We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.The potential power of quantum computing was first described by Feynman, who showed that the exponential growth of the Hilbert space of a quantum computer allows efficient simulations of quantum systems, whereas a classical computer would be overwhelmed [1]. Shor extended the applicability of quantum computing when he developed a quantum factorization algorithm that also provides exponential speedup over the best classical algorithm [2].More recently, Harrow et al.[3] demonstrated a quantum algorithm for solving a linear system of equations that, for well-conditioned matrices, gives exponential speedup over the best classical method. In that paper, the authors demonstrated how to invert a sparse matrix to solve the quantum linear system A|x = |b . The requirements for achieving exponential speedup were: 1) the elements of A be efficiently computable via a blackbox oracle; 2) the matrix A must to be sparse, or efficiently decomposable into sparse form; 3) the condition number of A must scale as polylog N where N is the size of the linear system. As presented, the algorithm had three features that made it difficult to apply to generic problem specifications and achieve the promised exponential speedup. These included: State preparation -preparing the generic state |b is an unsolved problem [4][5][6][7][8], and no mention on how one might do this was provided. Solution readoutsince the solution is stored in a quantum state |x , measurement of it is impractical. The authors suggested that it could be used to calculate some expectation values of an arbitrary operator x|R|x . However, no measurement procedure was specified, and estimating x|R|x is not trivial in general. Condition number -in order for the quantum algorithm to achieve exponential speedup, the condition number can scale at most poly logarithmically with the size of the matrix A. This is a very strict condition that greatly limits the class of problems that can achieve exponential speedup.In this letter, we provide solutions to these three problems, greatly expanding the applicability of the Quantum Linear Systems Algorithm (QLSA). In addition, we show how our new techniques enable the first start-to-finish application of the QLSA to a problem of broad interest and importance. Namely, we show how to solve for the scattering cross section of an arbit...

[1] The mean surface temperature of the Earth depends on various climate factors with much attention directed toward possible anthropogenic causes. However, one must first determine the stronger effects such as El Niño/La Niña and volcanoes. A weaker effect, which must exist, is solar irradiance. We have determined the solar effect on the temperature from satellites measurements (available since 1979) of the solar irradiance and the temperature of the lower troposphere. We find the sensitivity to solar irradiance to be about twice that expected from a no-feedback StefanBoltzmann radiation balance model. This climate gain of a factor of two implies positive feedback. We also have determined a linear trend in the data. These results are robust under truncation from either end of the of the data record. These measurements of solar sensitivity are consistent with prior estimates from ocean temperatures on decadal scales and of paleo-reconstructed temperatures on centennial scales.

We examine fully coherent two-pulse propagation in a lambda-type medium, under two-photon resonance conditions and including inhomogeneous broadening. We examine both the effects of short pulse preparation and the effects of medium preparation. We contrast cases in which the two pulses have matched envelopes or not, and contrast cases in which ground state coherence is present or not. We find that an extended interpretation of the Area Theorem for single-pulse self-induced transparency (SIT) is able to unify twopulse propagation scenarios, including some aspects of electromagnetically-induced transparency (EIT) and stimulated Raman scattering (SRS). We present numerical solutions of both three-level and adiabatically reduced two-level density matrix equations and Maxwell's equations, and show that many features of the solutions are quickly interpreted with the aid of analytic solutions that we also provide for restricted cases of pulse shapes and preparation of the medium. In the limit of large one-photon detuning, we show that the two-level equations commonly used are not reliable for pulse Areas in the 2π range, which allows puzzling features of previous numerical work to be understood. 0

We provide a review of recent progress in integrated nonlinear photonics with a focus on emerging applications in all-optical signal processing, ultra-low-power all-optical switching, and quantum information processing.

We describe an adiabatic state transfer mechanism that allows for high-fidelity transfer of a microwave quantum state from one cavity to another through an optical fiber. The conversion from microwave frequency to optical frequency is enabled by an optomechanical transducer. The transfer process utilizes a combined dark state of the mechanical oscillator and fiber modes, making it robust against both mechanical and fiber loss. We anticipate this scheme being an enabling component of a hybrid quantum computing architecture consisting of superconducting qubits with optical interconnects.Comment: 9 pages, 4 figures. Replaced with published versio