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Inspired by the striking phenomenon that cats can land on their feet when they fall, we consider a simple model to simulate a quantum version of the orientation change of a falling cat. Our model consists of a set of coupled harmonic oscillators where both the oscillators' eigen-frequencies and the couplings are time-dependent to mimic the time-dependent shape deformation of a cat's body. In our simulations, we use the gradient-based Krotov's method to find an optimal control shape, enabling the quantum system under consideration to realize the state control within limited times, which is a quantum analogue of a cat's remarkable ability to orient itself to land on its feet when falling. We find that the quantum state control of the "cat system" may be precisely achieved and explore the control's robustness against a generic environmental influence. Our findings will be of interest for the optimal control of open quantum systems that is a subject of great importance in quantum computing, quantum information and quantum technology in general., Comment: Report: 20 pages, 7 figures

Over the last decades, there have been many proposals for quantum computation. One of the promising candidates is adiabatic quantum computation (AQC). The central idea of AQC is about finding the ground state of a system with a problem Hamiltonian via particular adiabatic passages, starting from an initialized ground state of a simple Hamiltonian. One disadvantage of AQC is the significant growth of necessary runtime, in particular when there are quantum phase transitions during the AQC passages. Here we propose a nondeterministic ground state cooling quantum computation model based on selective projection measurements on an ancilla coupled to the system with the problem Hamiltonian previously cooled by conventional techniques. We illustrate the model by Grover search problem and show that our nondeterministic model requires a constant or at most logarithmic runtime and can also get rid of possible difficulties in preparing the ground state of the simple Hamiltonian.

We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to investigate the underlying physics in a different perspective. For particles with small mass such as the neutrino, the leading order equation has a Hermitian effective Hamiltonian, implying there is no leakage between the upper and lower spinors. In the weak relativistic regime, the leading order corresponds to a non-Hermitian correction to the Pauli equation, which takes into account the non-zero possibility of finding the lower-spinor state and offers a more precise description.