Related papers: Detailed Error Analysis of the HHL Algorithm
We propose a novel quantum algorithm for solving nuclear resonances, which is based on the iterative Harrow-Hassidim-Lloyd algorithm and eigenvector continuation with complex scaling. To validate this approach, we compute the resonant…
We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a…
Quantum algorithms have the ability to reduce runtime for executing tasks beyond the capabilities of classical algorithms. Therefore, identifying the resources responsible for quantum advantages is an interesting endeavour. We prove that…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$…
The eigenvalue of a Hamiltonian, $\mathcal{H}$, can be estimated through the phase estimation algorithm given the matrix exponential of the Hamiltonian, $exp(-i\mathcal{H})$. The difficulty of this exponentiation impedes the applications of…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the…
The evaluation of one-loop matrix elements is one of the main bottlenecks in precision calculations for the high-luminosity phase of the Large Hadron Collider. To alleviate this problem, a new C++ interface to the MCFM parton-level Monte…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…
We propose a general-purpose quantum algorithm for preparing ground states of quantum Hamiltonians from a given trial state. The algorithm is based on techniques recently developed in the context of solving the quantum linear systems…
Harrow-Hassidim-Lloyd algorithm (HHL) allows for the exponentially faster solution of a system of linear equations. However, this algorithm requires the postselection of an ancilla qubit to obtain the solution. This postselection makes the…
Experimental realization of automated error correction is demonstrated through IBM Quantum Experience for Bell and GHZ states using a measurement based approach upon ancilla qubits. The measurement automatically activates error correcting…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…