Quantum algorithms offer significant speed-ups over their classical counterparts for a variety
of problems. The strongest arguments for this advantage are borne by algorithms for …

Under suitable assumptions, some recently developed quantum algorithms can estimate the
ground-state energy and prepare the ground state of a quantum Hamiltonian with near …

We present the problem of approximating the time-evolution operator $ e^{-i\hat {H} t} $ to
error $\epsilon $, where the Hamiltonian $\hat {H}=(\langle G|\otimes\hat {\mathcal {I}})\hat …

Quantum signal processing (QSP) and quantum singular value transformation (QSVT)
currently stand as the most efficient techniques for implementing functions of block-encoded …

Preparing the ground state of a given Hamiltonian and estimating its ground energy are
important but computationally hard tasks. However, given some additional information, these …

We study the problem of simulating the time evolution of a lattice Hamiltonian, where the
qubits are laid out on a lattice and the Hamiltonian only includes geometrically local …

Preconditioning is the most widely used and effective way for treating ill-conditioned linear
systems in the context of classical iterative linear system solvers. We introduce a quantum …

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement
matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms …

Preparing ground states and thermal states is essential for simulating quantum systems on
quantum computers. Despite the hope for practical quantum advantage in quantum …

Many standard linear algebra problems can be solved on a quantum computer by using
recently developed quantum linear algebra algorithms that make use of block encodings …