We report structural and magnetic properties studies of large high quality single-crystals of the frustrated magnet, Nd$_2$Zr$_2$O$_7$. Powder x-ray diffraction analysis confirms that Nd$_2$Zr$_2$O$_7$ adopts the pyrochlore structure. Room-temperatur
e x-ray diffraction and time-of-flight neutron scattering experiments show that the crystals are stoichiometric in composition with no measurable site disorder. The temperature dependence of the magnetic susceptibility shows no magnetic ordering at temperatures down to 0.5 K. Fits to the magnetic susceptibility data using a Curie-Weiss law reveal a ferromagnetic coupling between the Nd moments. Magnetization versus field measurements show a local Ising anisotropy along the <111> axes of the Nd$^{3+}$ ions in the ground state. Specific heat versus temperature measurements in zero applied magnetic field indicate the presence of a thermal anomaly below $Tsim7$ K, but no evidence of magnetic ordering is observed down to 0.5 K. The experimental temperature dependence of the single-crystal bulk dc susceptibility and isothermal magnetization are analyzed using crystal field theory and the crystal field parameters and exchange coupling constants determined.
We report the results of neutron scattering on a powder sample of Gd3Ga5O12 at high magnetic fields. We find that in high fields (B>1.8 T) the system is not fully polarized, but has a small canting of the moments induced by the dipolar interaction. W
e show that the degree of canting is accurately predicted by the standard Hamiltonian which includes the dipolar interaction. The inelastic scattering is dominated at large momentum transfers by a band of almost dispersionless excitations. We show that these correspond to the spin waves localized on ten site rings, expected for a system described by a nearest neighbor interaction, and that the spectrum at high fields B>1.8 T is well-described by a spin wave theory. The phase for fields <1.8 T is characterized by an antiferromagnetic Bragg peak at (210) and an incommensurate peak.
Quantum error correction (QEC) is required for a practical quantum computer because of the fragile nature of quantum information. In QEC, information is redundantly stored in a large Hilbert space and one or more observables must be monitored to reve
al the occurrence of an error, without disturbing the information encoded in an unknown quantum state. Such observables, typically multi-qubit parities such as <XXXX>, must correspond to a special symmetry property inherent to the encoding scheme. Measurements of these observables, or error syndromes, must also be performed in a quantum non-demolition (QND) way and faster than the rate at which errors occur. Previously, QND measurements of quantum jumps between energy eigenstates have been performed in systems such as trapped ions, electrons, cavity quantum electrodynamics (QED), nitrogen-vacancy (NV) centers, and superconducting qubits. So far, however, no fast and repeated monitoring of an error syndrome has been realized. Here, we track the quantum jumps of a possible error syndrome, the photon number parity of a microwave cavity, by mapping this property onto an ancilla qubit. This quantity is just the error syndrome required in a recently proposed scheme for a hardware-efficient protected quantum memory using Schr{o}dinger cat states in a harmonic oscillator. We demonstrate the projective nature of this measurement onto a parity eigenspace by observing the collapse of a coherent state onto even or odd cat states. The measurement is fast compared to the cavity lifetime, has a high single-shot fidelity, and has a 99.8% probability per single measurement of leaving the parity unchanged. In combination with the deterministic encoding of quantum information in cat states realized earlier, our demonstrated QND parity tracking represents a significant step towards implementing an active system that extends the lifetime of a quantum bit.
We study the photon shot noise dephasing of a superconducting transmon qubit in the strong-dispersive limit, due to the coupling of the qubit to its readout cavity. As each random arrival or departure of a photon is expected to completely dephase the
qubit, we can control the rate at which the qubit experiences dephasing events by varying textit{in situ} the cavity mode population and decay rate. This allows us to verify a pure dephasing mechanism that matches theoretical predictions, and in fact explains the increased dephasing seen in recent transmon experiments as a function of cryostat temperature. We investigate photon dynamics in this limit and observe large increases in coherence times as the cavity is decoupled from the environment. Our experiments suggest that the intrinsic coherence of small Josephson junctions, when corrected with a single Hahn echo, is greater than several hundred microseconds.
