PennyLane is a Python 3 software framework for optimization and machine learning of quantum and hybrid quantumclassical computations. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware.We provide plugins for Strawberry Fields, Rigetti Forest, Qiskit, and ProjectQ, allowing PennyLane optimizations to be run on publicly accessible quantum devices provided by Rigetti and IBM Q. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, and autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.
We present a multiprobe recursive Green's function method to compute the transport properties of mesoscopic systems using the Landauer-Büttiker approach. By introducing an adaptive partition scheme, we map the multiprobe problem into the standard two-probe recursive Green's function method. We apply the method to compute the longitudinal and Hall resistances of a disordered graphene sample, a system of current interest. We show that the performance and accuracy of our method compares very well with other state-of-the-art schemes.
The challenge of simulating many-body models with analogue physical systems requires both experimental precision and very low operational temperatures. Atomically precise placement of dopants in Si permits the construction of nanowires by design. We investigate the suitability of these interacting electron systems as simulators of a fermionic extended Hubbard model on demand. We describe the single-particle wavefunctions as a linear combination of dopant orbitals (LCDO). The electronic states are calculated within configuration interaction (CI). Due to the peculiar oscillatory behavior of each basis orbital, properties of these chains are strongly affected by the interdonor distance R 0 , in a non-monotonic way. Ground state (T = 0 K) properties such as charge and spin correlations are shown to remain robust under temperatures up to 4 K for specific values of R 0 . The robustness of the model against disorder is also tested, allowing some fluctuation of the placement site around the target position. We suggest that finite donor chains in Si may serve as an analog simulator for strongly correlated model Hamiltonians. This simulator is, in many ways, complementary to those based on cold atoms in optical lattices-the trade-off between the tunability achievable in the latter and the survival of correlation at higher operation temperatures for the former suggests that both technologies are applicable for different regimes.
We construct a model to study the localization properties of nanowires of dopants in silicon (Si) fabricated by precise ionic implantation or STM lithography. Experiments have shown that Ohm's law holds in some cases, in apparent defiance to the Anderson localization theory in one dimension. We investigate how valley interference affects the traditional theory of electronic structure of disordered systems. Each isolated donor orbital is realistically described by multi-valley effective mass theory (MV-EMT). We extend this model to describe chains of donors as a linear combination of dopant orbitals. Disorder in donor positioning is taken into account, leading to an intricate disorder distribution of hoppings between nearest neighbor donor sites (donor-donor tunnel coupling) -an effect of valley interference. The localization length is obtained for phosphorous (P) donor chains from a transfer matrix approach and is further compared with the chain length. We quantitatively determine the impact of uncertainties δR in the implantation position relative to a target and also compare our results with those obtained without valley interference. We analyse systematically the aimed inter-donor separation dependence (R0) and show that fairly diluted donor chains (R0 = 7.7 nm) may be as long as 100 nm before the effective onset of Anderson localization, as long as the positioning error is under a lattice parameter (δR < 0.543 nm).
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