Engineering integrated photonics for heralded quantum gates
Thomas Meany, Devon N. Biggerstaff, Matthew A. Broome, Alessandro Fedrizzi, Michael Delanty, M. J. Steel, Alexei Gilchrist, Graham D. Marshall, Andrew G. White, Michael J. Withford
Scaling up linear-optics quantum computing will require multi-photon gates which are compact, phase-stable, exhibit excellent quantum interference, and have success heralded by the detection of ancillary photons. We investigate the design, fabrication and characterisation of the optimal known gate scheme which meets these requirements: the Knill controlled-Z gate, implemented in integrated laser-written waveguide arrays. We show device performance to be less sensitive to phase variations in the circuit than to small deviations in the coupler reflectivity, which are expected given the tolerance values of the fabrication method. The mode fidelity is also shown to be less sensitive to reflectivity and phase errors than the process fidelity. Our best device achieves a fidelity of 0.931 ± 0.001 with the ideal 4 × 4 unitary circuit and a process fidelity of 0.680 ± 0.005 with the ideal computational-basis process.
Scaling up linear-optics quantum computing will require multi-photon gates which are compact, phase-stable, exhibit excellent quantum interference, and have success heralded by the detection of ancillary photons. We investigate the design, fabrication and characterisation of the optimal known gate scheme which meets these requirements: the Knill controlled-Z gate, implemented in integrated laser-written waveguide arrays. We show device performance to be less sensitive to phase variations in the circuit than to small deviations in the coupler reflectivity, which are expected given the tolerance values of the fabrication method. The mode fidelity is also shown to be less sensitive to reflectivity and phase errors than the process fidelity. Our best device achieves a fidelity of 0.931 ± 0.001 with the ideal 4 × 4 unitary circuit and a process fidelity of 0.680 ± 0.005 with the ideal computational-basis process.
Optical quantum computing (QC) increasingly uses integrated optics based experiments which permit circuit compactness and phase stability [1]. However, despite the rapid adaptations of integrated waveguide devices for quantum photonics, initial gate demonstrations operate in post-selection, thus not allowing scaling of a quantum circuit beyond the depth of a single gate. Recently, a number of quantum circuits have been demonstrated using the femtosecond laser direct write (FLDW) technique [2]. This technique induces refractive index change in glass substrates which can form three-dimensional waveguide devices. Here we demonstrate a potentially scalable waveguide gate for QC, a controlled-phase gate or Knill gate, produced using the FLDW technique. This gate produces a phase shift on a target qubit conditional on the state of a control qubit, as shown in Fig. 1(a). It requires four photons for operation, two of which act as the target and control path-encoded qubits and two ancillas which herald the successful operation of the circuit [3].
Quantum information science aims to harness uniquely quantum mechanical properties to enhance measurement and information technologies, and to explore fundamental aspects of quantum physics. Of the various approaches to quantum computing [1], photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level [2]. Encoding quantum information in photons is also an appealing approach to quantum communication, metrology (eg. [3]), measurement (eg. [4]) and other quantum technologies [5]. However, the implementation of optical quantum circuits with bulk optics has reached practical limits. We have developed an integrated waveguide approach to photonic quantum circuits for high performance, miniaturisation and scalability [6]. Here we report high-fidelity silica-on-silicon integrated optical realisations of key quantum photonic circuits, including two-photon quantum interference and a controlled-NOT logic gate [7]. We have demonstrated controlled manipulation of up to four photons on-chip, including high-fidelity single qubit operations, using a lithographically patterned resistive phase shifter [8]. We have used this architecture to implement a small-scale compiled version of Shorʼs quantum factoring algorithm [9] and demonstrated heralded generation of tuneable four photon entangled states from a six photon input [10]. We have combined waveguide photonic circuits with superconducting single photon detectors [11]. We describe complex quantum interference behaviour in multi-mode interference devices with up to eight inputs and outputs [12], and quantum walks of correlated particles in arrays of coupled waveguides [13]. Finally, we give an overview of our recent work on fundamental aspects of quantum measurement [14,15] and single photon sources [16,17].
The design, fabrication, and detailed calibration of essential building blocks towards fully integrated linear-optics quantum computation are discussed. Photonic devices are made from silicon nitride rib waveguides, where measurements on ring resonators show small propagation losses. Directional couplers are designed to be insensitive to fabrication variations. Their offset and coupling lengths are measured, as well as the phase difference between the transmitted and reflected light. With careful calibrations, the insertion loss of the directional couplers is found to be small. Finally, an integrated controlled-NOT circuit is characterized by measuring the transmission through different combinations of inputs and outputs. The gate fidelity for the CNOT operation with this circuit is estimated to be 99.81% after post selection. This high fidelity is due to our robust design, good fabrication reproducibility, and extensive characterizations.
Quantum information science aims to harness uniquely quantum mechanical properties to enhance measurement and information technologies, and to explore fundamental aspects of quantum physics. Of the various approaches to quantum computing [1], photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level [2,3]. Encoding quantum information in photons is also an appealing approach to quantum communication, metrology (eg. [4]), measurement (eg. [5]) and other quantum technologies [6]. However, the implementation of optical quantum circuits with bulk optics has reached practical limits. We have developed an integrated waveguide approach to photonic quantum circuits for high performance, miniaturization and scalability [7]. Here we report high-fidelity silica-on-silicon integrated optical realizations of key quantum photonic circuits, including two-photon quantum interference and a controlled-NOT logic gate [8]. We have demonstrated controlled manipulation of up to four photons on-chip, including highfidelity single qubit operations, using a lithographically patterned resistive phase shifter [9]. We have used this architecture to implement a small-scale compiled version of Shor's quantum factoring algorithm [10], demonstrated heralded generation of tunable four photon entangled states from a six photon input [11], a reconfigurable two-qubit circuit [12], and combined waveguide photonic circuits with superconducting single photon detectors [13]. We describe complex quantum interference behavior in multi-mode interference devices with up to eight inputs and outputs [14], and quantum walks of correlated particles in arrays of coupled waveguides [15]. Finally, we give an overview of our recent work on fundamental aspects of quantum measurement [16,17] and diamond [18,19] and nonlinear [20,21] photon sources.
Integrated photonic circuits with many input and output modes are essential in applications ranging from conventional optical telecommunication networks, to the elaboration of photonic qubits in the integrated quantum information framework. In particular, the latter field has been object in the recent years of an increasing interest: the compactness and phase stability of integrated waveguide circuits are enabling experiments unconceivable with bulk-optics set-ups. Linear photonic devices for quantum information are based on quantum and classical interference effects: the desired circuit operation can be achieved only with tight fabrication control on both power repartition in splitting elements and phase retardance in the various paths. Here we report on a novel three-dimensional circuit architecture, made possible by the unique capabilities of femtosecond laser waveguide writing, which enables us to realize integrated multimode devices implementing arbitrary linear transformations. Networks of cascaded directional couplers can be built with independent control on the splitting ratios and the phase shifts in each branch. In detail, we show an arbitrarily designed 5×5 integrated interferometer: characterization with one- and two-photon experiments confirms the accuracy of our fabrication technique. We exploit the fabricated circuit to implement a small instance of the boson-sampling experiments with up to three photons, which is one of the most promising approaches to realize phenomena hard to simulate with classical computers. We will further show how, by studying classical and quantum interference in many random multimode circuits, we may gain deeper insight into the bosonic coalescence phenomenon.
The emerging field of quantum technologies requires a range of photonic devices, many with demanding specifications. The area of quantum information processing requires scaling in order to increase the complexity of experiments, this has led researchers towards integrated photonic platforms. The key property of these single photon devices is low-loss operation and as a consequence glass and silica devices have been a dominant platform. Whereas atom chip sensors require stable compact systems for converting optical fibre modes to free space beams for atom trapping. In this talk I will present the photonic engineering undertaken at the University of Southampton to fabricate devices for the quantum technology community. The key fabrication approach is a direct UV writing technique, where a UV laser beam is used to define waveguides, splitters/couplers, Bragg gratings and 2D tilted gratings. The fabricated devices include cascaded arrays of Mach-Zehnder interferometers to preform photon-photon interactions, single photon sources via spontaneous four-wave mixing, integrated superconducting single photon detectors and 2D diffraction gratings. In addition to the inscription method I will describe the fabrication of the substrates required for the UV writing process which are generated via Flame Hydrolysis Deposition. I will discuss our most recent work on single photon linear optical networks constructed from a number of identical reconfigurable modules. The modules are characterised separately to produce an accurate model of the network and the cellular approach permits the replacement of modules that are deficient. Each module comprises of an array of 10 Mach-Zehnder interferometers with 40 thermo-optic phase shifters on each chip that control both the amplitude and phase of the optical modes. By concatenating modules any arbitrary N ×N unitary network can be realised. The channel waveguides are engineered to be mode matched to standard optical fibre producing excellent coupling efficiency. I will present our recent work in this area and other photonic devices for the field of quantum technology.