25 research outputs found
Quantum Brachistochrone for Mixed States
We present a general formalism based on the variational principle for finding
the time-optimal quantum evolution of mixed states governed by a master
equation, when the Hamiltonian and the Lindblad operators are subject to
certain constraints. The problem reduces to solving first a fundamental
equation (the {\it quantum brachistochrone}) for the Hamiltonian, which can be
written down once the constraints are specified, and then solving the
constraints and the master equation for the Lindblad and the density operators.
As an application of our formalism, we study a simple one-qubit model where the
optimal Lindblad operators control decoherence and can be simulated by a
tunable coupling with an ancillary qubit. It is found that the evolution
through mixed states can be more efficient than the unitary evolution between
given pure states. We also discuss the mixed state evolution as a finite time
unitary evolution of the system plus an environment followed by a single
measurement. For the simplest choice of the constraints, the optimal duration
time for the evolution is an exponentially decreasing function of the
environment's degrees of freedom.Comment: 8 pages, 3 figure
Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
We give analytical solutions for the time-optimal synthesis of entangling
gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three
qubits subject to an Ising Hamiltonian interaction with equal coupling plus
a local magnetic field acting on the intermediate qubit. The energy available
is fixed, but we relax the standard assumption of instantaneous unitary
operations acting on single qubits. The time required for performing an
entangling gate which is equivalent, modulo local unitary operations, to the
between the indirectly coupled qubits 1 and 3 is
, i.e. faster than a previous estimate based on a similar
Hamiltonian and the assumption of local unitaries with zero time cost.
Furthermore, performing a simple Walsh-Hadamard rotation in the Hlibert space
of qubit 3 shows that the time-optimal synthesis of the (which acts as the identity when the control qubit 1 is in the state
, while if the control qubit is in the state the target
qubit 3 is flipped as ) also requires the same
time .Comment: 9 pages; minor modification