Quantum Fidelity Research Articles

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.

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

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.

Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments

Today’s experimental noisy quantum processors can compete with and surpass all known algorithms on state-of-the-art supercomputers for the computational benchmark task of Random Circuit Sampling (Boixo et al., 2018, Arute et al., 2019, Wu et al., 2021, Zhu et al., 2022, Morvan et al., 2023). Additionally, a circuit-based quantum simulation of quantum information scrambling (Mi et al., 2021), which measures a local observable, has already outperformed standard full wave function simulation algorithms, e.g., exact Schrodinger evolution and Matrix Product States (MPS). However, this experiment has not yet surpassed tensor network contraction for computing the value of the observable. Based on those studies, we provide a unified framework that utilizes the underlying effective circuit volume to explain the tradeoff between the experimentally achievable signal-to-noise ratio for a specific observable, and the corresponding computational cost. We apply this framework to recent quantum processor experiments of Random Circuit Sampling (Morvan et al., 2023), quantum information scrambling (Mi et al., 2021), and a Floquet circuit unitary (Kim et al., 2023). This allows us to reproduce the results of Ref. (Kim et al., 2023) in less than one second per data point using one GPU.

Geometric relations in Classical and Quantum Information Theory using the Lambert-Tsallis Wq(x) function

This work presents relations using the Lambert-Tsallis function Wq(x) that provide geometric characteristics in classical and quantum information theory. Firstly, the Wq(x) function is used to estimate parameters in discrete and continuous distributions knowing the a priori probability value. A lower bound for the probability density derived from the branch point of Wq(x). Secondly, we will represent the direct relationship between the Fisher distance in the HF2 hyperbolic model of normal distributions as a function of the distance associated with the Kulback-Leibler divergence in the argument of the Lambert-Tsallis function. Subsequently, using the disentropy based on Rényi, a functional that uses Wq(x) as its kernel, can be used as a measure of purity in the qubit state space (Bloch sphere), as well as for calculating quantum disentanglement of pure states of two qubits. Finally, representations for quantum fidelity and quantum affinity are defined as a function of Wq(x) once the Fisher and Wigner-Yanase quantum information metrics were known, connecting the Lambert-Tsallis function to the quantum speed limit (QSL) theory.

Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.

Resource-efficient simulation of noisy quantum circuits and application to network-enabled QRAM optimization

Giovannetti, Lloyd, and Maccone (2008) proposed a quantum random access memory (QRAM) architecture to retrieve arbitrary superpositions of N (quantum) memory cells via quantum switches and O(log (N)) address qubits. Toward physical QRAM implementations, Chen et al. (2021) recently showed that QRAM maps natively onto optically connected quantum networks with O(log (N)) overhead and built-in error detection. However, modeling QRAM on large networks has been stymied by exponentially rising classical compute requirements. Here, we address this bottleneck by: (1) introducing a resource-efficient method for simulating large-scale noisy entanglement, allowing us to evaluate hundreds and even thousands of qubits under various noise channels; and (2) analyzing Chen et al.’s network-based QRAM as an application at the scale of quantum data centers or near-term quantum internet; and (3) introducing a modified network-based QRAM architecture to improve quantum fidelity and access rate. We conclude that network-based QRAM could be built with existing or near-term technologies leveraging photonic integrated circuits and atomic or atom-like quantum memories.