A set of stabilizer operations augmented by some special initial states known as magic states, gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations that introd
uce noise. The most common method to eliminate the noise is magic state distillation (MSD) by stabilizer operations. Here we propose a hybrid MSD protocol by connecting a four-qubit H-type MSD with a five-qubit T-type MSD, in order to overcome some disadvantages of the previous MSD protocols. The hybrid MSD protocol further integrates distillable ranges of different existing MSD protocols and extends the T-type distillable range to the stabilizer octahedron edges. And it provides considerable improvement in qubit cost for almost all of the distillable range. Moreover, we experimentally demonstrate the four-qubit H-type MSD protocol using nuclear magnetic resonance technology, together with the previous five-qubit MSD experiment, to show the feasibility of the hybrid MSD protocol.
Topological orders are exotic phases of matter existing in strongly correlated quantum systems, which are beyond the usual symmetry description and cannot be distinguished by local order parameters. Here we report an experimental quantum simulation o
f the Wen-plaquette spin model with different topological orders in a nuclear magnetic resonance system, and observe the adiabatic transition between two $Z_2$ topological orders through a spin-polarized phase by measuring the nonlocal closed-string (Wilson loop) operator. Moreover, we also measure the entanglement properties of the topological orders. This work confirms the adiabatic method for preparing topologically ordered states and provides an experimental tool for further studies of complex quantum systems.
We experimentally demonstrate a new dynamic fashion of quantum Zeno effect in nuclear magnetic resonance systems. The frequent measurements are implemented through quantum entanglement between the target qubit(s) and the measuring qubit, which dynami
cally results from the unitary evolution of duration $tau_{m}$ due to dispersive-coupling. Experimental results testify the presence of the critical measurement time effect, that is, the quantum Zeno effect does not occur when $tau_{m}$ takes the some critical values, even if the measurements are frequent enough. Moreover, we provide a first experimental demonstration of an entanglement preservation mechanism based on such dynamic quantum Zeno effect.
Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system undergoes a quali
tative change in the ground state when a control parameter in its Hamiltonian is varied. Here we report the first experimental study using the geometric phase as a topological test of quantum transitions of the ground state in a Heisenberg XY spin model. Using NMR interferometry, we measure the geometric phase for different adiabatic circuits that do not pass through points of degeneracy.
Quantum phase transitions occur at zero temperature, when the ground state of a Hamiltonian undergoes a qualitative change as a function of a control parameter. We consider a particularly interesting system with competing one-, two- and three-body in
teractions. Depending on the relative strength of these interactions, the ground state of the system can be a product state, or it can exhibit genuine tripartite entanglement. We experimentally simulate such a system in an NMR quantum simulator and observe the different ground states. By adiabatically changing the strength of one coupling constant, we push the system from one ground state to a qualitatively different ground state. We show that these ground states can be distinguished and the transitions between them observed by measuring correlations between the spins or the expectation values of suitable entanglement witnesses.
Local or nonlocal character of quantum states can be quantified and is subject to various bounds that can be formulated as complementarity relations. Here, we investigate the local vs. nonlocal character of pure three-qubit states by a four-way inter
ferometer. The complete entanglement in the system can be measured as the entanglement of a specific qubit with the subsystem consisting of the other two qubits. The quantitative complementarity relations are verified experimentally in an NMR quantum information processor.
Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum system whos
e state is to be determined is first coupled to a second quantum system (the assistant) in such a way that part of the information in the quantum state is transferred to the assistant. The actual measurement is then performed on the enlarged system including the original system and the assistant. We discuss in detail the requirements of this procedure and experimentally implement it on a simple quantum system consisting of nuclear spins.
Finding the factors of an integer can be achieved by various experimental techniques, based on an algorithm developed by Schleich et al., which uses specific properties of Gauss{}sums. Experimental limitations usually require truncation of these seri
es, but if the truncation parameter is too small, it is no longer possible to distinguish between factors and so-called ghost factors. Here, we discuss two techniques for distinguishing between true factors and ghost factors while keeping the number of terms in the sum constant or only slowly increasing. We experimentally test these modified algorithms in a nuclear spin system, using NMR.
