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Register a new userAlgebraic fidelity decay for local perturbations
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From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such perturbations can be considered as {em local} since wave functions are influenced only locally, in contrast to, e. g., the situation where the fidelity decay is caused by the shift of one billiard wall. Using the random-plane-wave conjecture, an analytic expression for the fidelity decay due to the shift of one scatterer has been obtained, yielding an algebraic $1/t$ decay for long times. A perfect agreement between experiment and theory has been found, including a predicted scaling behavior concerning the dependence of the fidelity decay on the shift distance. The only free parameter has been determined independently from the variance of the level velocities.
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Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution based on exponentiated linear response will be given. For one representative case the exact solution is obtained from a supersymmetric calculation. The results agree well with dynamical calculations for a kicked top.
The fidelity susceptibility has been used to detect quantum phase transitions in the Hermitian quantum many-body systems over a decade, where the fidelity susceptibility density approaches $+infty$ in the thermodynamic limits. Here the fidelity susceptibility $chi$ is generalized to non-Hermitian quantum systems by taking the geometric structure of the Hilbert space into consideration. Instead of solving the metric equation of motion from scratch, we chose a gauge where the fidelities are composed of biorthogonal eigenstates and can be worked out algebraically or numerically when not on the exceptional point (EP). Due to the properties of the Hilbert space geometry at EP, we found that EP can be found when $chi$ approaches $-infty$. As examples, we investigate the simplest $mathcal{PT}$ symmetric $2times2$ Hamiltonian with a single tuning parameter and the non-Hermitian Su-Schriffer-Heeger model.
The flip-flop qubit, encoded in the states with antiparallel donor-bound electron and donor nuclear spins in silicon, showcases long coherence times, good controllability, and, in contrast to other donor-spin-based schemes, long-distance coupling. Electron spin control near the interface, however, is likely to shorten the relaxation time by many orders of magnitude, reducing the overall qubit quality factor. Here, we theoretically study the multilevel system that is formed by the interacting electron and nuclear spins and derive analytical effective two-level Hamiltonians with and without periodic driving. We then propose an optimal control scheme that produces fast and robust single-qubit gates in the presence of low-frequency noise and relatively weak magnetic fields without relying on parametrically restrictive sweet spots. This scheme increases considerably both the relaxation time and the qubit quality factor.
Precise control of quantum systems is of fundamental importance for quantum device engineering, such as is needed in the fields of quantum information processing, high-resolution spectroscopy and quantum metrology. When scaling up the quantum registers in such devices, several challenges arise: individual addressing of qubits in a dense spectrum while suppressing crosstalk, creation of entanglement between distant nodes, and decoupling from unwanted interactions. The experimental implementation of optimal control is a prerequisite to meeting these challenges. Using engineered microwave pulses, we experimentally demonstrate optimal control of a prototype solid state spin qubit system comprising thirty six energy levels. The spin qubits are associated with proximal nitrogen-vacancy (NV) centers in diamond. We demonstrate precise single-electron spin qubit operations with an unprecedented fidelity F approx 0.99 in combination with high-efficiency storage of electron spin states in a nuclear spin quantum memory. Matching single-electron spin operations with spin-echo techniques, we further realize high-quality entangled states (F > 0.82) between two electron spins on demand. After exploiting optimal control, the fidelity is mostly limited by the coherence time and imperfect initialization. Errors from crosstalk in a crowded spectrum of 8 lines as well as detrimental effects from active dipolar couplings have been simultaneously eliminated to unprecedented extent. Finally, by entanglement swapping to nuclear spins, nuclear spin entanglement over a length scale of 25 nm is demonstrated. This experiment underlines the importance of optimal control for scalable room temperature spin-based quantum information devices.
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work, we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate CNOT, CPHASE, and CZ gates with average fidelities greater than 99.99% and gate times as short as 45 ns. Moreover, using the local invariants of the systems evolution operator, we show that a simple square pulse generates a CNOT gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to $sqrt{mathrm{CNOT}}$ and $sqrt{mathrm{CZ}}$ that are used to implement simple two-piece pulse sequences that produce high-fidelity CNOT and CZ gates in the presence of low-frequency noise.
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