Given a Lagrangian V cong CP^n in a symplectic manifold (M,omega), there is an associated symplectomorphism phi_V of M. We define the notion of a CP^n-object in an A-infinity-category A and use this to construct algebraically an A-infinity-functor Ph
i_V and prove that it induces an autoequivalence of the derived category DA. We conjecture that Phi_V corresponds to the action of phi_V and prove this in the lowest dimension n=1. The construction is designed to be mirror to a construction of Huybrechts and Thomas.
We investigate the uniqueness of so-called exotic structures on certain exact symplectic manifolds by looking at how their symplectic properties change under small nonexact deformations of the symplectic form. This allows us to distinguish between tw
o examples based on those found in cite{maydanskiy,maydanskiyseidel}, even though their classical symplectic invariants such as symplectic cohomology vanish. We also exhibit, for any $n$, an exact symplectic manifold with $n$ distinct but exotic symplectic structures, which again cannot be distinguished by symplectic cohomology.
A superconducting chip containing a regular array of flux qubits, tunable interqubit inductive couplers, an XY-addressable readout system, on-chip programmable magnetic memory, and a sparse network of analog control lines has been studied. The archit
ecture of the chip and the infrastructure used to control it were designed to facilitate the implementation of an adiabatic quantum optimization algorithm. The performance of an eight-qubit unit cell on this chip has been characterized by measuring its success in solving a large set of random Ising spin glass problem instances as a function of temperature. The experimental data are consistent with the predictions of a quantum mechanical model of an eight-qubit system coupled to a thermal environment. These results highlight many of the key practical challenges that we have overcome and those that lie ahead in the quest to realize a functional large scale adiabatic quantum information processor.
A novel rf-SQUID flux qubit that is robust against fabrication variations in Josephson junction critical currents and device inductance has been implemented. Measurements of the persistent current and of the tunneling energy between the two lowest ly
ing states, both in the coherent and incoherent regime, are presented. These experimental results are shown to be in agreement with predictions of a quantum mechanical Hamiltonian whose parameters were independently calibrated, thus justifying the identification of this device as a flux qubit. In addition, measurements of the flux and critical current noise spectral densities are presented that indicate that these devices with Nb wiring are comparable to the best Al wiring rf-SQUIDs reported in the literature thusfar, with a $1/f$ flux noise spectral density at $1 $Hz of $1.3^{+0.7}_{-0.5} muPhi_0/sqrt{text{Hz}}$. An explicit formula for converting the observed flux noise spectral density into a free induction decay time for a flux qubit biased to its optimal point and operated in the energy eigenbasis is presented.
An improved tunable coupling element for building networks of coupled rf-SQUID flux qubits has been experimentally demonstrated. This new form of coupler, based upon the compound Josephson junction rf-SQUID, provides a sign and magnitude tunable mutu
al inductance between qubits with minimal nonlinear crosstalk from the coupler tuning parameter into the qubits. Quantitative agreement is shown between an effective one-dimensional model of the couplers potential and measurements of the coupler persistent current and susceptibility.
A circuit consisting of a network of coupled compound Josephson junction rf-SQUID flux qubits has been used to implement an adiabatic quantum optimization algorithm. It is shown that detailed knowledge of the magnitude of the persistent current as a
function of annealing parameters is key to implementation of the algorithm on this particular type of hardware. Experimental results contrasting two annealing protocols, one with and one without active compensation for the growth of the qubit persistent current during annealing, are presented in order to illustrate this point.
A practical strategy for synchronizing the properties of compound Josephson junction rf-SQUID qubits on a multiqubit chip has been demonstrated. The impacts of small ($sim1%$) fabrication variations in qubit inductance and critical current can be min
imized by the application of a custom tuned flux offset to the CJJ structure of each qubit. This strategy allows for simultaneous synchronization of the qubit persistent current and tunnel splitting over a range of external bias parameters that is relevant for the implementation of an adiabatic quantum processor.
