Displaying items by tag: NISQ algorithms

Qu&Co comments on this publication:

Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. In Quantum Computational Chemistry solutions, the Variational Quantum Eigensolver (VQE) algorithm offers a hybrid classical-quantum, and thus low quantum circuit depth, alternative to the Phase Estimation algorithm used to measure the ground-state energy of a molecular Hamiltonian. In VQE the quantum computer is used to prepare variational trial states that depend on a set of parameters. Then, the expectation value of the energy is estimated and used by a classical optimizer to generate a new set of improved parameters. The advantage of VQE over classical simulation methods is that in VQE one can prepare trial states that are not amenable to efficient classical numerics. In this paper, Kandala et al. demonstrate the experimental results for determining the ground state energy for molecules of increasing size, up to BeH2 using the VQE algorithm.

Published in Blog

Qu&Co comments on this publication:

Efficient quantum simulations of classically intractable instances of the associated electronic structure problem promise breakthroughs in our understanding of basic chemistry and could revolutionize research into new materials, pharmaceuticals, and industrial catalysts. In Quantum Computational Chemistry solutions, the Variational Quantum Eigensolver (VQE) algorithm offers a hybrid classical-quantum, and thus low quantum circuit depth, alternative to the Phase Estimation algorithm used to measure the ground-state energy of a molecular Hamiltonian. In this paper, Hempel et al. use a digital quantum simulator based on trapped ions to experimentally investigate the VQE algorithm for the calculation of molecular ground state energies of two simple molecules  (H2 and LiH) and experimentally demonstrate and compare different encoding methods using up to four qubits. 

Published in Blog

Qu&Co comments on this publication:

In this paper Bian et al. compare four different quantum simulation methods to simulate the ground state energy of the Hamiltonian for the water molecule on a quantum computer, being 1) the phase estimation algorithm based on Trotter decomposition, 2) phase estimation based on the direct implementation of the Hamiltonian, 3) direct measurement based on the implementation of the Hamiltonian and 4) the variational quantum eigensolver (classical-quantum hybrid) algorithm. They compare a.o. the required number of qubits, gate-complexity, accuracy/error. 

Published in Blog

Qu&Co comments on this publication:

Understanding and modeling the behavior of large numbers of interacting fermions is key to understanding the macroscopic properties of matter. However, the memory required to represent such a many-body state scales exponentially with the number of fermions, which makes simulation of many interesting cases intractable on classical computers. Algorithms leveraging the advantages of quantum computers for quantum simulations have steadily been developed in the past two decades. Variational quantum eigensolvers (VQE) have recently appeared as a promising class of quantum algorithms designed to prepare states for such quantum simulations. Low-depth circuits for such state preparation and quantum simulation are needed for practical quantum chemistry applications on near-term quantum devices with limited coherence. In this paper, Dallaire-Demers et al. present a new type of low-depth VQE ansatz, which should be in reach of near-term quantum devices and which can accurately prepare the ground state of correlated fermionic systems.

Published in Blog

Qu&Co comments on this publication:

Quantum computers promise to reduce the computational complexity of simulating quantum many-body systems from exponential to polynomial. Much effort is being put in reducing the complexity of the necessary algorithms, to allow them to be run on noisy intermediate scale quantum computers. In this paper, Dumitrescu et al. report a quantum simulation of the deuteron binding energy on 2 such small-scale noisy cloud accessible quantum processors (the IBM QX5 and Rigetti 19Q).

Published in Blog

Qu&Co comments on this publication:

One hallmark problem in computational linear algebra is the binary linear least squares (BLLS), which is formally in the NP-Hard complexity class. Efficient classical methods for solving this problem exists with limited approximations to the solution. Quantum computing may solve these problems with a better approximation ratio and/or in a faster runtime scaling. So-far, this problem has only been considered on a quantum annealing by mapping it to a QUBO. In this paper, the problem is solved using a QAOA approach on the gate-based model of quantum computing. The performance is assessed both on a wavefunction simulator, shotnoise simulator and on the 5-qubit IBM cloud computing quantum device ibmq_london. As an outlook: BLLS may serve as a building block for other problems such as Non-negative Binary Matrix Factorization, or clubbed together for a fixed-point approximation of real variables. This paper was partially supervised by Vincent Elfving from Qu & Co.

Published in Blog

Qu&Co comments on this publication:

In this paper, Patrick J. Coles et al., aim to explain the principles of quantum programming straight-forward algebra that makes understanding the underlying quantum mechanics optional (but still fascinating). The authors give an introduction to quantum computing algorithms and their implementation on real quantum hardware and survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. They show how these algorithms can be implemented on an actual quantum-processor (in this case an IBM QPU) and in each case discuss the results of the implementation with respect to differences of the results on a simulator (QVM) or the actual processor (QPU).

Published in Blog
Tagged under
Page 3 of 3

What's Interesting?

How can we help you?

Invalid Input

Invalid Input

Invalid Input

Invalid Input

Invalid Input

Invalid Input

Copyright © Qu & Co BV
close