Demonstration of nondeterministic quantum logic operations using linear optical elements

High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source

Compared to other types of qubits, photon is one of a kind due to its unparalleled advantages in long-distance quantum information exchange. Therefore, photon is a natural candidate for building a large-scale, modular optical quantum computer operating at room temperature. However, low-fidelity two-photon quantum logic gates and their probabilistic nature result in a large resource overhead for fault tolerant quantum computation. While the probabilistic problem can, in principle, be solved by employing multiplexing and error correction, the fidelity of linear-optical quantum logic gate is limited by the imperfections of single photons. Here, we report the demonstration of a linear-optical quantum logic gate with truth table fidelity of 99.84(3)% and entangling gate fidelity of 99.69(4)% post-selected upon the detection of photons. The achieved high gate fidelities are made possible by our near-optimal Rydberg single-photon source. Our work paves the way for scalable photonic quantum applications based on near-optimal single-photon qubits and photon-photon gates.

The current main source of errors for photonic quantum logic gates is the imperfections of the single photons. Here, by using high-quality photons from Rydberg atoms, the authors are able to reach 99.7% entangling gate fidelity in a photonic CNOT gate.

Proposal for a destructive controlled phase gate using linear optics

Knill, Laflamme, and Milburn showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate for a single-rail target qubit that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.

Heralded Nondestructive Quantum Entangling Gate with Single-Photon Sources

Heralded entangling quantum gates are an essential element for the implementation of large-scale optical quantum computation. Yet, the experimental demonstration of genuine heralded entangling gates with free-flying output photons in linear optical system, was hindered by the intrinsically probabilistic source and double-pair emission in parametric down-conversion. Here, by using an on-demand single-photon source based on a semiconductor quantum dot embedded in a micropillar cavity, we demonstrate a heralded controlled-NOT (CNOT) operation between two single photons for the first time. To characterize the performance of the CNOT gate, we estimate its average quantum gate fidelity of (87.8±1.2)%. As an application, we generated event-ready Bell states with a fidelity of (83.4±2.4)%. Our results are an important step towards the development of photon-photon quantum logic gates.

Observation of second-order interference beyond the coherence time with true thermal photons

It has recently been shown that counter-intuitive Franson-like second-order interference can be observed with a pair of classically correlated pseudo thermal light beams and two separate unbalanced interferometers (UIs): the second-order interference visibility remains fixed at 1/3 even though the path length difference in each UI is increased significantly beyond the coherence length of the pseudo thermal light [Phys. Rev. Lett.119, 223603 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.223603]. However, as the pseudo thermal beam itself originated from a long-coherence laser (and by using a rotating ground disk), there exists the possibility of a classical theoretical model to account for second-order interference beyond the coherence time on the long coherence time of the original laser beam. In this work, we experimentally explore this counter-intuitive phenomenon with a true thermal photon source generated via quantum thermalization, i.e., obtaining a mixed state from a pure two-photon entangled state. This experiment not only demonstrates the unique second-order coherence properties of thermal light clearly but may also open up remote sensing applications based on such effects.

Measuring the Single-Photon Temporal-Spectral Wave Function

Temporal-spectral modes of light provide a fundamental window into the nature of quantum systems and offer a robust means for information encoding. Methods to precisely characterize the temporal-spectral state of light at the single-photon level thus play a central role in understanding single-photon sources and their applications in emerging optical quantum technologies. Here we demonstrate an optical reference-free method, which melds techniques from ultrafast metrology and single-photon spectral detection, to characterize the pulse-mode structure of heralded single photons.

Pulsed single-photon spectrometer by frequency-to-time mapping using chirped fiber Bragg gratings

A fiber-integrated spectrometer for single-photon pulses outside the telecommunications wavelength range based upon frequency-to-time mapping, implemented by chromatic group delay dispersion (GDD), and precise temporally-resolved single-photon counting, is presented. A chirped fiber Bragg grating provides low-loss GDD, mapping the frequency distribution of an input pulse onto the temporal envelope of the output pulse. Time-resolved detection with fast single-photon-counting modules enables monitoring of a wavelength range from 825 nm to 835 nm with nearly uniform efficiency at 55 pm resolution (24 GHz at 830 nm). To demonstrate the versatility of this technique, spectral interference of heralded single photons and the joint spectral intensity distribution of a photon-pair source are measured. This approach to single-photon-level spectral measurements provides a route to realize applications of time-frequency quantum optics at visible and near-infrared wavelengths, where multiple spectral channels must be simultaneously monitored.

Realization of a Cascaded Quantum System: Heralded Absorption of a Single Photon Qubit by a Single-Electron Charged Quantum Dot

Photonic losses pose a major limitation for the implementation of a quantum state transfer between nodes of a quantum network. A measurement that heralds a successful transfer without revealing any information about the qubit may alleviate this limitation. Here, we demonstrate the heralded absorption of a single photonic qubit, generated by a single neutral quantum dot, by a single-electron charged quantum dot that is located 5 m away. The transfer of quantum information to the spin degree of freedom takes place upon the emission of a photon; for a properly chosen or prepared quantum dot, the detection of this photon yields no information about the qubit. We show that this process can be combined with local operations optically performed on the destination node by measuring classical correlations between the absorbed photon color and the final state of the electron spin. Our work suggests alternative avenues for the realization of quantum information protocols based on cascaded quantum systems.

Faithful conditional quantum state transfer between weakly coupled qubits

One of the strengths of quantum information theory is that it can treat quantum states without referring to their particular physical representation. In principle, quantum states can be therefore fully swapped between various quantum systems by their mutual interaction and this quantum state transfer is crucial for many quantum communication and information processing tasks. In practice, however, the achievable interaction time and strength are often limited by decoherence. Here we propose and experimentally demonstrate a procedure for faithful quantum state transfer between two weakly interacting qubits. Our scheme enables a probabilistic yet perfect unidirectional transfer of an arbitrary unknown state of a source qubit onto a target qubit prepared initially in a known state. The transfer is achieved by a combination of a suitable measurement of the source qubit and quantum filtering on the target qubit depending on the outcome of measurement on the source qubit. We experimentally verify feasibility and robustness of the transfer using a linear optical setup with qubits encoded into polarization states of single photons.

Logical operations with single x-ray photons via dynamically-controlled nuclear resonances

Photonic qubits lie at the heart of quantum information technology, often encoding information in their polarization state. So far, only low-frequency optical and infrared photons have been employed as flying qubits, as the resources that are at present easiest to control. With their essentially different way of interacting with matter, x-ray qubits would bear however relevant advantages: they are extremely robust, penetrate deep through materials, and can be focused down to few-nm waveguides, allowing unprecedented miniaturization. Also, x-rays are resonant to nuclear transitions, which are very well isolated from the environment and present long coherence times. Here, we show theoretically that x-ray polarization qubits can be dynamically controlled by nuclear Mössbauer resonances. The control knob is played by nuclear hyperfine magnetic fields, that allow via fast rotations precise processing of single x-ray quanta polarization. With such rotations, single-qubit and binary logical operations such as a destructive C-NOT gate can be implemented.

No-go theorem for passive single-rail linear optical quantum computing

Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.

Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion

Optical parametric down-conversion (PDC) is a central tool in quantum optics experiments. The number of collected down-converted modes greatly affects the quality of the produced photon state. We use Silicon Photomultiplier (SiPM) number-resolving detectors in order to observe the photon-number distribution of a PDC source, and show its dependence on the number of collected modes. Additionally, we show how the stimulated emission of photons and the partition of photons into several modes determine the overall photon number. We present a novel analytical model for the optical crosstalk effect in SiPM detectors, and use it to analyze the results.

Experimental realization of programmable quantum gate array for directly probing commutation relations of Pauli operators

We experimentally demonstrate an advanced linear-optical programmable quantum processor that combines two elementary single-qubit programmable quantum gates. We show that this scheme enables direct experimental probing of quantum commutation relations for Pauli operators acting on polarization states of single photons. Depending on a state of two-qubit program register, we can probe either commutation or anticommutation relations. Very good agreement between theory and experiment is observed, indicating high-quality performance of the implemented quantum processor.

Probabilistic growth of large entangled states with low error accumulation

The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple "probabilistic" operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe overhead in terms of the accumulation of errors. Here, we describe a method that can rapidly generate large entangled states with an error accumulation that depends only logarithmically on the failure probability. We find that the approach may be practical for success rates in the sub-10% range. The assumptions that we make, including parallelism and high connectivity, are appropriate for real systems including those based on measurement-induced entanglement. This result therefore indicates the feasibility of such devices.

Complete deterministic linear optics Bell state analysis

We show how hyperentanglement allows us to deterministically distinguish between all four polarization Bell states of two photons. In this proof-of-principle experiment, we employ the intrinsic time-energy correlation of photon pairs generated with high temporal definition in addition to the polarization entanglement obtained from parametric down-conversion. For the identification, no nonlinear optical elements or auxiliary photons are needed. The new possibilities this complete Bell measurement offers are demonstrated by realizing an optimal dense coding protocol.

Optical implementation of quantum orienteering

We present results from an optical implementation of quantum orienteering, a protocol for communicating directions in space using quantum bits. We show how different types of measurements and encodings can be used to increase the communication efficiency. In particular, if Alice and Bob use two spin- particles for communication and employ joint measurements, they do better than is possible with local operations and classical communication. Furthermore, by using oppositely oriented spins, the achievable communication efficiency is further increased. Finally, we discuss the limitations of an optical approach: our results highlight the usually overlooked nonequivalence of different physical encodings of quantum bits.

Realization of a minimal disturbance quantum measurement

We report the first experimental realization of an "optimal" quantum device able to perform a minimal disturbance measurement on polarization encoded qubits saturating the theoretical boundary established between the classical knowledge acquired of any input state, i.e., a "classical guess," and the fidelity of the same state after disturbance due to measurement. The device has been physically realized by means of a linear optical qubit manipulation, postselection measurement, and a classical feed-forward process.

Demonstration of an optical quantum controlled-NOT gate without path interference

We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittance and reflectance. The performance of the device is evaluated using a recently proposed method, by which the quantum process fidelity and the entanglement capability can be estimated from the 32 measurement results of two classical truth tables, significantly less than the 256 measurement results required for full quantum tomography.

Demonstration of a simple entangling optical gate and its use in bell-state analysis

We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realizations, using partially polarizing beam splitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-z gate in both continuous-wave and pulsed regimes of operation, fully characterizing it in each case using quantum process tomography. We also demonstrate a fully resolving, nondeterministic optical Bell-state analyzer based on this controlled-z gate. This new architecture is ideally suited to guided optics implementations of optical gates.

Optimizing linear optics quantum gates

In this Letter, the problem of finding optimal success probabilities of linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of networks realizing single-mode gates can be derived, which hold in generality for postselected networks of arbitrary size, any number of auxiliary modes, and arbitrary photon numbers. As a corollary, the previously formulated conjecture is proven that the optimal success probability of a nonlinear sign shift without feedforward is 1/4, a gate playing the central role in the scheme of Knill-Laflamme-Milburn for quantum computation. The concept of Lagrange duality is shown to be applicable to provide rigorous proofs for such bounds, although the original problem is a difficult nonconvex problem in infinitely many objective variables. The versatility of this approach is demonstrated.

Measurement of geometric phase for mixed states using single photon interferometry

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.

Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits

Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum information processing. However, photons, one of the best candidates for qubits, suffer from a lack of strong nonlinear coupling, which is required for quantum logic operations. Here we show how this drawback can be overcome by reporting a proof-of-principle experimental demonstration of a nondestructive controlled-NOT (CNOT) gate for two independent photons using only linear optical elements in conjunction with single-photon sources and conditional dynamics. Moreover, we exploit the CNOT gate to discriminate all four Bell states in a teleportation experiment.

Experimental teleportation of a quantum controlled-NOT gate

Teleportation of quantum gates is a critical step for the implementation of quantum networking and teleportation-based models of quantum computation. We report an experimental demonstration of teleportation of the prototypical quantum controlled-NOT (CNOT) gate. Assisted with linear optical manipulations, photon entanglement produced from parametric down-conversion, and postselection from the coincidence measurements, we teleport the quantum CNOT gate from acting on local qubits to acting on remote qubits. The quality of the quantum gate teleportation is characterized through the method of quantum process tomography, with an average fidelity of 0.84 demonstrated for the teleported gate.

Deterministic controlled-NOT gate for single-photon two-qubit quantum logic

We demonstrate a robust implementation of a deterministic linear-optical controlled-not gate for single-photon two-qubit quantum logic. A polarization Sagnac interferometer with an embedded 45 degrees -oriented dove prism is used to enable the polarization control qubit to act on the momentum (spatial) target qubit of the same photon. The optical controlled-not gate requires no active stabilization because the two spatial modes share a common path, and it is used to entangle the polarization and momentum qubits.

Experimental demonstration of five-photon entanglement and open-destination teleportation

Quantum-mechanical entanglement of three or four particles has been achieved experimentally, and has been used to demonstrate the extreme contradiction between quantum mechanics and local realism. However, the realization of five-particle entanglement remains an experimental challenge. The ability to manipulate the entanglement of five or more particles is required for universal quantum error correction. Another key process in distributed quantum information processing, similar to encoding and decoding, is a teleportation protocol that we term 'open-destination' teleportation. An unknown quantum state of a single particle is teleported onto a superposition of N particles; at a later stage, this teleported state can be read out (for further applications) at any of the N particles, by a projection measurement on the remaining particles. Here we report a proof-of-principle demonstration of five-photon entanglement and open-destination teleportation (for N = 3). In the experiment, we use two entangled photon pairs to generate a four-photon entangled state, which is then combined with a single-photon state. Our experimental methods can be used for investigations of measurement-based quantum computation and multi-party quantum communication.

Realization of a photonic controlled-NOT gate sufficient for quantum computation

We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed forwardable. In the experiment, we achieved this goal with only the use of linear optics, an entangled ancillary pair of photons, and postselection. The techniques developed in our experiment are of significant importance for quantum information processing with linear optics.

Optimal quantum cloning on a beam splitter

We demonstrate how a beam splitter in combination with different light sources can be used as an optimal universal 1-->2 quantum cloner and as an optimal universal quantum NOT machine for the polarization qubit of a single photon. For the cloning a source of single photons with maximally mixed polarization is required and for the NOT operation a source of maximally entangled photon pairs. We demonstrate both operations with near optimal fidelity. Our scheme can be generalized in a natural way to clone and NOT the spin state of electrons.

All linear optical quantum memory based on quantum error correction

When photons are sent through a fiber as part of a quantum communication protocol, the error that is most difficult to correct is photon loss. Here we propose and analyze a two-to-four qubit encoding scheme, which can recover the loss of one qubit in the transmission. This device acts as a repeater, when it is placed in series to cover a distance larger than the attenuation length of the fiber, and it acts as an optical quantum memory, when it is inserted in a fiber loop. We call this dual-purpose device a "quantum transponder."

Experimental entanglement purification of arbitrary unknown states

Distribution of entangled states between distant locations is essential for quantum communication over large distances. But owing to unavoidable decoherence in the quantum communication channel, the quality of entangled states generally decreases exponentially with the channel length. Entanglement purification--a way to extract a subset of states of high entanglement and high purity from a large set of less entangled states--is thus needed to overcome decoherence. Besides its important application in quantum communication, entanglement purification also plays a crucial role in error correction for quantum computation, because it can significantly increase the quality of logic operations between different qubits. Here we demonstrate entanglement purification for general mixed states of polarization-entangled photons using only linear optics. Typically, one photon pair of fidelity 92% could be obtained from two pairs, each of fidelity 75%. In our experiments, decoherence is overcome to the extent that the technique would achieve tolerable error rates for quantum repeaters in long-distance quantum communication. Our results also imply that the requirement of high-accuracy logic operations in fault-tolerant quantum computation can be considerably relaxed.

Multimode Hong-Ou-mandel interference

We consider multimode two-photon interference at a beam splitter by photons created by spontaneous parametric down-conversion. The resulting interference pattern is shown to depend upon the transverse spatial symmetry of the pump beam. In an experiment, we employ the first-order Hermite-Gaussian modes in order to show that, by manipulating the pump beam, one can control the resulting two-photon interference behavior. We expect these results to play an important role in the engineering of quantum states of light for use in quantum information processing and quantum imaging.

Experimental extraction of an entangled photon pair from two identically decohered pairs

Entanglement is considered to be one of the most important resources in quantum information processing schemes, including teleportation, dense coding and entanglement-based quantum key distribution. Because entanglement cannot be generated by classical communication between distant parties, distribution of entangled particles between them is necessary. During the distribution process, entanglement between the particles is degraded by the decoherence and dissipation processes that result from unavoidable coupling with the environment. Entanglement distillation and concentration schemes are therefore needed to extract pairs with a higher degree of entanglement from these less-entangled pairs; this is accomplished using local operations and classical communication. Here we report an experimental demonstration of extraction of a polarization-entangled photon pair from two decohered photon pairs. Two polarization-entangled photon pairs are generated by spontaneous parametric down-conversion and then distributed through a channel that induces identical phase fluctuations to both pairs; this ensures that no entanglement is available as long as each pair is manipulated individually. Then, through collective local operations and classical communication we extract from the two decohered pairs a photon pair that is observed to be polarization-entangled.

High-fidelity quantum logic operations using linear optical elements

Knill, Laflamme, and Milburn [Nature (London) 409, 46 ((2001))]] have shown that quantum logic operations can be performed using linear optical elements and additional ancilla photons. Their approach is probabilistic in the sense that the logic devices fail to produce an output with a failure rate that scales as 1/n, where n is the number of ancilla. Here we present an alternative approach in which the logic devices always produce an output with an intrinsic error rate that scales as 1/n(2), which may have several advantages in quantum computing applications.