Related papers: Geometric Control Methods for Quantum Computations
We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude…
We show how to realize, by means of non-abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner we bring together the quantum coherence stabilization virtues of…
In holonomic quantum computation, single-qubit gates are performed using driving protocols that trace out closed loops on the Bloch sphere, making them robust to certain pulse errors. However, dephasing noise that is transverse to the…
High-fidelity and robust quantum manipulation is the key for scalable quantum computation. Therefore, due to the intrinsic operational robustness, quantum manipulation induced by geometric phases is one of the promising candidates. However,…
In a topological space, a family of continuous mappings is called universal if its action, in at least one element of the space, is dense. If the mappings are unitary or trace-preserving completely positive, the notion of universality is…
Optimal control can be used to significantly improve multi-qubit gates in quantum information processing hardware architectures based on superconducting circuit quantum electrodynamics. We apply this approach not only to dispersive gates of…
Information science is entering into a new era in which certain subtleties of quantum mechanics enables large enhancements in computational efficiency and communication security. Naturally, precise control of quantum systems required for…
When initially introduced, a Hamiltonian that realises perfect transfer of a quantum state was found to be analogous to an x-rotation of a large spin. In this paper we extend the analogy further to demonstrate geometric effects by…
We study the application of a generalized form of the level set method used in classical physical contexts to quantum optimal control situations. The set of OCT equations needed to keep the expectation value of an observable constant is…
The non-adiabatic holonomic quantum computation with the advantages of fast and robustness attracts widespread attention in recent years. Here, we propose the first scheme for realizing universal single-qubit gates based on an…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space-time grid. More specifically, we show how, introducing a quantum memory for each of the spatial grid, this result can be…
We present a criterion that serves as the basis for a polynomial-time algorithm to decide whether a finite set of qudit gates exponentiated by some Hamiltonians is universal. Our approach formulates universality in Lie algebraic terms and…
The successful application of Quantum Optimal Control (QOC) over the past decades unlocked the possibility of directing the dynamics of quantum systems. Nevertheless, solutions obtained from QOC algorithms are usually highly irregular,…
Entangled resources enable quantum sensing that achieves Heisenberg scaling, a quadratic improvement on the standard quantum limit, but preparing large scale entangled states is challenging in the presence of decoherence. We present a…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoidable for universality in general. We are interested in the…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…