2,694 research outputs found
Notions of controllability for quantum mechanical systems
In this paper, we define four different notions of controllability of
physical interest for multilevel quantum mechanical systems. These notions
involve the possibility of driving the evolution operator as well as the state
of the system. We establish the connections among these different notions as
well as methods to verify controllability.
The paper also contains results on the relation between the controllability
in arbitrary small time of a system varying on a compact transformation Lie
group and the corresponding system on the associated homogeneous space. As an
application, we prove that, for the system of two interacting spin 1/2
particles, not every state transfer can be obtained in arbitrary small time.Comment: Replaced by a new version which contains the proof
Optimal control of circuit quantum electrodynamics in one and two dimensions
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 two qubits inside a cavity, but, more generally, to architectures
based on two-dimensional arrays of cavities and qubits. For high-fidelity gate
operations, simultaneous evolutions of controls and couplings in the two
coupling dimensions of cavity grids are shown to be significantly faster than
conventional sequential implementations. Even under experimentally realistic
conditions speedups by a factor of three can be gained. The methods immediately
scale to large grids and indirect gates between arbitrary pairs of qubits on
the grid. They are anticipated to be paradigmatic for 2D arrays and lattices of
controllable qubits.Comment: Published version
Parallelism for Quantum Computation with Qudits
Robust quantum computation with d-level quantum systems (qudits) poses two
requirements: fast, parallel quantum gates and high fidelity two-qudit gates.
We first describe how to implement parallel single qudit operations. It is by
now well known that any single-qudit unitary can be decomposed into a sequence
of Givens rotations on two-dimensional subspaces of the qudit state space.
Using a coupling graph to represent physically allowed couplings between pairs
of qudit states, we then show that the logical depth of the parallel gate
sequence is equal to the height of an associated tree. The implementation of a
given unitary can then optimize the tradeoff between gate time and resources
used. These ideas are illustrated for qudits encoded in the ground hyperfine
states of the atomic alkalies Rb and Cs. Second, we provide a
protocol for implementing parallelized non-local two-qudit gates using the
assistance of entangled qubit pairs. Because the entangled qubits can be
prepared non-deterministically, this offers the possibility of high fidelity
two-qudit gates.Comment: 9 pages, 3 figure
Quantum Control Theory for State Transformations: Dark States and their Enlightenment
For many quantum information protocols such as state transfer, entanglement
transfer and entanglement generation, standard notions of controllability for
quantum systems are too strong. We introduce the weaker notion of accessible
pairs, and prove an upper bound on the achievable fidelity of a transformation
between a pair of states based on the symmetries of the system. A large class
of spin networks is presented for which this bound can be saturated. In this
context, we show how the inaccessible dark states for a given
excitation-preserving evolution can be calculated, and illustrate how some of
these can be accessed using extra catalytic excitations. This emphasises that
it is not sufficient for analyses of state transfer in spin networks to
restrict to the single excitation subspace. One class of symmetries in these
spin networks is exactly characterised in terms of the underlying graph
properties.Comment: 14 pages, 3 figures v3: rewritten for increased clarit
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