Related papers: Quantum expectation value estimation by doubling t…
In projective measurements of energy, a target system is projected to an eigenstate of the system Hamiltonian, and the measurement outcomes provide the information of corresponding eigen-energies. Recently, it has been shown that such a…
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to…
We propose a new quantum computational way of obtaining a ground-state energy and expectation values of observables of interacting Hamiltonians. It is based on the combination of the adiabatic quantum evolution to project a ground state of…
Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give…
Trotter approximation in conjunction with Quantum Phase Estimation can be used to extract eigen-energies of a many-body Hamiltonian on a quantum computer. There were several ways proposed to assess the quality of this approximation based on…
The quantum information science community has seen a surge in new algorithmic developments across scientific domains. These developments have demonstrated polynomial or better improvements in computational and space complexity,…
Recent advances in quantum computing devices have brought attention to hybrid quantum-classical algorithms like the Variational Quantum Eigensolver (VQE) as a potential route to practical quantum advantage in chemistry. However, it is not…
Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $\epsilon$ in Heisenberg-limited time $T=\Theta(1/\epsilon)$. Standard gate-based implementations of QPE require…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
We describe an algorithm for finding angle sequences in quantum signal processing, with a novel component we call halving based on a new algebraic uniqueness theorem, and another we call capitalization. We present both theoretical and…
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational…
Quantum sensors are among the most promising quantum technologies, allowing to attain the ultimate precision limit for parameter estimation. In order to achieve this, it is required to fully control and optimize what constitutes the…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
Here we revisit one of the prototypical tasks for characterizing the structure of noise in quantum devices: estimating every eigenvalue of an $n$-qubit Pauli noise channel to error $\epsilon$. Prior work [14] proved no-go theorems for this…
Characterization of qubit couplings in many-body quantum systems is essential for benchmarking quantum computation and simulation. We propose a tomographic measurement scheme to determine all the coupling terms in a general many-body…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…