Related papers: NISQ algorithm for the matrix elements of a generi…
We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…
Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that…
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…
Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for these algorithms require…
Variational Quantum Algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In variational quantum algorithm, wavefunction represented by a parametrized…
We discuss a method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal,…
We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the…
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…
Efficient computation of molecular energies is an exciting application of quantum computing for quantum chemistry, but current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, limiting existing variational…
The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular…
Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this work we introduce a method for…
We propose a variational method for constructing the eigenvalues and generalized eigenvalues for an arbitrary $N\times N$ complex matrix. The quantum part of our algorithm is based on encoding the matrix elements into the pure state of a…
The recently developed Projective Quantum Eigensolver (PQE) has been demonstrated as an elegant methodology to compute the ground state energy of molecular systems in Noisy Intermdiate Scale Quantum (NISQ) devices. The iterative…
We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a…
Quantum networks are of high interest nowadays. In short, they describe the distribution of quantum sources represented by edges to different parties represented by nodes in the networks. Bundles of tools have been developed recently to…
We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical…
Efficient classical simulation of noisy intermediate-scale quantum (NISQ) circuits has been a topic of intense study over the past few years. The majority of results on efficient simulation assume that the circuits undergo some variant of…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
A practical fault-tolerant quantum computer is worth looking forward to as it provides applications that outperform their known classical counterparts. However, millions of interacting qubits with stringent criteria are required, which is…