We experimentally construct a novel three-qubit entangled W-superposition ($rm W bar{rm W}$) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the $rm
W bar{rm W}$ state to the GHZ state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party $rm W bar{rm W}$ state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the $rm W bar{rm W}$ state which is equivalent to the GHZ state under ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that although the $rm W bar{rm W}$ state is interconvertible with the GHZ state, it stores entanglement very differently.
The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a circuit deco
mposition of the QFT for hybrid qudits based on generalized Hadamard and generalized controlled-phase gates, which can be implemented using selective rotations in NMR. We experimentally implement the hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate a single qutrit coupled to two qubits.
We experimentally explore the state space of three qubits on an NMR quantum information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a non-
trivial combination of GHZ and W-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and W states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and W-states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the W-state, we demonstrate this method of reconstruction by comparing it with the directly tomographed three-qubit state.
We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, speedup requires the presence of entanglement and thus cannot be achieved by a single qub
it. On the other hand, a qutrit is qualitatively more quantum than a qubit because of the existence of quantum contextuality and a single qutrit can be used for computing. We use the deuterium nucleus oriented in a liquid crystal as the experimental qutrit. This is the first experimental exploitation of a single qutrit to carry out a computational task.
