Quantum Fidelity Research Articles

Quantum-inspired attribute selection algorithms

Abstract In this study, we propose the use of quantum information gain (QIG) and fidelity as quantum splitting criteria to construct an efficient and balanced quantum decision tree. QIG is a circuit-based criterion in which angle embedding is used to construct a quantum state, which utilizes quantum mutual information to compute the information between a feature and the class attribute. For the fidelity-based criterion, we construct a quantum state using the occurrence of random events in a feature and its corresponding class. We use the constructed state to further compute fidelity for determining the splitting attribute among all features. Using numerical analysis, our results clearly demonstrate that the fidelity-based criterion ensures the construction of a balanced tree. We further compare the efficiency of our quantum information gain and fidelity-based quantum splitting criteria with different classical splitting criteria on balanced and imbalanced datasets. Our analysis shows that the quantum splitting criteria lead to quantum advantage in comparison to classical splitting criteria for different evaluation metrics.

Quantum intrusion detection system using outlier analysis

In the field of cybersecurity, hackers often enter computer systems despite current security measures, owing to the huge amount of network traffic that makes intruder identification difficult. Differentiating between authorized traffic and abnormal data produced by Distributed Denial of Service (DDoS) attackers is still a major difficulty. This research provides a unique technique that uses Quantum Machine Learning (QML) to improve security protocols for secure communication between two parties. Our strategy enhances detection accuracy and speed by using the characteristics of quantum neural networks. The approach includes creating a dataset from network traffic patterns, preprocessing it, and then turning it into quantum bits via angle embedding. The research uses outlier analysis, min-entropy, and quantum state fidelity to distinguish between normal and abnormal data patterns. The dispersed randomness of network header data is measured using entropy, which aids in identifying security concerns. The suggested QML-based methodology outperforms conventional approaches and current models, including AMM-CNN and ANN models, with a detection accuracy of 99.87% for DDoS attacks. This advancement leads to more effective and secure communication networks.

Benchmarking of quantum fidelity kernels for Gaussian process regression

Abstract Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an unbiased benchmarking of quantum kernels, it is necessary to construct the most optimal functional form of the classical kernels and the most optimal quantum kernels for each given data set. We develop an algorithm that uses an analog of the Bayesian information criterion to optimize the sequence of quantum gates used to estimate quantum kernels for Gaussian process models. The algorithm increases the complexity of the quantum circuits incrementally, while improving the performance of the resulting kernels, and is shown to yield much higher model accuracy with fewer quantum gates than a fixed quantum circuit ansatz. We demonstrate that quantum kernels thus obtained can be used to build accurate models of global potential energy surfaces (PES) for polyatomic molecules. The average interpolation error of the six-dimensional PES obtained with a random distribution of 2000 energy points is 16 cm−1 for H3O+, 15 cm−1 for H2CO and 88 cm−1 for HNO2. We show that a compositional optimization of classical kernels for Gaussian process regression converges to the same errors. This indicates that quantum kernels can achieve the same, though not better, expressivity as classical kernels for regression problems.

Loophole-Free Test of Local Realism via Hardy's Violation.

Bell's theorem states that the quantum mechanical description of physical quantities cannot be fully explained by local realistic theories, laying a solid basis for various quantum information applications. Hardy's paradox is celebrated as the simplest form of Bell's theorem concerning its "All versus Nothing" approach to test local realism. However, due to experimental imperfections, existing tests of Hardy's paradox require additional assumptions of the experimental systems, and these assumptions constitute potential loopholes for faithfully testing local realistic theories. Here, we experimentally demonstrate Hardy's nonlocality through a photonic entanglement source. By achieving a detection efficiency of 82.2%, a quantum state fidelity of 99.10%, and applying high-speed quantum random number generators for the measurement setting switching, the experiment is implemented in a loophole-free manner. During 6h of running, a strong violation of P_{Hardy}=4.646×10^{-4} up to 5 standard deviations is observed with 4.32×10^{9} trials. A null hypothesis test shows that the results can be explained by local realistic theories with an upper bound probability of 10^{-16348}. These testing results provide affirmative evidence against local realism, and establish an advancing benchmark for quantum information applications based on Hardy's paradox.

Higher-Dimensional Communications Using Multimode Fibers and Compact Components to Enable a Dense Set of Communicating Channels

Higher-dimensional communications are of interest for multiple reasons, including increasing the classical transmission capacity and, more recently, the quantum state transfer through fibers using the many modes within the fiber. For quantum communications, this enables an increase in the number of bits per photon, increasing quantum fidelity, increasing error thresholds and enabling hyperentanglement transfer, among other possibilities. A high-dimensional quantum state transfer can be transported through multimode fiber using the many modes available. However, this transfer of information through multimode optical fiber is limited by attenuation and mode coupling among the various spatial and polarization modes. Here, we consider how this mode coupling impacts the transfer process. We consider the fiber’s modal properties, including orbital angular momentum, modal group numbers, and principal modes. We also investigate and propose input and output optical components, as well as fiber properties, which better mitigate the deleterious effects of mode coupling. We use the WKB approximation to the scaler wave equation as a guidance to quantify this coupling and then implement corrections to this approximation using exact solutions to the scaler wave equation. We consider methods to circumvent this mode coupling using optical fiber designs, holographic optical components and devices that are commercially available today. Some of these components, such as the holographic gratings and lenses, could be implemented using flat optics.

Nonlocality activation using local filtering operations based on CGLMP inequality

Entanglement is necessary but not sufficient to demonstrate nonlocality as there exist local entangled states which do not violate any Bell inequality. In recent years, the activation of nonlocality (known as hidden nonlocality) by using local filtering operations has gained considerable interest. In the original proposal of Popescu [Phys. Rev. Lett. 74, 2619 (1995)] the hidden nonlocality was demonstrated for the Werner class of states in d ≥ 5. In this paper, we demonstrate the hidden nonlocality for a class of mixed entangled states (convex mixture of a pure state and color noise) in an arbitrary d-dimensional system using suitable local filtering operations. For our demonstration, we consider the quantum violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality which has hitherto not been considered for this purpose. We show that when the pure state in the aforementioned mixed entangled state is a maximally entangled state, the range of the mixing parameter for revealing hidden nonlocality increases with increasing the dimension of the system. Importantly, we find that for d ≥ 8, hidden non-locality can be revealed for the whole range of mixing parameter. Further, by considering another pure state, the maximally CGLMP-violating state, we demonstrate the activation of nonlocality by using the same local filtering operation. We have also shown the activation of quantum fidelity for mixed entangled states using the same local filtering operator.

Versatile Fidelity Estimation with Confidence.

As quantum devices become more complex and the requirements on these devices become more demanding, it is crucial to be able to verify the performance of such devices in a scalable and reliable fashion. A cornerstone task in this challenge is quantifying how close an experimentally prepared quantum state is to the desired one. Here we present a method to construct an estimator for the quantum state fidelity that is compatible with any measurement protocol. Our method provides a confidence interval on this estimator that is guaranteed to be nearly minimax optimal for the specified measurement protocol. For a well-chosen measurement scheme, our method is competitive in the number of measurement outcomes required for estimation. We demonstrate our method using simulations and experimental data from a trapped-ion quantum computer and compare the results to state-of-the-art techniques. Our method can be easily extended to estimate the expectation value of any observable, such as entanglement witnesses.

Multimode interference coupler based on general interference for integrated optical and quantum optic devices: a review

Integrated optics play important role in the development for optical network devices, optical processing, instrumentation and quantum information device. Here, multimode interference (MMI) coupler is one of basic component preferred for these integrated optic devices in which MMI coupler based on general interference (GIMMI) has been focused for large scale integrated optic devices because of compact size in comparison to MMI coupler based restricted interference (RIMMI). In this paper, we have reviewed different GIMMI structures reported previously. Different waveguide materials are mentioned and compared for fabrication of GIMMI device. The coupling behaviors and modal analysis of GIMMI couplers and their different tapered structures are estimated by using simple model based on sinusoidal modes showing reduced coupling lengths in down tapered structures in comparison to other structures. The excess loss, polarization dependence loss and crosstalk versus fabrication tolerances are obtained to compare their performances revealing almost same losses and fabrication tolerance. The paper reports the use of the GIMMI coupler in wavelength multiplexing, power splitting, switching, optical processing. Finally, Quantum optic application of GIMMI coupler is shown indicating high quantum fidelity of 50:50 coupling ratio.

Integrated preparation and manipulation of high-dimensional flying structured photons

The hope for a futuristic global quantum internet that provides robust and high-capacity quantum information transfer lies largely on qudits, the fundamental quantum information carriers prepared in high-dimensional superposition states. However, preparing and manipulating N-dimensional flying qudits as well as subsequently establishing their entanglement are still challenging tasks, which require precise and simultaneous maneuver of 2 (N-1) parameters across multiple degrees of freedom. Here, using an integrated approach, we explore the synergy from two degrees of freedom of light, spatial mode and polarization, to generate, encode, and manipulate flying structured photons and their formed qudits in a four-dimensional Hilbert space with high quantum fidelity, intrinsically enabling enhanced noise resilience and higher quantum data rates. The four eigen spin–orbit modes of our qudits possess identical spatial–temporal characteristics in terms of intensity distribution and group velocity, thereby preserving long-haul coherence within the entirety of the quantum data transmission link. Judiciously leveraging the bi-photon entanglement, which is well preserved in the integrated manipulation process, we present versatile spin–orbit cluster states in an extensive dimensional Hilbert space. Such cluster states hold the promise for quantum error correction which can further bolster the channel robustness in long-range quantum communication.

Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility.

In this study, we explore the quantum critical phenomena in generalized Aubry-André models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-André model. Based on the Diophantine equationconjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments.

Experimental Direct Quantum Fidelity Learning via a Data-Driven Approach.

Fidelity estimation is an important technique for evaluating prepared quantum states in noisy quantum devices. A recent theoretical work proposed a frugal approach called neural quantum fidelity estimation (NQFE) [X. Zhang et al., Phys. Rev. Lett. 127, 130503 (2021).PRLTAO0031-900710.1103/PhysRevLett.127.130503]. While this requires a much smaller number of measurement operators than full quantum state tomography, it uses a weight-based floating measurement strategy that predetermines the top global Pauli operators that contribute the most to the fidelity and uses discrete fidelity intervals as predictions. In this Letter, we develop a measurement-fixed NQFE based on a transformer model which requires less measurement cost and can output continuous estimates of fidelity. Here we further experimentally apply the NQFE in a realistic situation using a nuclear spin quantum processor. We prepare the ground states of local Hamiltonians and arbitrary states and investigate how to estimate their fidelity with reference states, and we compare the fidelity estimation strategy with our and the original NQFE to conventional tomography. It is shown that NQFE can estimate the fidelity with comparable accuracy to the tomography approach. In the future, NQFE will become an important tool for benchmarking quantum states ahead of the advent of well-trusted fault-tolerant quantum computers.

Quantum fidelity and Von Neumann entropy of a Bose-Fermi Mixture in 1D double well potential

Abstract The time evolution of probability density, the ground-state fidelity and the entanglement of a Bose-Fermi mixture in a 1D double well potential, are studied through the two-mode approximation.

We found that the behavior of the quantum return probability shows three distinct regions. The first region is characterized by a complete miscibility, and correlated tunneling of bosons and fermion. The second region is characterized by correlated sequential tunneling and in the last region we found an increase in the tunneling frequency of the two species.

Through the Von Neumann entropy, we found that the boson-fermion coupling allows a maximum entanglement of quantum correlations of bosons and fermions in the same value. \textcolor{red}{Finally, Considering variations in the interaction between pairs of fermions $\lambda_{FF}$, pairs of bosons $\lambda_{BB}$, and variations in the interaction between particles of different species $\lambda_{BF}$, we calculated the fidelity in the $\lambda_{FF}-\lambda_{BF}$ and $\lambda_{BB}-\lambda_{BF}$ planes and we found that the drop of the two fidelities becomes deeper and deeper as the boson-fermion interaction decreases.}

Quantum fidelity kernel with a trapped-ion simulation platform

Quantum fidelity kernel with a trapped-ion simulation platform

Continuous variable quantum teleportation network with star topology

Quantum network allows communication among more than two users with quantum teleportation and high quantum fidelity enabled by non-classical resources. As one of the most versatile architectures, all users are connected mediated by the central station in the star topology network, leading to the realization of the information interconnection and interoperability. In this work, we experimentally demonstrate a 4-branch continuous variable (CV) quantum teleportation network with star topology by employing entangled sideband modes from one squeezed state of light. Here, multiple pairs of entangled sideband modes are distributed on demand to central station and four nodes, respectively. Each node linked to the network has its own communication channel with the central station, where the deterministic CV quantum teleportation protocol is implemented with the fidelities above 0.830.

Modeling Low- and High-Frequency Noise in Transmon Qubits with Resource-Efficient Measurement

Transmon qubits experience open-system effects that manifest as noise at a broad range of frequencies. We present a model of these effects using the Redfield master equation with a hybrid bath consisting of low- and high-frequency components. We use two-level fluctuators to simulate 1/f-like noise behavior, which is a dominant source of decoherence for superconducting qubits. By measuring quantum state fidelity under free evolution with and without dynamical decoupling (DD), we can fit the low- and high-frequency noise parameters in our model. We train and test our model using experiments on quantum devices available through IBM quantum experience. Our model accurately predicts the fidelity decay of random initial states, including the effect of DD pulse sequences. We compare our model with two simpler models and confirm the importance of including both high frequency and 1/f noise in order to accurately predict transmon behavior. Published by the American Physical Society 2024

Bright source of narrowband polarization-entangled photons from a thick type-II ppKTP crystal.

We demonstrate a high brightness (∼2.36 × 105 pairs/s/mW) polarization-entangled photon-pair source at 800-nm via spontaneous parametric down-conversion (SPDC) in a 3-cm long type-II ppKTP crystal pumped unidirectionally in a single-pass geometry. A high coincidences-to-accidentals ratio (CAR ∼ 1200) depicted by our source indicates a strong temporal correlation between the generated photon pairs. This correlated photon source is tunable from collinear to non-collinear emission of the photons and over a range of signal/idler wavelengths ∼8 - 9nm corresponding to a temperature range of 20-60°C. We measure a quantum state fidelity F>95% with the singlet entangled state |ψ -⟩=12(|H V⟩-|V H⟩) along with a violation of the CHSH-Bell's inequality by ∼485 standard deviations (S = 2.68 ± 0.0014).

A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity

A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity

Analysis of quantum properties of two-mode coupled harmonic oscillator based on entangled state representation

<sec>The quantum oscillator model plays a significant role in quantum optics and quantum information and has been one of the hot topics in related research fields. Inspired by the single-mode linear harmonic oscillator and the two-mode entangled state representation, we construct a two-mode coupled harmonic oscillator in this work. Different from the quantum transformation method used in previous literature, the entangled state representation is directly used in this work to solve its energy eigenvalues and eigenfunctions easily. The energy eigenvalues and eigenfunctions of this two-mode coupled harmonic oscillator are continuous compared with those of the one-mode harmonic oscillator.</sec><sec>Using the matrix theory of quantum operators, we derive the transformation and inverse transformation of the time evolution operator corresponding to the two-mode coupled harmonic oscillator. In addition, using the entangled state representation, the specific form of the time evolution of the two-mode vacuum state under the action of the oscillator is obtained. Through the analysis of quantum fidelity, it is found that the fidelity of the output quantum state decreases with the oscillator frequency increasing, and the fidelity eventually tends to zero with the increase of time.</sec><sec>When analyzing the orthogonal squeezing properties of the output quantum state, this type of two-mode oscillator does not have the orthogonal squeezing effect, but it has a strong quantum dissipation effect instead. This conclusion is further verified by the quasi-probability distribution Q function of the quantum state phase space. Therefore, the two-mode coupled harmonic oscillator has a major reference value in quantum control such as quantum decoherence and quantum information transmission.</sec><sec>Like the two-mode squeezed vacuum state, the photon distribution of the output quantum light field corresponding to the two-mode harmonic oscillator presents a super-Poisson distribution, and the photons exhibit a strong anti-bunching effect. Using the three-dimensional discrete plot of the photon number distribution, the super-Poisson distribution and quantum dissipation effect of the output quantum state are intuitively demonstrated.</sec><sec>Finally, the SV, which is an entanglement criterion, is used to determine that the output quantum state has a high degree of entanglement. Further numerical analysis shows that the degree of entanglement increases with the action time and the oscillator frequency.</sec><sec>In summary, the two-mode coupled harmonic oscillator constructed in this work can be used to prepare highly entangled quantum states through a complete quantum dissipation process. This provides theoretical support for experimental preparing quantum entangled states based on dissipative mechanisms.</sec>

On the geometric phases in entangled states

Correlation relations for the spin measurements on a pair of entangled particles scattered by the two separate arms of interferometers in hybrid setups of different types are investigated. Concurrence, entanglement of formation, quantum fidelity, Bures distance are used to clarify how the geometric phase affects the initial bipartite state. This affect causes a quantum interference due to the movement of charged particles in regions where electromagnetic fields are not present. We shown that in some cases the geometric phase information is carried over to the final bipartite entangled state.

Hybrid Quantum Key Distribution Protocol with Chaotic System for Securing Data Transmission

This research proposes a combination of Quantum Key Distribution (QKD) based on the BB84 protocol with Improved Logistic Map (ILM) to improve data transmission security. This method integrates quantum key formation from BB84 with ILM encryption. This combination creates an additional layer of security, where by default, the operation on BB84 is only XOR-substitution, with the addition of ILM creating a permutation operation on quantum keys. Experiments are measured with several quantum measurements such as Quantum Bit Error Rate (QBER), Polarization Error Rate (PER), Quantum Fidelity (QF), Eavesdropping Detection (ED), and Entanglement-based detection (EDB), as well as classical cryptographic analysis such as Bit Error Ratio (BER), Entropy, Histogram Analysis, and Normalized Pixel Change Rate (NPCR) and Unified Average Changing Intensity (UACI). As a result, the proposed method obtained satisfactory results, especially perfect QF and BER, and EBD, which reached 0.999.