José P. Palao

Quantum computing by an optimal control algorithm for unitary transformations.

Quantum computation is based on implementing selected unitary transformations representing algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The approach is independent of the physical implementation of the quantum computer and it is illustrated for one and two qubit gates in model molecular systems, where only part of the Hilbert space is used for computation.

Optimal control theory for unitary transformations

The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time-dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory is used to solve the inversion problem irrespective of the initial input state. A unified formalism based on the Krotov method is developed leading to a different scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the

Stabilization of ultracold molecules using optimal control theory

X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}

Quantum-enhanced absorption refrigerators

electronic state of

Quantum thermodynamic cooling cycle.

{\mathrm{Na}}_{2}.

Performance bound for quantum absorption refrigerators.

Raman-like transitions through the

SPACE-TIME PROPERTIES OF FREE-MOTION TIME-OF-ARRIVAL EIGENFUNCTIONS

A{}^{1}{\ensuremath{\Sigma}}_{u}^{+}

Arrival time distributions and perfect absorption in classical and quantum mechanics

electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Of the schemes studied, the square modulus scheme converges fastest. A study of the implementation of the Q qubit Fourier transform in the

Protecting coherence in optimal control theory: State-dependent constraint approach

{\mathrm{Na}}_{2}

The time of arrival concept in quantum mechanics

molecule was carried out for up to five qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.