Related papers: Optimal control, geometry, and quantum computing
We study the conditions under which, given a generic quantum system, complexity metrics provide actual lower bounds to the circuit complexity associated to a set of quantum gates. Inhomogeneous cost functions ---many examples of which have…
For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…
A quantum gate is realized by specific unitary transformations operating on states representing qubits. Considering a quantum system employed as an element in a quantum computing scheme, the task is therefore to enforce the pre-specified…
The control of ensembles of dynamical systems is an intriguing and challenging problem, arising for example in quantum control. We initiate the investigation of optimal control of ensembles of discrete-time systems, focusing on minimising…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations…
We study the optimal quantum control of heteronuclear two-qubit systems described by a Hamiltonian containing both nonlocal internal drift and local control terms. We derive an explicit formula to compute the minimum time required to steer…
We study the time optimal control problem for the evolution operator of an n-level quantum system from the identity to any desired final condition. For the considered class of quantum systems the control couples all the energy levels to a…
Determining the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry [Nielsen et al, Science 311, 1133-1135 (2006)]. This paper investigates many…
We use a specific geometric method to determine speed limits to the implementation of quantum gates in controlled quantum systems that have a specific class of constrained control functions. We achieve this by applying a recent theorem of…
We formulate and investigate the simplest version of time-optimal quantum computation theory (t-QCT), where the computation time is defined by the physical one and the Hamiltonian contains only one- and two-qubit interactions. This version…
Quantum optimal control plays a crucial role in the development of quantum technologies, particularly in the design and implementation of fast and accurate gates for quantum computing. Here, we present a method to synthesize gates using the…
We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyse their…
We study the Hamiltonian-independent contribution to the complexity of quantum optimal control problems. The optimization of controls that steer quantum systems to desired objectives can itself be considered a classical dynamical system…
We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared…
All quantum systems are subject to noise from the environment or external controls. This noise is a major obstacle to the realization of quantum technology. For example, noise limits the fidelity of quantum gates. Employing optimal control…
For addressing optimisation tasks on finite dimensional quantum systems, we give a comprehensive account of the foundations of gradient flows on Riemannian manifolds including new developments: we extend former results from Lie groups such…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
Quantum Optimal Control (QOC) enables the realization of accurate operations, such as quantum gates, and support the development of quantum technologies. To date, many QOC frameworks have been developed but those remain only naturally…
The optimal cost of a three-qubit Fredkin gate is 5 two-qubit entangling gates, and the overhead climbs to 8 when restricted to controlled-not (CNOT) gates. By harnessing higher-dimensional Hilbert spaces, we reduce the cost of a…