High-dimensional quantum key distribution (QKD) allows to achieve information-theoretic secure communications, providing high key generation rates which cannot in principle be obtained by QKD protocols with binary encoding. Nonetheless, the amount of experimental resources needed increases as the quantum states to be detected belong to a larger Hilbert space, thus raising the costs of practical high-dimensional systems. Here, we present a novel scheme for fiber-based 4-dimensional QKD, with time and phase encoding and one-decoy state technique. Quantum states transmission is tested over different channel lengths up to 145 km of standard single-mode fiber, evaluating the enhancement of the secret key rate in comparison to the three-state 2-dimensional BB84 protocol, which is tested with the same experimental setup. Our scheme allows to measure the 4-dimensional states with a simplified and compact receiver, where only two single-photon detectors are necessary, thus making it a cost-effective solution for practical and fiber-based QKD.
We propose and discuss a specific scheme allowing to realize a Quantum Cryptography qutrit protocol. This protocol exploits the polarization properties of single frequency and single spatial mode biphotons.
Within the quantum computing, there are two ways to encode a normalized vector $\{ α_i \}$. They are one-hot encoding and binary coding. The one-hot encoding state is denoted as $\left | ψ_O^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle \left |0 \right \rangle ^{\otimes i}$ and the binary encoding state is denoted as $\left | ψ_B^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |b_i \right \rangle$, where $b_i$ is interpreted in binary of $i$ as the tensor product sequence of qubit states. In this paper, we present a method converting …
Several emerging quantum technologies, including quantum networks, modular and fusion-based quantum computing, rely crucially on the ability to perform photonic Bell state measurements. Therefore, photon losses and the 50\% success probablity upper bound of Bell state measurements pose a critical limitation to photonic quantum technologies. Here, we develop protocols that overcome these two key challenges through logical encoding of photonic qubits. Our approach uses a tree graph state logical encoding, which can be produced deterministically with a few quantum emitters, and achieves near-dete…
We propose a scheme for the generation of hybrid states entangling a single-photon time-bin qubit with a coherent-state qubit encoded on phases. Compared to other reported solutions, time-bin encoding makes hybrid entanglement particularly well adapted to applications involving long-distance propagation in optical fibers. This makes our proposal a promising resource for future out-of-the-laboratory quantum communication. In this perspective, we analyze our scheme by taking into account realistic experimental resources and discuss the impact of their imperfections on the quality of the obtained…
Practical block encodings of matrix polynomials that can also be trivially controlled
Technical University of Munich（慕尼黑工业大学）；KU Leuven, University of Leuven（荷语鲁汶大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Google Quantum AI（谷歌量子人工智能）
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 b…
Quantum annealing is a heuristic algorithm for solving combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware for implementing this algorithm. The current version of the D-Wave quantum annealer can solve unconstrained binary optimization problems with a limited number of binary variables, although cost functions of many practical problems are defined by a large number of integer variables. To solve these problems with the quantum annealer, the integer variables are generally binarized with one-hot encoding, and the binarized problem is partitioned into small subpro…
Practical quantum computing requires robust encoding of logical qubits in physical systems to protect fragile quantum information. Currently, the lack of scalability limits the logical encoding in most physical systems, and thus the high scalability of propagating light can be a game changer for realizing a practical quantum computer. However, propagating light also has a drawback: the difficulty of logical encoding due to weak nonlinearity. Here, we propose Gaussian breeding that encodes arbitrary Gottesman-Kitaev-Preskill (GKP) qubits in propagating light. The key idea is the efficient and i…
We study the potential of general quantum operations, Trace-Preserving Completely-Positive Maps (TPCPs), as encoding and decoding mechanisms in quantum authentication protocols. The study shows that these general operations do not offer significant advantage over unitary encodings. We also propose a practical authentication protocol based on the use of two successive unitary encodings.
The encoding of quantum information in photonic time-bin qubits is apt for long distance quantum communication schemes. In practice, due to technical constraints such as detector response time, or the speed with which co-polarized time-bins can be switched, other encodings, e.g. polarization, are often preferred for operations like state detection. Here, we present the conversion of qubits between polarization and time-bin encodings using a method that is based on an ultrafast optical Kerr shutter and attain efficiencies of 97% and an average fidelity of 0.827+/-0.003 with shutter speeds near …
We analyze the method of encoding pairwise interactions of higher-than-binary discrete variables (these models are sometimes referred to as discrete quadratic models) into binary variables based on domain walls on one dimensional Ising chains. We discuss how this is relevant to quantum annealing, but also many gate model algorithms such as VQE and QAOA. We theoretically show that for problems of practical interest for quantum computing and assuming only quadratic interactions are available between the binary variables, it is not possible to have a more efficient general encoding in terms of nu…
A scheme for the implementation of the cluster state model of quantum computing in optical fibers, which enables the feedforward feature, is proposed. This scheme uses the time-bin encoding of qubits. Following previously suggested methods of applying arbitrary one-qubit gates in optical fibers, two different ways for the realization of fusion gate types I and II for cluster production are proposed: a fully time-bin based encoding scheme and a combination of time-bin and polarization based encoding scheme. Also the methods of measurement in any desired bases for the purpose of the processing o…
Quantum key distribution (QKD) gradually has become a crucial element of practical secure communication. In different scenarios, the security analysis of genuine QKD systems is complicated. A universal secret key rate calculation method, used for realistic factors such as multiple degrees of freedom encoding, asymmetric protocol structures, equipment flaws, environmental noise, and so on, is still lacking. Based on the correlations of statistical data, we propose a security analysis method without restriction on encoding schemes. This method makes a trade-off between applicability and accuracy…
Especially sparse quantum states can be efficiently encoded with simple classical data structures. We show the admissibility of using a classical database to encode quantum states for a few practical examples and argue in favor of further optimizations for quantum simulation targeting simpler, only 'semi-quantum' circuits.
It was recently shown by Motes, Gilchrist, Dowling & Rohde [PRL 113, 120501 (2014)] that a time-bin encoded fiber-loop architecture can implement an arbitrary passive linear optics transformation. This was shown in the case of an ideal scheme whereby the architecture has no sources of error. In any realistic implementation, however, physical errors are present, which corrupt the output of the transformation. We investigate the dominant sources of error in this architecture --- loss and mode-mismatch --- and consider how it affects the BosonSampling protocol, a key application for passive linea…
Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding are of particular interest because their QEC protection is hardware efficient, but gate operations on QEC protected logical qubits remain elusive. Here, we experimentally demonstrate full control on a single logical qubit with a binomial bosonic code, including encoding, decoding, repetitive QEC, and …
Floodlight quantum key distribution (FL-QKD) uses binary phase-shift keying (BPSK) of multiple optical modes to achieve Gbps secret-key rates (SKRs) at metropolitan-area distances. We show that FL-QKD's SKR can be doubled by using 32-ary PSK.
Compact quantum data representations are essential to the emerging field of quantum algorithms for data analysis. We introduce two new data encoding schemes, QCrank and QBArt, which have a high degree of quantum parallelism through uniformly controlled rotation gates. QCrank encodes a sequence of real-valued data as rotations of the data qubits, allowing for high storage density. QBArt directly embeds a binary representation of the data in the computational basis, requiring fewer quantum measurements and lending itself to well-understood arithmetic operations on binary data. We present several…
We present a scheme to encode M extra classical bits to a dense-coded pair of photons. By tuning the delay of an entangled pair of photons to one of 2^M time-bins and then applying one of the quantum dense coding protocols, a receiver equipped with a synchronized clock of reference is able to decode M bits (via classical time-bin encoding) + 2 bits (via quantum dense coding). This protocol, yet simple, does not dispense several special features of the used programmable delay apparatus to maintain the coherence of the two-photon state. While this type of time-domain encoding may be thought to b…
Frequency encoding is quickly becoming an attractive prospect for quantum information protocols owing to larger Hilbert spaces and increased resilience to noise compared to other photonic degrees of freedom. To fully make use of frequency encoding as a practical paradigm for QIP, an efficient and simple source of frequency entanglement is required. Here we present a single-pass source of discrete frequency-bin entanglement which does not use filtering or a resonant cavity. We use a domain-engineered nonlinear crystal to generate an eight-mode frequency-bin entangled source at telecommunication…
We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used for practical implementations of quantum computation. This determination is accomplished by applying ideal error correction to the encoded state which demonstrates the correctability of errors that occurred during the encoding process. We then apply single-qubit Clifford gates to the encoded state and determine the accuracy with which these gates can be applie…
A one-way quantum key distribution scheme based on intrinsically stable Faraday-mirror type Michelson interferometers with four-port polarizing beampslitters has been demonstrated which can compensate for birefringence effects automatically. The encoding is performed with phase modulators, but decoding is accomplished through measurement of the polarization state of Bob's photons. An extinction ratio of about 30dB was maintained for several hours over 50km of fiber at 1310nm without any adjustment to the setup, which shows its good potential for practical systems
We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the codespace performed via passive linear optics, and with generalized non-linear phase operations that are polynomials of the photon-number operator in the codespace. This encoding scheme can thus be applied to any computation with coherent state inputs, and the computation proceeds via a combination of passive linear optics and generalized non-linear phase operations. An example of s…
Recent advancements in quantum annealing hardware and numerous studies in this area suggests that quantum annealers have the potential to be effective in solving unconstrained binary quadratic programming problems. Naturally, one may desire to expand the application domain of these machines to problems with general discrete variables. In this paper, we explore the possibility of employing quantum annealers to solve unconstrained quadratic programming problems over a bounded integer domain. We present an approach for encoding integer variables into binary ones, thereby representing unconstraine…
Practical insights on the effect of different encodings, ansätze and measurements in quantum and hybrid convolutional neural networks
Quantum Lab, CTIC Centro Tecnol\'ogico, Parque Cient\'ifico Tecnol\'ogico de Gij\'on, Asturias, Spain；Eurecat, Centre Tecnol\`ogic de Catalunya, Multimedia Technologies, Barcelona, Spain；Centre de Visi\'o per Computador (CVC), Barcelona, Spain.；Fsas International Quantum Center (Fujitsu), Santiago de Compostela, Spain.
We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of qubits. The underlying encoding scheme allows for a systematic increase in correlations among the classical variables captured by a variational quantum state by progressively increasing the number of qubits involved. We first examine the simplest limit where all correlations are neglected, i.e. when the quantum state can only describe statistically independen…
Time-bin qudits have emerged as a promising encoding platform in many quantum photonic applications. However, the requirement for efficient single-shot measurement of time-bin qudits instead of reconstructive detection has restricted their widespread use in experiments. Here, we propose an efficient method to measure arbitrary superposition states of time-bin qudits and confirm it up to dimension 4. This method is based on encoding time bins at the picosecond time scale, also known as ultrafast time bins. By doing so, we enable the use of robust and phase-stable single spatial mode temporal in…
We introduce an electro-optical arrangement that is able to produce time-bin encoded symbols with the decoy state method over a standard optical fiber in the C-band telecom window. The device consists of a specifically designed pulse pattern generator for pulse production, a field-programmable gate array that controls timing and synchronization. The electrical pulse output drive a sequence of intensity modulators acting on a continuous laser that deliver bursts of weak optical pulse pairs of discrete intensity values. Such transmitter allows for the generation of all the quantum states needed …
Entanglement offers substantial advantages in quantum information processing, but loss and noise hinder its applications in practical scenarios. Although it has been well known for decades that the classical communication capacity over lossy and noisy bosonic channels can be significantly enhanced by entanglement, no practical encoding and decoding schemes are available to realize any entanglement-enabled advantage. Here, we report structured encoding and decoding schemes for such an entanglement-assisted communication scenario. Specifically, we show that phase encoding on the entangled two-mo…
