The noisy gates approach and its applications to quantum computation

Quantum computers promise to reshape the computational landscape, by offering new and faster tools to solve optimization problems, to expand artificial intelligence and to simulate more complex molecules and materials. However, current quantum computers are affected by noises altering their ideal working. The standard belief is that quantum error correction techniques will allow quantum computers to run as expected. However, quantum error correction is a challenge that requires several technological breakthroughs to be successfully implemented. Given the current stage of development of quantum computers, it is not possible to ignore their inherent noises and errors. The practical usage of noisy quantum devices has to be accelerated by pairing improvements of the imperfect hardware with error mitigation strategies, that are software techniques aiming at reducing as much as possible the impact of noises. This sets one of the main goals at this stage: understand and accurately model the effects of noises on quantum computation. In particular there are two key objectives: characterize and model the noises acting on quantum devices and, secondly, have good simulation tools allowing to simulate as accurately as possible the effects of a given noise model on quantum circuits. The core result of this thesis is a new method for simulating the noisy behavior of quantum circuits. The proposed approach, differently from standard approaches, allows for the efficient incorporation of environmental effects in the driven evolution of gates, resulting in what is termed the noisy gates approach. From the computational point of view, the simulation directly models the evolution of state vectors, without requiring evolving density matrices and thus offering a quadratic speed up. The methodology, specified to superconducting devices, is rigorously compared with standard simulations method, demonstrating closer adherence to analytical solutions of the Lindblad equation and to the behavior of real noisy quantum computers. The noisy gate approach emerges as an efficient and more accurate simulation method for noisy quantum circuits. The application of the noisy gate approach is extended to the simulation of noisy optical circuits within the dual rail framework, which is rooted in the second quantization formalism. This makes the adaptation of the approach not straightforward. The noisy version of optical elements is successfully derived, and the versatility of the approach is demonstrated through testing on both gate-based and measurement-based quantum computing models for linear optics. In the second part of the thesis, two complementary results are presented. First, it is shown how a suitable modification of the noisy gates approach can be used to go beyond error analysis in quantum circuits. The thesis introduces an efficient quantum algorithm for simulating open quantum systems, grounded in the generalization of the noisy gate approach to quantum stochastic Schrödinger equations. The algorithm employs random unitary gates acting on system qubits and a single ancillary bath qubit representing the environment. Notably the ancilla overhead remains constant and equal to one, regardless of the system size. Moreover, differently from other approaches, the algorithm provides a perturbative approximation of the full Lindblad equation. Finally, the impact of fundamental noises on superconducting transmon qubits is examined. In particular, the thesis derive the effects of the Continuous Spontaneous Localization (CSL) model, that is an alternative formulation of quantum mechanics coupling the wavefunctions to a classical noise field that collapses superpositions of macroscopic systems. We calculate the steady state quasiparticle density induced by CSL, providing insights into the limitations imposed on the performance of transmon qubits, potentially compromising the practical implementation of large-scale quantum algorithms.