Related papers: Robust ground-state energy estimation under depola…
A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…
While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical…
In 2011, the fundamental gap conjecture for Schr\"odinger operators was proven. This can be used to estimate the ground state energy of the time-independent Schr\"odinger equation with a convex potential and relative error \epsilon.…
Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…
Quantum annealing (QA) is one of the efficient methods to calculate the ground-state energy of a problem Hamiltonian. In the absence of noise, QA can accurately estimate the ground-state energy if the adiabatic condition is satisfied.…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
Fidelity is one of the most valuable and commonly used metrics for assessing the performance of quantum circuits on error-prone quantum processors. Several approaches have been proposed to estimate circuit fidelity without executing it on…
Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
Reflecting the increasing interest in quantum computing, the variational quantum eigensolver (VQE) has attracted much attentions as a possible application of near-term quantum computers. Although the VQE has often been applied to quantum…
Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. As a novel approach, quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the…
Estimating molecular ground-state energies is a central application of quantum computing, requiring both the preparation of accurate quantum states and efficient energy readout. Understanding the effect of hardware noise on these…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
Quantum phase estimation (QPE) is a cornerstone algorithm for extracting Hamiltonian eigenvalues, but its standard, eigenstate-centric form relies on carefully prepared coherent inputs that are costly or impractical for many strongly…
We present error mitigation (EM) techniques for noisy intermediate-scale quantum computers (QC) based on density matrix purification and perturbative corrections to the target energy. We incorporate this scheme into the variational quantum…
Quantum computers hold immense potential in the field of chemistry, ushering new frontiers to solve complex many body problems that are beyond the reach of classical computers. However, noise in the current quantum hardware limits their…
Over the past three decades significant reductions have been made to the cost of estimating ground-state energies of molecular Hamiltonians with quantum computers. However, comparatively little attention has been paid to estimating the…