace diagonalization (QKSD) is an emerging method used in place of quantum phase estimation in the early fault-tolerant era, where limited quantum circuit depth is available. In contrast to the classical Krylov subspace…
Quantum Krylov subspace diagonalization is a prominent candidate for early fault tolerant quantum simulation of many-body and molecular systems, but so far the focus has been mainly on computing ground-state energies. We go beyond this by…
The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for…
Approximating the ground state of many-body systems is a key computational bottleneck underlying important applications in physics and chemistry. The most widely known quantum algorithm for ground state approximation, quantum phase…
We evaluate the Sample-based Krylov Quantum Diagonalization (SKQD) algorithm on one- and two-dimensional Heisenberg models, including strongly correlated regimes in which the ground state is dense. Using problem-informed initial states and…
Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the…
Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in…
We apply the recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) method to lattice gauge theories, using the Schwinger model with a $\theta$-term as a benchmark. SKQD approximates the ground state of a Hamiltonian,…
Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy…
Quantum subspace diagonalization and quantum Krylov algorithms offer a feasible, pre- or early-fault tolerant alternative to quantum phase estimation for using quantum computers to estimate the low-lying spectra of quantum systems. However,…
Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in…
Simulating quantum systems is one of the most promising tasks where quantum computing can potentially outperform classical computing. However, the robustness needed for reliable simulations of medium to large systems is beyond the reach of…
This thesis investigates sampling-based quantum algorithms for electronic ground state energy estimation, focusing on Quantum-Selected Configuration Interaction (QSCI) and Sample-Based Quantum Diagonalization (SQD) as near-term alternatives…
Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a…
Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting…
Krylov subspace methods are among the most extensively studied early fault-tolerant quantum algorithms for estimating ground-state energies of quantum systems. However, the rapid onset of ill-conditioning might make accurate energies…