quantumalgorithms on noisy intermediate-scale quantum ( NISQ) devices are expected to soon simulate quantum systems that are classically intractable. However, the non- negligible gate error present on NISQ devices im...
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quantumalgorithms on noisy intermediate-scale quantum ( NISQ) devices are expected to soon simulate quantum systems that are classically intractable. However, the non- negligible gate error present on NISQ devices impedes the implementation of many purely quantumalgorithms, necessitating the use of hybrid quantum-classical algorithms. One such hybridquantum- classicalalgorithm, is based upon quantum computed Hamiltonian moments.j <^> H n j.D E on 1/4 1,2, THORN, with respect to quantum state j.i. In this tutorial review, we will give a brief review of these quantumalgorithms with focuses on the typical ways of computing Hamiltonian moments using quantum hardware and improving the accuracy of the estimated state energies based on the quantum computed moments. We also present a computation of the Hamiltonian moments of a four-site Heisenberg model and compute the energy and magnetization of the model utilizing the imaginary time evolution on current IBM-Q hardware. Finally, we discuss some possible developments and applications of Hamiltonian moment methods.
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the quantum Phase Estimation algorithm, which stores the sign ...
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An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a Hermitian matrix in one ancillary qubit. The signature of the matrix is extracted from the mean value of a spin operator in this single ancillary qubit. The algorithm is probabilistic, but it shows good performance, achieving 97% of correct classifications with few qubits. The computational cost scales comparably to the classical one in the case of a generic matrix, but improves significantly for restricted classes of matrices like k-local or sparse Hamiltonians.
hybridquantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an...
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hybridquantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an efficient variational optimization approach to simulate open system dynamics under the Noisy-Intermediate Scale quantum computer. Using the time-dependent variational principle (TDVP) method and extending it to McLachlan TDVP for density matrix which involves minimization of Frobenius norm of the error, we apply the unitary quantum circuit to obtain the time evolution of the open quantum system in the Lindblad formalism. Finally, we illustrate the use of our methods with detailed examples which are in good agreement with analytical calculations.
We introduce a new quantum optimization algorithm for dense linear programming problems, which can be seen as the quantization of the interior point predictor-corrector algorithm [1] using a quantum linear system algo...
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We introduce a new quantum optimization algorithm for dense linear programming problems, which can be seen as the quantization of the interior point predictor-corrector algorithm [1] using a quantum linear system algorithm [2]. The (worst case) work complexity of our method is, up to polylogarithmic factors, O(L root n(n+m)(parallel to M parallel to) over bar (F) (kappa)over bar> over bar epsilon(-2)) for n the number of variables in the cost function,mthe number of constraints,epsilon(-1)the target precision,Lthe bit length of the input data, (parallel to M parallel to) over bar (F) over bar (F), and (kappa) over bar an upper bound to the condition number kappa of those systems of equations. This represents a quantum speed-up in the number n of variables in the cost function with respect to the comparable classical interior point algorithms when the initial matrix of the problem A is dense: if we substitute the quantum part of the algorithm by classicalalgorithms such as conjugate gradient descent, that would mean the whole algorithm has complexity O(L root n(n + m)(2) (kappa) over bar log(epsilon(-1))), or with exact methods, at least O(L root n(n + m)(2.373)). Also, in contrast with any quantum linear system algorithm, the algorithm described in this article outputs a classical description of the solution vector, and the value of the optimal solution.
Variational quantum-classicalhybridalgorithms are emerging as important tools for simulating quantum chemistry with quantum devices. These algorithms can be applied to evaluate various molecular properties, includin...
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Variational quantum-classicalhybridalgorithms are emerging as important tools for simulating quantum chemistry with quantum devices. These algorithms can be applied to evaluate various molecular properties, including potential energy surfaces. Here in, recent progresses on the development of the so-called variational quantum eigensolver (VQE) are surveyed. The eigensolver aims at reducing the consumption of quantum resources as much as possible. The key feature of VQE is that variation quantum states are optimized by a feedback process, where the measurement of the Hamiltonian is implemented term by term. This approach avoids the need of encoding all of the information about the molecular Hamiltonian in a quantum circuit. The VQE method is also compatible with classical methods in quantum chemistry, such as unitary coupled-cluster ansatz. Furthermore, basic elements of VQE are covered, such as qubit encoding, mapping rules of the fermionic operators, ansatz preparation, together with several techniques for improving the performance, including constraining, and error mitigation.
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