Quantum algorithm | EPFL Graph Search

In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is usually used for those algorithms which seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement. Problems which are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms interesting is that they might be able to solve some problems faster

Novel materials and algorithms for quantum technologies

Francesco Libbi

The enormous advancements in the ability to detect and manipulate single quantum states have lead to the emerging field of quantum technologies. Among these, quantum computation is the most far-reaching and challenging, aiming to solve problems that the classic computers could never address because of the exponential scaling, while quantum sensing exploits the ability to address single quantum states to realize ultra-sensitive and precise detectors. Defect centers in semiconductors play a primary role in these fields. The possibility to store information in the spin of their ground state, manipulate it through microwaves, and read it optically allows to use them as qubits. In addition, the very sharp dependence of their properties on temperature, strain and magnetic fields makes them very promising quantum sensors. In this Thesis we aim at contributing to the progress of quantum technologies both at the hardware and software level. From a hardware point of view, we study a key property of defect centers in semiconductors, the phonon-assisted luminescence, which can be measured to perform the readout of the information stored in a quantum bit, or to detect temperature variations. We predict the luminescence and study the exciton-phonon couplings within a rigorous many-body perturbation theory framework,an analysis that has never been performed for defect centers.In particular, we study the optical emission of the negatively-charged boron vacancy in 2D hexagonal boron nitride, which currently stands out among defect centers in 2D materials thanks to its promise for applications in quantum information and quantum sensing. We show that phonons are responsible for the observed luminescence, which otherwise would be dark due to symmetry. We also show that the symmetry breaking induced by the static Jahn-Teller effect is not able to describe the presence of the experimentally observed peak at 1.5 eV.The knowledge of the coupling between electrons and phonons is fundamental for the accurate prediction of all the features of the photoluminescence spectrum. However, the large number of atoms in a defect supercell hinders the possibility use density functional perturbation theory to study this coupling. In this work we present a finite-differences technique to calculate the electron-phonon matrix elements, which exploits the symmetries of the defect in such a way to use the very same set of displacement needed for the calculation of phonons. The computation of electron-phonon coupling thus becomes a simple post-processing of the finite-differences phonons calculation. On the quantum software side, we propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the 2-, 3- and 4-site Hubbard models. This novel protocol significantly reduces the number of controlled operations when compared to those previously suggested in literature. Such reduction is quite remarkable when considering the 2-site Hubbard model, for which we show that it is possible to obtain the exact time propagation of the

\ket{N\pm 1}

states by exponentiating one single Pauli component of the Hamiltonian, allowing us to perform the calculations on an actual superconducting quantum processor.

EPFL2022

A quantum algorithm for the direct estimation of the steady state of open quantum systems

Nathan Ramusat, Vincenzo Savona

Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been developed. However, computing the non-equilibrium steady state as the long-time limit of the system dynamics is often not a viable solution, because of exceedingly long transient features or strong quantum correlations in the dynamics. Here, we develop an efficient quantum algorithm for the direct estimation of averaged expectation values of observables on the non-equilibrium steady state, thus bypassing the time integration of the master equation. The algorithm encodes the vectorized representation of the density matrix on a quantum register, and makes use of quantum phase estimation to approximate the eigenvector associated to the zero eigenvalue of the generator of the system dynamics. We show that the output state of the algorithm allows to estimate expectation values of observables on the steady state. Away from critical points, where the Liouvillian gap scales as a power law of the system size, the quantum algorithm performs with exponential advantage compared to exact diagonalization.

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2021

An efficient quantum algorithm for the time evolution of parameterized circuits

Stefano Barison, Giuseppe Carleo, Filippo Vicentini

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected - Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimisation of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimisation algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2021

Novel materials and algorithms for quantum technologies

Francesco Libbi

\ket{N\pm 1}

states by exponentiating one single Pauli component of the Hamiltonian, allowing us to perform the calculations on an actual superconducting quantum processor.

EPFL2022