Together towards quantum advantage

Quantum computing made relevant for you

from qucochemistry.vqe import VQEexperiment from openfermion.hamiltonians import MolecularData
filename = 'molecules/H2_pyscf_equi.hdf5'
molecule = MolecularData(filename=filename)
vqe = VQEexperiment(molecule=molecule)
E = vqe.get_exact_gs()
result = vqe.get_results()
print('Difference between VQE optimized and exact GS energy:')
print(str(( + 'kcal/mol')

I highly value our research collaboration with Qu&Co because, with their deep understanding of the computational needs of their clients, we can finally develop truly relevant quantum solutions

dr. Oleksandr Kyriienko, University of Exeter

What do we offer?

Quantum algorithm research with scientific rigor

"Solving nonlinear differential equations with differentiable quantum circuits"

Qu&Co in collaboration with our academic advisor Oleksandr Kyriienko at the University of Exeter has developed a proprietary quantum algorithm which promises a generic and efficient way to solve nonlinear differential equations. The algorithm is compatible with near-term quantum-processors, with promising extensions for fault-tolerant implementation. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to represent function derivatives in an analytical form as differentiable quantum circuits (DQCs), thus avoiding inaccurate finite difference procedures for calculating gradients. We describe a hybrid quantum-classical workflow where DQCs are trained to satisfy differential equations and specified boundary conditions. As a particular example setting, we show how this approach can implement a spectral method for solving differential equations in a high-dimensional feature space. From a technical perspective, we design a Chebyshev quantum feature map that offers a powerful basis set of fitting polynomials and possesses rich expressivity. We simulate the algorithm to solve an instance of Navier-Stokes equations, and compute density, temperature and velocity profiles for the fluid flow in a convergent-divergent nozzle.

This manuscript describes results from an ongoing collaboration betweenn the University of Exeter and Qu&Co.

"How will quantum computers provide a relevant computational advantage in quantum chemistry?"

In this work we review the current status, and potential future outlook, of quantum hardware and algorithm theory in the field of quantum chemistry simulations. We go over subtle complications of quantum chemical research that tend to be overlooked in discussions involving quantum computers. As particular examples of the resources and timings associated with classical and quantum computer simulations, we compare the molecules H2 for increasing basis set sizes, and Cr2 for a variety of complete active spaces (CAS) and simulated to chemical accuracy within that orbital set. The results enable us to estimate the size of the active space at which computations of non-dynamic correlation on a quantum computer should take less time than on a classical computer. Using this result, we speculate on the types of chemical applications for which the use of quantum computers would be both beneficial and relevant to industrial applications in the short term.

This manuscript materialized from the collaboration between Schrödinger and Qu & Co.

"Quantum Approximate Optimization for Hard Problems in Linear Algebra"

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 project was partially supervised by Vincent Elfving from Qu & Co.

"Simulating quantum chemistry in the restricted Hartree-Fock space on a qubit-based quantum computing device"

Accurate quantum chemistry simulations remain challenging on classical computers for problems of industrially relevant sizes and there is reason for hope that quantum computing may help push the boundaries of what is technically feasible. We in this research combine the so-called paired-electron approximation with techniques for simulating molecular chemistry on gate-based quantum computers and obtained a much more resource efficient algorithm, with little accuracy loss. We require half as many qubits, or conversely can increase the considered basis set size, which in turn leads to more accurate results together with reductions in the necessary number of quantum computing runs (shots) by several orders of magnitude, with runtime estimates and coherence requirements favourable to NISQ implementation.

This manuscript describes results from an ongoing collaboration between Covestro and Qu&Co

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