Decoherence and Stochastic Schrödinger Equations: Applications to Quantum Computing and Wave Function Collapse Models

The primary results of this thesis demonstrate how Stochastic Schrödinger Equations (SSEs) can be effectively utilized in a novel manner to both simulate the dynamics of open quantum systems on quantum computers and model the behavior of noisy quantum devices. We developed an efficient quantum algorithm leveraging Quantum Stochastic Differential Equations (QSDEs) for simulating Lindblad dynamics. The algorithm employs random unitary gates on a set of n system qubits and, remarkably, only a single ancillary qubit representing the environment. This advancement is particularly significant for near-term quantum computers, where minimizing the circuit width is crucial due to inherent noise.. While our algorithm is fundamentally designed for noise-free quantum computers, current technological limitations mean that we cannot avoid their intrinsic noisy behavior due to unwanted interactions with the surrounding environment. Consequently, we investigate the impact of noise on quantum simulations. Standard methods for classically simulating noisy quantum circuits effectively decouple the action of the gate from the noise. While this approximation is valid when quantum gates operate almost instantaneously relative to the noise, it has limitations, as quantum gates and noise can potentially influence each other during gate execution. To address this, we propose an alternative simulation method, the Noisy Gates approach. We successfully apply the Noisy Gates approach to simulate superconducting devices and dual-rail encoding photonic platforms. The second part of the research activity focused on building and studying the simplest universal dissipative Lindblad master equation for many-body systems with the purpose of a new dissipative extension of existing non-relativistic theories of fundamental spontaneous decoherence and spontaneous wave function collapse. Then, we establish experimental bounds on free parameters of the so-constructed linear-friction dissipative Diósi-Penrose (dDP) and Continuous Spontaneous localisation (dCSL) models by exploiting experiments in the field of levitated optomechanics. Specifically, we analyze the dynamics of the center of mass of a rigid body composed of N particles and after having suitably linearised the dynamics, we derive the modified Langevin equations describing the dynamics of the mechanical oscillator.

The primary results of this thesis demonstrate how Stochastic Schrodinger Equations (SSEs) can be effectively utilized in a novel manner to both simulate the dynamics of open quantum systems on quantum computers and model the behavior of noisy quantum devices. We developed an efficient quantum algorithm leveraging Quantum Stochastic Differential Equations (QSDEs) for simulating Lindblad dynamics. The algorithm employs random unitary gates on a set of n system qubits and, remarkably, only a single ancillary qubit representing the environment. This advancement is particularly significant for near-term quantum computers, where minimizing the circuit width is crucial due to inherent noise.. While our algorithm is fundamentally designed for noise-free quantum computers, current technological limitations mean that we cannot avoid their intrinsic noisy behavior due to unwanted interactions with the surrounding environment. Consequently, we investigate the impact of noise on quantum simulations. Standard methods for classically simulating noisy quantum circuits effectively decouple the action of the gate from the noise. While this approximation is valid when quantum gates operate almost instantaneously relative to the noise, it has limitations, as quantum gates and noise can potentially influence each other during gate execution. To address this, we propose an alternative simulation method, the Noisy Gates approach. We successfully apply the Noisy Gates approach to simulate superconducting devices and dual-rail encoding photonic platforms. The second part of the research activity focused on building and studying the simplest universal dissipative Lindblad master equation for many-body systems with the purpose of a new dissipative extension of existing non-relativistic theories of fundamental spontaneous decoherence and spontaneous wave function collapse. Then, we establish experimental bounds on free parameters of the so-constructed linear-friction dissipative Diósi-Penrose (dDP) and Continuous Spontaneous localisation (dCSL) models by exploiting experiments in the field of levitated optomechanics. Specifically, we analyze the dynamics of the center of mass of a rigid body composed of N particles and after having suitably linearised the dynamics, we derive the modified Langevin equations describing the dynamics of the mechanical oscillator.