Generalized Quantum Fast Transformations via Femtosecond Laser Writing Technique
Fulvio Flamini, Niko Viggianiello, Marco Bentivegna, Nicolò Spagnolo, Paolo Mataloni, Andrea Crespi, Roberta Ramponi, Roberto Osellame, Fabio Sciarrino
Quantum computers promise to be able to solve tasks beyond the reach of standard computational platforms.Among the others, photonic quantum walks prove to be great candidates for their implementation, since single photon sources, passive linear optics and photo-detectors are sufficient for universal quantum computation.To this aim, a device performing the quantum Fourier transform represents a fundamental building block for quantum algorithms, whose applications are not limited to the field of quantum computation.Recently, an algorithm has been developed to efficiently realize a quantum Fourier transform of an input photonic state by using a quantum walk on elementary linear-optical components.Here we provide a simple operative description of the algorithm, introducing a whole class of quantum transformations achievable through a generalization of this procedure.We finally discuss how femtosecond laser writing technology well represents an efficient and scalable platform for the implementation of this class of photonic quantum walks.
Quantum computers promise to be able to solve tasks beyond the reach of standard computational platforms.Among the others, photonic quantum walks prove to be great candidates for their implementation, since single photon sources, passive linear optics and photo-detectors are sufficient for universal quantum computation.To this aim, a device performing the quantum Fourier transform represents a fundamental building block for quantum algorithms, whose applications are not limited to the field of quantum computation.Recently, an algorithm has been developed to efficiently realize a quantum Fourier transform of an input photonic state by using a quantum walk on elementary linear-optical components.Here we provide a simple operative description of the algorithm, introducing a whole class of quantum transformations achievable through a generalization of this procedure.We finally discuss how femtosecond laser writing technology well represents an efficient and scalable platform for the implementation of this class of photonic quantum walks.
The integrated photonic platform has established itself as a versatile tool for experimental implementation of linear optical quantum computations, that base on unitary transformation of the input states. In this paper we investigate the potential application of the waveguide lattice architecture to realization of arbitrary unitary matrices. We propose a waveguide lattice construction and find its parameters using methods of numerical optimization. Also we showed that a necessary lattice parameters are within the reach femtosecond laser writing technology.
Photonics is a powerful framework for testing in experiments quantum information ideas, which promise significant advantages in computation, cryptography, measurement and simulation tasks. Linear optics is in principle sufficient to achieve universal quantum computation, but stability requirements become severe when experiments have to be implemented with bulk components. Integrated photonic circuits, on the contrary, due to their compact monolithic structure, easily overcome stability and size limitations of bench-top setups. Anyway, for quantum information applications, they have been operated so far only with fixed polarization states of the photons. On the other hand, many important quantum information processes and sources of entangled photon states are based on the polarization degree of freedom. In our work we demonstrate femtosecond laser fabrication of novel integrated components which are able to support and manipulate polarization entangled photons. The low birefringence and the unique possibility of engineering three-dimensional circuit layouts, allow femtosecond laser written waveguides to be eminently suited for quantum optics applications. In fact, this technology enables to realize polarization insensitive circuits which have been employed for entangled Bell state filtration and implementation of discrete quantum walk of entangled photons. Polarization sensitive devices can also be fabricated, such as partially polarizing directional couplers, which have enabled on-chip integration of quantum logic gates reaching high fidelity operation.
Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.
Photonic integrated circuits (PICs) are a technology with a growing interest in a wide range of applications in quantum information, from computation to communications and sensing. Amongst the various types of PICs, universal quantum photonic processors (UQPPs) are programmable photonic integrated circuits on which any arbitrary unitary transformation can be implemented on a given input quantum photonic state, sometimes also referred to as quantum photonic FPGAs. Various kinds of UQPPs have been reported, mostly with a reconfigurable Mach-Zehnder interferometer (MZI) as building block, in photonic platforms ranging from silicon nitride to glass-based direct laser writing. Among them, femtosecond laser writing (FLW) is a versatile fabrication technique that allows for cost-effective fabrication of waveguides in glass substrates with low insertion losses (down to 0.1 dB cm−1 for the propagation and 0.2 dB per facet for the coupling) over a wide wavelength range, a key requirement for quantum applications. Moreover, FLW allows for the fabrication of microstructures in the substrate such as trenches, which can act as thermal isolation structures that significantly reduce the power dissipation of thermal phase shifters and their thermal crosstalk. In this work, firstly we present the fabrication of a 6-mode FLW-UQPP in a rectangular MZI mesh layout operating at 785 nm with average amplitude fidelity as high as 0.9963 when implementing switching unitaries and 0.9979 when implementing Haar random unitaries. Secondly, we demonstrate the versatility of the FLW platform by fabricating another 6-mode UQPP with waveguides optimized for operation at 1550 nm wavelength, with similar performance, on which we repeated the implementation of Haar random unitaries with 0.9969 average amplitude fidelity.
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multiparticle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transformation in the Fock space. In this work we develop a scalable approach for the implementation of quantum fast Fourier transform using 3-D photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the quantum suppression of a large number of output states with 4- and 8-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms.
Femtosecond laser direct writing (FLDW) technique has been widely applied for fabrications of various photonic quantum chips in glass, such as chips for quantum computation, quantum walk, quantum simulation and quantum metrology. Photonic quantum logic gates are the building blocks for the realization of linear optical universal quantum computation. Up to now, several photonic quantum logic gates have been fabricated by FLDW, such as polarization encoded Hadamard (H) gate, Controlled NOT (CNOT) gate, herald CNOT gate and path encoded herald Controlled phase (CZ) gate and CNOT gate. By combining several single-qubit and two-qubit gates together, the constructed quantum circuits can realize some special functions, such as generating entangled states and perform quantum computation algorithms. Based on the successful fabrication of path encoded CNOT gate by FLDW, we further realized the fabrication of photonic quantum chips by cascading one H gate and one CNOT gate at the control qubit to generate path encoded Bell states, whose fidelity of truth table can reach 97.60.3%. Further, we cascaded one H gate and two parallel CNOT gates at the same control qubit to generate path encoded GHZ states, but which need three photons. Both Bell states and GHZ states are important entangled photon resources, which are widely used in quantum communication and quantum computation, and both combinations of logic gates above can be applied in many quantum circuits, so this work is of great importance and lays the technical foundation for the FLDW of more complex and powerful photonic quantum computation chips.