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The ability to accurately control a quantum system is a fundamental requirement in many areas of modern science such as quantum information processing and the coherent manipulation of molecular systems. It is usually necessary to realize these quantum manipulations in the shortest possible time in order to minimize decoherence, and with a large stability against fluctuations of the control parameters. While optimizing a protocol for speed leads to a natural lower bound in the form of the quantum speed limit rooted in the Heisenberg uncertainty principle, stability against parameter variations typically requires adiabatic following of the system. The ultimate goal in quantum control is to prepare a desired state with 100% fidelity. Here we experimentally implement optimal control schemes that achieve nearly perfect fidelity for a two-level quantum system realized with Bose-Einstein condensates in optical lattices. By suitably tailoring the time-dependence of the systems parameters, we transform an initial quantum state into a desired final state through a short-cut protocol reaching the maximum speed compatible with the laws of quantum mechanics. In the opposite limit we implement the recently proposed transitionless superadiabatic protocols, in which the system perfectly follows the instantaneous adiabatic ground state. We demonstrate that superadiabatic protocols are extremely robust against parameter variations, making them useful for practical applications.
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We analyze a system of fermionic $^{6}$Li atoms in an optical trap, and show that an atom on demand can be prepared with ultra-high fidelity, exceeding 0.99998. This process can be scaled to many sites in parallel, providing a realistic method to initialize N qubits at ultra-high fidelity for quantum computing. We also show how efficient quantum gate operation can be implemented in this system, and how spatially resolved single-atom detection can be performed.
In the current work we address the problem of quantum process tomography (QPT) in the case of imperfect preparation and measurement of the states which are used for QPT. The fuzzy measurements approach which helps us to efficiently take these imperfections into account is considered. However, to implement such a procedure one should have a detailed information about the errors. An approach for obtaining the partial information about them is proposed. It is based on the tomography of the ideal identity gate. This gate could be implemented by performing the measurement right after the initial state preparation. By using the result of the identity gate tomography we were able to significantly improve further QPT procedures. The proposed approach has been tested experimentally on the IBM superconducting quantum processor. As a result, we have obtained an increase in fidelity from 89% to 98% for Hadamard transformation and from 77% to 95% for CNOT gate.
We study collective excitations of rotational and spin states of an ensemble of polar molecules, which are prepared in a dipolar crystalline phase, as a candidate for a high fidelity quantum memory. While dipolar crystals are formed in the high density limit of cold clouds of polar molecules under 1D and 2D trapping conditions, the crystalline structure protects the molecular qubits from detrimental effects of short range collisions. We calculate the lifetime of the quantum memory by identifying the dominant decoherence mechanisms, and estimate their effects on gate operations, when a molecular ensemble qubit is transferred to a superconducting strip line cavity (circuit QED). In the case rotational excitations coupled by dipole-dipole interactions we identify phonons as the main limitation of the life time of qubits. We study specific setups and conditions, where the coupling to the phonon modes is minimized. Detailed results are presented for a 1D dipolar chain.
Effective transport of quantum information is an essential element of quantum computation. We consider the problem of transporting a quantum state by using a moving potential well, while maintaining the encoded quantum information. In particular, we look at a set of cases where the input control defining the position of the potential well is subject to different types of distortion, each of which is motivated by experimental considerations. We show that even under these conditions, we are able to perfectly transfer the quantum information non-adiabatically over any given distance.
We derive the optimal analytical quantum-state-transfer control solutions for two disparate quantum memory blocks. Employing the SLH formalism description of quantum network theory, we calculate the full quantum dynamics of system populations, which lead to the optimal solution for the highest quantum fidelity attainable. We show that, for the example where the mechanical modes of two optomechanical oscillators act as the quantum memory blocks, their optical modes and a waveguide channel connecting them can be used to achieve a quantum state transfer fidelity of 96% with realistic parameters using our derived optimal control solution. The effects of the intrinsic losses and the asymmetries in the physical memory parameters are discussed quantitatively.
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