We develop quantum computational tools to predict the 3D structure of proteins, one of the most important problems in current biochemical research. We explain how to combine recent deep learning advances with the well known technique of quantum walks applied to a Metropolis algorithm. The result, QFold, is a fully scalable hybrid quantum algorithm that, in contrast to previous quantum approaches, does not require a lattice model simplification and instead relies on the much more realistic assumption of parameterization in terms of torsion angles of the amino acids. We compare it with its classical analog for different annealing schedules and find a polynomial quantum advantage, and implement a minimal realization of the quantum Metropolis in IBMQ Casablanca quantum system.

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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 √ n(n + m)||M ||Fκ −2 ) for n the number of variables in the cost function, m the number of constraints, −1 the target precision, L the bit length of the input data, ||M ||F an upper bound to the Frobenius norm of the linear systems of equations that appear, ||M ||F , andκ an upper bound to the condition number κ 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 classical algorithms such as Conjugate Gradient Descent, that would mean the whole algorithm has complexity O(L √ n(n+m) 2κ log( −1 )), or with exact methods, at least O(L √ 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.

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Quantum Phase Estimation is one of the most useful quantum computing algorithms for quantum chemistry and as such, significant effort has been devoted to designing efficient implementations. In this article, we introduce TFermion, a library designed to estimate the T-gate cost of such algorithms, for an arbitrary molecule. As examples of usage, we estimate the T-gate cost of a few simple molecules and compare the same Taylorization algorithms using Gaussian and plane-wave basis.