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.
Integrated optics is an engineering solution proposed for exquisite control of photonic quantum information. Here we use silicon photonics and the linear combination of quantum operators scheme to realise a fully programmable two-qubit quantum processor. The device is fabricated with readily available CMOS based processing and comprises four nonlinear photon-sources, four filters, eightytwo beam splitters and fifty-eight individually addressable phase shifters. To demonstrate performance, we programmed the device to implement ninety-eight various two-qubit unitary operations (with average quantum process fidelity of 93.2±4.5%), a two-qubit quantum approximate optimization algorithm and efficient simulation of Szegedy directed quantum walks. This fosters further use of the linear combination architecture with silicon photonics for future photonic quantum processors.The range and quality of control that a device has over quantum physics determines the extent of quantum information processing (QIP) tasks that it can perform. One device capable of performing any given QIP task is an ultimate goal 1 and silicon quantum photonics 2 has attractive traits to achieve this: photonic qubits are robust to environmental noise 5 , single qubit operations can be performed with high precision 16 , a high density of reconfigurable components have been used to manipulate coherent light 5,6 and established fabrication processes are CMOS compatible. However, quantum control needs to include entangling operations to be relevant to QIPthis is recognised as one of the most challenging tasks for photonics because of the extra resources required for each entangling step 5,6 . Here, we demonstrate a programmable silicon photonics chip that generates two photonic qubits, on which it then performs arbitrary twoqubit untiary operations, including arbitrary entangling operations. This is achieved by using silicon photonics to reach the complexity required to implement an iteration of the linear combination of unitaries architecture 8,9 that we have adapted to realise universal two-qubit processing. The device's performance shows that the design and fabrication techniques used in its implementation work well with the linear combination architecture and can be used to realise larger and more powerful photonic quantum processors.Miniaturisation of quantum-photonic experiments into chip-scale waveguide circuits started 10 from the need to realise many-mode devices with inherent sub-wavelength stability for generalised quantum-interference experi-ments, such as multi-photon quantum walks 11 and boson sampling 12-14 . Universal six-mode linear optics implemented with a silica waveguide chip (coupled to free-space photon sources and fibre-coupled detectors) demonstrated the principle that single photonic devices can be configured to perform any given linear optics task 15 . Silicon waveguides promise even greater capability for large-scale photonic processing, because of their third order nonlinearity that enables photon pair generation within integ...
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor.
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum algorithm to encode the Fourier coefficients in the computational basis, with fidelity 1 − δ and desired precision . Its time complexity depends polynomially on log(N ), where N is the problem size, and linearly on 1/δ and 1/ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
Following recent developments in quantum PageRanking, we present a comparative analysis of discrete-time and continuous-time quantum-walk-based PageRank algorithms. For the discrete-time case, we introduce an alternative PageRank measure based on the maximum probabilities achieved by the walker on the nodes. We demonstrate that the required time of evolution does not scale significantly with increasing network size. We affirm that all three quantum PageRank measures considered here distinguish clearly between outerplanar hierarchical, scale-free, and Erdös-Rényi network types. Relative to classical PageRank and to different extents, the quantum measures better highlight secondary hubs and resolve ranking degeneracy among peripheral nodes for the networks we studied in this paper.
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