During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

https://iopscience.iop.org/article/10.1088/1361-6633/aa7e1a/pdf

Quantum information processing with superconducting circuits: a review

Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We include a discussion of recent developments and near-term applications of quantum algorithms.

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Quantum algorithms: an overview

Photonics is a promising platform for implementing universal quantum information processing. Its main challenges include precise control of massive circuits of linear optical components and effective implementation of entangling operations on photons. By using large-scale silicon photonic circuits to implement an extension of the linear combination of quantum operators scheme, we realize a fully programmable two-qubit quantum processor, enabling universal two-qubit quantum information processing in optics. The quantum processor is fabricated with mature CMOS-compatible processing and comprises more than 200 photonic components. We programmed the device to implement 98 different two-qubit unitary operations (with an 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.

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Large-scale silicon quantum photonics implementing arbitrary two-qubit processing

Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field, with a due balance between theoretical, experimental and technological results. When more convenient, we will present significant achievements in tables or in schematic figures, in order to convey a global perspective of the several horizons that fall under the name of photonic quantum information.

https://iopscience.iop.org/article/10.1088/1361-6633/aad5b2/pdf

Photonic quantum information processing: a review

Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. Here, we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. When revealed on local observables of a bipartite system, such uncertainty defines an entire class of bona fide measures of nonclassical correlations. For the case of $2\ifmmode\times\else\texttimes\fi{}d$ systems, we find that a unique measure is defined, which we evaluate in closed form. We then discuss the role that these correlations, which are of the ``discord'' type, can play in the context of quantum metrology. We show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision, as quantified by the quantum Fisher information, in the optimal phase estimation protocol.

Characterizing nonclassical correlations via local quantum uncertainty.

Quantum discord is the total non-classical correlation between two systems This includes, but is not limited to, entanglement Photonic experiments now demonstrate that separable states with non-zero quantum discord are a useful resource for quantum information processing and can even outperform entangled states

Quantum discord as resource for remote state preparation

Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations.

/pdf/a-two-qubit-photonic-quantum-processor-and-its-application-2rrz4ixwnn.pdf

A two-qubit photonic quantum processor and its application to solving systems of linear equations

Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers, making for one of the most promising applications of quantum computation. Here, we demonstrate this quantum algorithm by implementing various instances on a photonic quantum computing architecture. Our implementation involves the application of two consecutive entangling gates on the same pair of polarisation-encoded qubits. We realize two separate controlled-NOT gates where the successful operation of the first gate is heralded by a measurement of two ancillary photons. Our work thus demonstrates the implementation of a quantum algorithm with high practical significance as well as an important technological advance which brings us closer to a comprehensive control of photonic quantum information.

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Solving systems of linear equations on a quantum computer

Borivoje Dakic1†, Yannick Ole Lipp1†, Xiaosong Ma2,3†, Martin Ringbauer1†, Sebastian Kropatschek3, Stefanie Barz2, Tomasz Paterek4, Vlatko Vedral4,5, Anton Zeilinger2,3, Caslav Brukner1,3 & Philip Walther1,3 1 Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria. 2 Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria. 3 Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria. 4 Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, 117543 Singapore. 5 Department of Atomic and Laser Physics, University of Oxford, Oxford OX1 3PU, UK. † These authors contributed equally to this work (listed alphabetically). (Dated: March 9, 2012)

Quantum Discord as Optimal Resource for Quantum Communication

Much of the anticipation accompanying the development of a quantum computer relates to its application to simulating dynamics of another quantum system of interest. Here we study the building blocks for simulating quantum spin systems with linear optics. We experimentally generate the eigenstates of the XY Hamiltonian under an external magnetic field. The implemented quantum circuit consists of two CNOT gates, which are realized experimentally by harnessing entanglement from a photon source and by applying a CPhase gate. We tune the ratio of coupling constants and magnetic field by changing local parameters. This implementation of the XY model using linear quantum optics might open the door to the future studies of quenching dynamics using linear optics.

Yannick Ole Lipp

Papers

Quantum discord as resource for remote state preparation

A two-qubit photonic quantum processor and its application to solving systems of linear equations

Solving systems of linear equations on a quantum computer

Quantum Discord as Optimal Resource for Quantum Communication

Linear-optical generation of eigenstates of the two-site XY model