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Register a new userCounteracting dephasing in Molecular Nanomagnets by optimized qudit encodings
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Molecular Nanomagnets may enable the implementation of qudit-based quantum error-correction codes which exploit the many spin levels naturally embedded in a single molecule, a promising step towards scalable quantum processors. To fully realize the potential of this approach, a microscopic understanding of the errors corrupting the quantum information encoded in a molecular qudit is essential, together with the development of tailor-made quantum error correction strategies. We address these central points by first studying dephasing effects on the molecular spin qudit produced by the interaction with surrounding nuclear spins, which are the dominant source of errors at low temperatures. Numerical quantum error correction codes are then constructed, by means of a systematic optimisation procedure based on simulations of the coupled system-bath dynamics, that provide a striking enhancement of the coherence time of the molecular computational unit. The sequence of pulses needed for the experimental implementation of the codes is finally proposed.
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In this work, we study a bipartite system composed by a pair of entangled qudits coupled to an environment. Initially, we derive a master equation and show how the dynamics can be restricted to a diagonal sector that includes a maximally entangled state (MES). Next, we solve this equation for mixed qutrit pairs and analyze the $I$-concurrence $C(t)$ for the effective state, which is needed to compute the geometric phase when the initial state is pure. Unlike (locally operated) isolated systems, the coupled system leads to a nontrivial time-dependence, with $C(t)$ generally decaying to zero at asymptotic times. However, when the initial condition gets closer to a MES state, the effective concurrence is more protected against the effects of decoherence, signaling a transition to an effective two-qubit MES state at asymptotic times. This transition is also observed in the geometric phase evolution, computed in the kinematic approach. Finally, we explore the system-environment coupling parameter space and show the existence of a Weyl symmetry among the various physical quantities.
The magnetization of the prototypical molecular magnet Mn12-acetate exhibits a series of sharp steps at low temperatures due to quantum tunneling at specific resonant values of magnetic field applied along the easy c-axis. An abrupt reversal of the magnetic moment of such a crystal can also occur as an avalanche, where the spin reversal proceeds along a deflagration front that travels through the sample at subsonic speed. In this article we review experimental results that have been obtained for the ignition temperature and the speed of propagation of magnetic avalanches in molecular nanomagnets. Fits of the data with the theory of magnetic deflagration yield overall qualitative agreement. However, numerical discrepancies indicate that our understanding of these avalanches is incomplete.
We address the dephasing dynamics of a qubit as an effective process to estimate the temperature of its environment. Our scheme is inherently quantum, since it exploits the sensitivity of the qubit to decoherence, and does not require thermalization with the system under investigation. We optimize the quantum Fisher information with respect to the interaction time and the temperature in the case of Ohmic-like environments. We also find explicitly the qubit measurement achieving the quantum Cramer- Rao bound to precision. Our results show that the conditions for optimal estimation originate from a non-trivial interplay between the dephasing dynamics and the Ohmic structure of the environment. In general, optimal estimation is achieved neither when the qubit approaches the stationary state, nor for full dephasing.
We report observation of coherent quantum oscilations in spin-10 Fe8 molecular clusters. The powder of magnetically oriented Fe8 crystallites was placed inside a resonator, in a dc magnetic field perpendicular to the magnetization axis. The field dependence of the ac-susceptibility was measured up to 5 T, at 680 MHz, down to 25 mK. Two peaks in the imaginary part of the susceptibility have been detected, whose positions coincide, without any fitting parameters, with the predicted two peaks corresponding to the quantum splitting of the ground state in the magnetic field parallel and perpendicular to the hard magnetization axis.
We consider the task of performing quantum state tomography on a $d$-state spin qudit, using only measurements of spin projection onto different quantization axes. By an exact mapping onto the classical problem of signal recovery on the sphere, we prove that full reconstruction of arbitrary qudit states requires a minimal number of measurement axes, $r_d^{mathrm{min}}$, that is bounded by $2d-1le r_d^{mathrm{min}}le d^2$. We conjecture that $r_d^{mathrm{min}}=2d-1$, which we verify numerically for all $dle200$. We then provide algorithms with $O(rd^3)$ serial runtime, parallelizable down to $O(rd^2)$, for (i) computing a priori upper bounds on the expected error with which spin projection measurements along $r$ given axes can reconstruct an unknown qudit state, and (ii) estimating a posteriori the statistical error in a reconstructed state. Our algorithms motivate a simple randomized tomography protocol, for which we find that using more measurement axes can yield substantial benefits that plateau after $rapprox3d$.
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