The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.
The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.
Tensor network formalisms have emerged as powerful tools for simulating quantum state evolution. While widely applied in the study of optical quantum circuits, such as boson sampling, existing tensor network approaches fail to address the complexity mismatch between tensor contractions and the calculation of photon-counting probability amplitudes. Here, we present an alternative tensor network framework that exploits the input-output relations of quantum optical circuits encoded in the unitary interferometer matrix. Our approach bridges the complexity gap by enabling the computation of the permanent—central to boson sampling—with the same computational complexity as the best known classical algorithm based on a graphical representation of the operator-basis matrix product states that we introduce. Furthermore, we exploit the flexibility of tensor networks to extend our formalism to incorporate partial distinguishability and photon loss, two key imperfections in practical interferometry experiments. This work offers a significant step forward in the simulation of large-scale quantum optical systems and the understanding of their computational complexity.
Photons offer a myriad of bases for encoding quantum information, including such popular choices as polarization, spatial modes, and time bins. And due to frequency’s inherent stability and compatibility with optical fiber, spectral modes provide a particularly attractive Hilbert space for quantum computation. Yet control and processing of such modes can prove quite challenging, typically requiring complicated operations and strong classical pump fields. In this talk, I will describe our paradigm for universal quantum computation based on frequency-bin qubits and standard lightwave technology: electro-optic phase modulators and Fourier-transform pulse shapers. Our approach offers excellent resource scaling, parallelizability, and compatibility with fiber-optic technology. I will discuss experiments so far, including frequency-bin Hadamard and tritter gates, both with ultrahigh fidelity and broad bandwidth; quantum interference and independent spectral control of two photons in the same optical fiber; and a frequency-bin controlled-NOT, the first of its kind. Such experiments are augmented by Bayesian machine learning techniques, allowing for more detailed gate analysis than possible with conventional approaches. Finally, I will conclude with an outlook on future work, highlighting opportunities to address current challenges and summarizing the potential for our technique, not only in quantum computation proper, but also quantum interconnects, frequency-multiplexed networks, and on-chip integration.
The non-classical interference undergone by multiple photons in passive, linear optical networks gives rise to a surprising computational power of such quantum systems. This is prominently highlighted by boson sampling, a scheme for quantum computation which relies solely on such multiphoton interference and omits the usage of more sophisticated techniques such as entangling gates or feed-forward control. Despite these limitations, it still allows to efficiently solve a class of computational problems which is intractable for classical computers. In this thesis, several open challenges on the way to an experimental realization of boson sampling are addressed. To that end, the idealized model for boson sampling is extended to account, for example, for inner degrees of freedom of the single-photon pulses or the probabilistic nature of single-photon sources. It is shown that the difficulties arising from these real-world effects can be overcome by suitably adapting existing boson sampling schemes. Additionally, the extended model for such interference is applied to reveal its intricate dependence on input state, evolution inside the interferometer, and the detection process. Finally, a novel description of SPDC in terms of temporal Bogoliubov transformations is provided, revealing new, intuitive insights into the temporal structure of photon correlations for such sources.
Quantum states encoded in the time-bin degree of freedom of photons represent a fundamental resource for quantum information protocols. Traditional methods for generating and measuring time-bin-encoded quantum states face severe challenges due to optical instabilities, complex setups, and timing resolution requirements. To circumvent these issues, we leverage an approach based on Hong-Ou-Mandel interference and we propose and demonstrate a robust and scalable protocol to generate and measure arbitrary high-dimensional time-bin quantum states. We experimentally implement the protocol in a photonic setup reaching high-fidelity quantum state tomographies of two- and three-dimensional quantum states encoded in time bins with short temporal separation. We also certify intrasystem polarization-time entanglement of single photons through a nonclassicality test. The demonstrated approach enables access to high-dimensional states and tasks that are practically inaccessible with standard schemes, thereby advancing fundamental quantum information science and opening applications in quantum communication.
This thesis presents results under the topics of quantum correlations and quantum information processing using linear-optical networks. The first part of this thesis concerns with quantum correlations, specially in Gaussian states, which play a central role as resource in quantum protocols. The second part is about quantum information processing using linear-optical networks that are of great practical interest due to their simple physical realization. In the first part, we present a measurement-based method for verifying nonzero quantum discord, a measure of quantum correlations, in bipartite systems that can be used for both continuous and discrete-variable systems. Based on this method, we show that the only bipartite Gaussian states with zero quantum discord are product states. We also present a simple and efficient experimental method for verifying quantum correlations in Gaussian states using homodyne measurements. Moreover, we introduce an operational measure for quantifying quantum correlations in Gaussian states that is purely based on Gaussian measurements. We then illustrate the operational significance of the measure in terms of a Gaussian quantum protocol. In the second part, we present results on linear quantum-optics experiments, specifically boson sampling, an intermediate model of quantum computation that can be implemented using single-photon states, linear-optical networks, and photodetectors. We first present an efficient experimental method for characterization of linear-optical networks, which is essential for practical implementation of boson sampling. We show that using coherent states one can directly measure all the nontrivial phases and moduli of the matrix describing the network. Next, we consider the problem of boson sampling with Gaussian states. We derive a general formula for calculating the output photon-counting probabilities. We show that for input thermal states, sampling from the output probability distribution can be efficiently classically simulated. Using this, we find that permanents of positive-semidefinite Hermitian matrices can be approximated to within a multiplicative error in BPPNP. We also discuss boson sampling with squeezed vacuum states. Finally, we provide a sufficient condition for the efficient classical simulation of the general sampling problem using linear-quantum optics, which involves a multimode input quantum state to a linear-optical network and set of measurements at the output. This condition is based on the phase-space quasiprobability distributions, and suggests that negativity is a quantum resource. We apply this condition to implementations of boson sampling using single-photon or spontaneous parametric down-conversion sources. We show that above some threshold for loss and noise in the experiment, boson sampling is classically simulatable.
We present an architecture for arbitrarily scalable boson sampling using two nested fiber loops. The architecture has fixed experimental complexity, irrespective of the size of the desired interferometer, whose scale is limited only by fiber and switch loss rates. The architecture employs time-bin encoding, whereby the incident photons form a pulse train, which enters the loops. Dynamically controlled loop coupling ratios allow the construction of the arbitrary linear optics interferometers required for boson sampling. The architecture employs only a single point of interference and may thus be easier to stabilize than other approaches. The scheme has polynomial complexity and could be realized using demonstrated present-day technologies.