Related papers: Phase estimation using an approximate eigenstate
The random phase approximation (RPA) as formulated as an orbital-dependent, fifth-rung functional within the density functional theory (DFT) framework offers a promising approach for calculating the ground-state energies and the derived…
Computing the excited states of a given Hamiltonian is computationally hard for large systems, but methods that do so using quantum computers scale tractably. This problem is equivalent to the PCA problem where we are interested in…
We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…
We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one…
Quantum phase estimation is fundamental to advancing quantum science and technology. While much of the research has concentrated on estimating a single phase, the simultaneous estimation of multiple phases can yield significantly enhanced…
In this work we investigate a binned version of Quantum Phase Estimation (QPE) set out by [Somma 2019] and known as the Quantum Eigenvalue Estimation Problem (QEEP). Specifically, we determine whether the circuit decomposition techniques we…
The random phase approximation (RPA) and the $GW$ approximation share the same total energy functional but RPA is defined on a restricted domain of Green's functions determined by a local Kohn-Sham (KS) potential. In this work, we perform…
Quantum chemistry is envisioned as an early and disruptive application for quantum computers. Yet, closer scrutiny of the proposed algorithms shows that there are considerable difficulties along the way. Here, we propose two criteria for…
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…
In this paper, we present an online adaptive PCA algorithm that is able to compute the full dimensional eigenspace per new time-step of sequential data. The algorithm is based on a one-step update rule that considers all second order…
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the…
The Quasiparticle Random Phase Approximation equations are solved taking into account the Pauli Principle at the expectation value level, and allowing changes in the mean field occupation numbers to minimize the energy while having the…
Simulating time evolution under quantum Hamiltonians is one of the most natural applications of quantum computers. We introduce TE-PAI, which simulates time evolution exactly by sampling random quantum circuits for the purpose of estimating…
Distributed quantum computation is the key to high volume computation in the NISQ era. This investigation explores the key aspects necessary for the construction of a quantum network by numerically simulating the execution of the…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
Apoptosis is one of the most basic biological processes. In apoptosis, tens of species are involved in many biochemical reactions with times scales of widely differing orders of magnitude. By the law of mass action, the process is…
The unavoidable finite time intervals between the sequential operations needed for performing practical quantum computing can degrade the performance of quantum computers. During these delays, unwanted relative dynamical phases are produced…
Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There…