Related papers: Threshold theorem in isolated quantum dynamics wit…
In this paper, the optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the…
In this work, we present analytical solution of Schr\"odinger equation of confined pseudoharmonic potential in presence of a moving boundary condition, for an arbitrary angular momentum state. It turns out that an important quantity to…
This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…
We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla…
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and…
We consider an agent trying to bring a system to an acceptable state by repeated probabilistic action. Several recent works on algorithmizations of the Lovasz Local Lemma (LLL) can be seen as establishing sufficient conditions for the agent…
Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of probabilistic…
Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field…
We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such…
Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we…
Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control -- it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence,…
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
This approach to the incorporation of stochastic thermodynamics into quantum theory is based on the conception of consistent inclusion of the holistic stochastic environmental influence described by wave functions of the arbitrary vacuum,…
In this paper, we consider a general time-inconsistent optimal control problem for a non homogeneous linear system, in which its state evolves according to a stochastic differential equation with deterministic coefficients, when the noise…
Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for \textit{a single…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
This paper aims to give an overview of the current state of fault-tolerant quantum computing, by surveying a number of results in the field. We show that thresholds can be obtained for a simple noise model as first proved in [AB97, Kit97,…
We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary…
Realistic multi-qubit noise processes often result in error mechanisms that are not captured by the probabilistic, Markovian error models commonly employed in circuit-level analyses of quantum fault-tolerance. By working within an…