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Register a new userScalable quantum computation in systems with Bose-Hubbard dynamics
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Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.
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We propose a novel scheme of solid state realization of a quantum computer based on single spin enhancement mode quantum dots as building blocks. In the enhancement quantum dots, just one electron can be brought into initially empty dot, in contrast to depletion mode dots based on expelling of electrons from multi-electron dots by gates. The quantum computer architectures based on depletion dots are confronted by several challenges making scalability difficult. These challenges can be successfully met by the approach based on ehnancement mode, capable of producing square array of dots with versatile functionalities. These functionalities allow transportation of qubits, including teleportation, and error correction based on straightforward one- and two-qubit operations. We describe physical properties and demonstrate experimental characteristics of enhancement quantum dots and single-electron transistors based on InAs/GaSb composite quantum wells. We discuss the materials aspects of quantum dot quantum computing, including the materials with large spin splitting such as InAs, as well as perspectives of enhancement mode approach in materials such as Si.
We show that braidings of the metaplectic anyons $X_epsilon$ in $SO(3)_2=SU(2)_4$ with their total charge equal to the metaplectic mode $Y$ supplemented with measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal computing models can be constructed for all metaplectic anyon systems $SO(p)_2$ for any odd prime $pgeq 5$. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.
The hopes for scalable quantum computing rely on the threshold theorem: once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based on a number of assumptions, which are supposed to be satisfied exactly, like axioms, e.g. zero undesired interactions between qubits, etc. However in the physical world no continuous quantity can be exactly zero, it can only be more or less small. Thus the error per qubit per gate threshold must be complemented by the required precision with which each assumption should be fulfilled. This issue was never addressed. In the absence of this crucial information, the prospects of scalable quantum computing remain uncertain.
We propose and analyse analogs of optical cavities for atoms using three-well Bose-Hubbard models with pumping and losses. We consider triangular configurations. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, preserving good coherence between the wells in the steady-state. We find quadrature squeezing and mode entanglement for some parameter regimes and demonstrate that the trimer with pumping and damping at the same well is the stronger option for producing non-classical states. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict.
In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behaviour in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numerically from binned phase-space trajectories in a truncated Wigner approximation. Although the evolving Wigner function becomes very irregular in the chaotic regions, the truncated Wigner method is nevertheless able to capture accurately the beyond mean-field dynamics.
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