arXiv subjects

L. Pereira

Publications and source records attributed to L. Pereira.

18 recordsLinked to original sources

arXiv2024

Efficient Experimental Qudit State Estimation via Point Tomography

Point tomography is a new approach to the problem of state estimation, which is arguably the most efficient and simple method for modern high-precision quantum information experiments. In this scenario, the experimenter knows the target state that their device should prepare, except that intrinsic systematic errors will create small discrepancies in the state actually produced. By introducing a new kind of informationally complete measurement, dubbed Fisher-symmetric measurements, point tomography determines deviations from the expected state with optimal efficiency. In this method, the number of outcomes of a measurement saturating the Gill-Massar limit for reconstructing a $d$-dimensional quantum states can be reduced from $\sim 4d-3$ to only $2d-1$ outcomes. Thus, providing better scalability as the dimension increases. Here we demonstrate the experimental viability of point tomography. Using a modern photonic platform constructed with state-of-the-art multicore optical fiber technology, we generate 4-dimensional quantum states and implement seven-outcome Fisher-symmetric measurements. Our experimental results exhibit the main feature of point tomography, namely a precision close to the Gill-Massar limit with a single few-outcome measurement. Specifically, we achieved a precision of $3.8/N$ while the Gill-Massar limit for $d=4$ is $3/N$ ($N$ being the ensemble size).

quant-ph↗

arXiv2024

Near-optimal pure state estimation with adaptive Fisher-symmetric measurements

Quantum state estimation is important for various quantum information processes, including quantum communications, computation, and metrology, which require the characterization of quantum states for evaluation and optimization. We present a three-stage adaptive method for estimating arbitrary $d$-dimensional pure quantum states using locally informationally complete Fisher symmetric measurements (FSM) and a single-shot measurement basis. We derive finite-sample high-probability error bounds for the protocol and demonstrate that our approach scales as $O(d/N)$ for large sample sizes, thereby guaranteeing the advantage of adaptation. Moreover, numerical simulations indicate that the protocol achieves an average infidelity close to the optimal given by the Gill-Massar lower bound (GMB). The total number of measurement outcomes scales linearly with $7d-3$, avoiding the need for collective measurements on multiple copies of the unknown state. This work highlights the potential of adaptive estimation techniques in quantum state characterization while maintaining efficiency in the number of measurement outcomes.

quant-ph↗

arXiv2024

Geometrically constrained sine-Gordon field: BPS solitons and their collisions

We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $\phi$ and $\chi$ whose scalar potential $V(\phi,\chi)$ has a standard $\chi^4$ sector and a sine-Gordon one for $\phi$. These fields are coupled through a generalizing function $f(\chi)$ that appears in the scalar potential and controls the nontrivial dynamics of $\phi$. We minimize the effective energy via the implementation of the BPS technique. We then obtain the Bogomol'nyi bound for the energy and the first-order equations whose solutions saturate that bound. We solve these equations for a nontrivial $f(\chi)$. As the result, BPS kinks with internal structures emerge. They exhibit a two-kink profile. i.e. an effect due to geometrical constrictions. We consider the linear stability of these new configurations. In this sense, we study the existence of internal modes that play an important role during the scattering process. We then investigate the kink-antikink collisions, and present the numerical results for the most interesting cases. We also comment about their most relevant features.

hep-th↗

arXiv2023

Stochastic optimization algorithms for quantum applications

Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with values of the objective function obtained in a quantum processor. A proper choice of optimization algorithm is essential to achieve good performance. Here, we review the use of first-order, second-order, and quantum natural gradient stochastic optimization methods, which are defined in the field of real numbers, and propose new stochastic algorithms defined in the field of complex numbers. The performance of all methods is evaluated by means of their application to variational quantum eigensolver, quantum control of quantum states, and quantum state estimation. In general, complex number optimization algorithms perform best, with first-order complex algorithms consistently achieving the best performance, closely followed by complex quantum natural algorithms, which do not require expensive hyperparameters calibration. In particular, the scalar formulation of the complex quantum natural algorithm allows to achieve good performance with low classical computational cost.

quant-ph↗

arXiv2023

Parallel tomography of quantum non-demolition measurements in multi-qubit devices

An efficient characterization of QND measurements is an important ingredient towards certifying and improving the performance and scalability of quantum processors. In this work, we introduce a parallel tomography of QND measurements that addresses single- and two-qubit readout on a multi-qubit quantum processor. We provide an experimental demonstration of the tomographic protocol on a 7-qubit IBM-Q device, characterizing the quality of conventional qubit readout as well as generalized measurements such as parity or measurement-and-reset schemes. Our protocol reconstructs the Choi matrices of the measurement processes, extracts relevant quantifiers -- fidelity, QND-ness, destructiveness -- and identifies sources of errors that limit the performance of the device for repeated QND measurements. We also show how to quantify measurement cross-talk and use it to certify the quality of simultaneous readout on multiple qubits.

quant-ph↗

arXiv2023

Detecting entanglement of unknown states by violating the Clauser-Horne-Shimony-Holt inequality

Entangled states play a fundamental role in Quantum Mechanics and are at the core of many contemporary applications, such as quantum communication and quantum computing. Therefore, determining whether a state is entangled or not is an important task. Here, we propose a method to detect the entanglement of unknown two-qubit quantum states. Our method is based on the violation of the Clauser-Horne-Shimony-Holt inequality. This maximizes the value of the inequality even when \lp{it} contains an unknown quantum state. The method iteratively generates local measurement settings that lead to increasing values of the inequality. We show by numerical simulations for pure and mixed states that our algorithm exceeds the classical limit of 2 after a few iterations.

quant-ph↗

arXiv2022

Complete physical characterization of QND measurements via tomography

We introduce a self-consistent tomography for arbitrary quantum non-demolition (QND) detectors. Based on this, we build a complete physical characterization of the detector, including the measurement processes and a quantification of the fidelity, ideality, and back-action of the measurement. This framework is a diagnostic tool for the dynamics of QND detectors, allowing us to identify errors, and to improve their calibration and design. We illustrate this on a realistic Jaynes-Cummings simulation of superconducting qubit readout. We characterize non-dispersive errors, quantify the back-action introduced by the readout cavity, and calibrate the optimal measurement point.

quant-ph↗

arXiv2022

Variational determination of multi-qubit geometrical entanglement in NISQ computers

Current noise levels in physical realizations of qubits and quantum operations limit the applicability of conventional methods to characterize entanglement. In this adverse scenario, we follow a quantum variational approach to estimate the geometric measure of entanglement of multiqubit pure states. The algorithm requires only single-qubit gates and measurements, so it is well suited for NISQ devices. This is demonstrated by successfully implementing the method on IBM Quantum devices for Greenberger-Horne-Zeilinger states of $3$, $4$, and $5$ qubits. Numerical simulations with random states show the robustness and accuracy of the method. The scalability of the protocol is numerically demonstrated via matrix product states techniques up to $25$ qubits.

quant-ph↗

arXiv2022

Training quantum measurement devices to discriminate unknown non-orthogonal quantum states

Here, we study the problem of decoding information transmitted through unknown quantum states. We assume that Alice encodes an alphabet into a set of orthogonal quantum states, which are then transmitted to Bob. However, the quantum channel that mediates the transmission maps the orthogonal states into non-orthogonal states, possibly mixed. If an accurate model of the channel is unavailable, then the states received by Bob are unknown. In order to decode the transmitted information we propose to train a measurement device to achieve the smallest possible error in the discrimination process. This is achieved by supplementing the quantum channel with a classical one, which allows the transmission of information required for the training, and resorting to a noise-tolerant optimization algorithm. We demonstrate the training method in the case of minimum-error discrimination and show that it achieves error probabilities very close to the optimal one. In particular, in the case of two unknown pure states our proposal approaches the Helstrom bound. A similar result holds for a larger number of states in higher dimensions. We also show that a reduction of the search space, which is used in the training process, leads to a considerable reduction in the required resources. Finally, we apply our proposal to the case of the dephasing channel reaching an accurate value of the optimal error probability.

quant-ph↗

arXiv2022

Complex Field Formulation of the Quantum Estimation Theory

We present a complex field formulation of the quantum estimation theory that works natively with complex statistics on the dependence of complex parameters. This formulation states new complex versions of the main quantities and results of the estimation theory depending on complex parameters, such as Fisher information matrices and Cram\'er-Rao bounds. This can be useful in contexts where the quantum states are described through complex parameters, such as coherent states or squeezed states. We show an example of an application of our theory in quantum communication with coherent states.

quant-ph↗

arXiv2021

Mean-squared-error-based adaptive estimation of pure quantum states and unitary transformations

In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its estimate. We show by means of numerical experiments that the estimation accuracy of the present method, which is given by the expectation of the squared error on the sample space of estimates, is state independent. Furthermore, the estimation accuracy delivered by our method is close to twice the Gill-Massar lower bound, which represents the best achievable accuracy, for all inspected dimensions. The minimization problem is solved via the concatenation of the Complex simultaneous perturbation approximation, an iterative stochastic optimization method that works within the field of the complex numbers, and Maximum likelihood estimation, a well-known statistical inference method. This can be carried out with the help of a multi-arm interferometric array. In the case of a single qubit, a Mach-Zehnder interferometer suffices. We also show that our estimation procedure can be easily extended to estimate unknown unitary transformations acting on a single qudit. Thereby, the estimation of unitary transformations achieves a higher accuracy than that achieved by processes based on tomographic methods for mixed states.

quant-ph↗

arXiv2021

Scalable estimation of pure multi-qubit states

We introduce an inductive $n$-qubit pure-state estimation method. This is based on projective measurements on states of $2n+1$ separable bases or $2$ entangled bases plus the computational basis. Thus, the total number of measurement bases scales as $O(n)$ and $O(1)$, respectively. Thereby, the proposed method exhibits a very favorable scaling in the number of qubits when compared to other estimation methods. Monte Carlo numerical experiments show that the method can achieve a high estimation fidelity. For instance, an average fidelity of $0.88$ on the Hilbert space of $10$ qubits is achieved with $21$ separable bases. The use of separable bases makes our estimation method particularly well suited for applications in noisy intermediate-scale quantum computers, where entangling gates are much less accurate than local gates. We experimentally demonstrate the proposed method in one of IBM's quantum processors by estimating 4-qubit Greenberger-Horne-Zeilinger states with a fidelity close to $0.875$ via separable bases. Other $10$-qubit separable and entangled states achieve an estimation fidelity in the order of $0.85$ and $0.7$, respectively.

quant-ph↗

arXiv2020

High-accuracy adaptive quantum tomography for high-dimensional quantum systems

The accuracy of estimating $d$-dimensional quantum states is limited by the Gill-Massar bound. It can be saturated in the qubit ($d=2$) scenario using adaptive standard quantum tomography. In higher dimensions, however, this is not the case and the accuracy achievable with adaptive quantum tomography quickly deteriorates with increasing $d$. Moreover, it is not known whether or not the Gill-Massar bound can be reached for an arbitrary $d$. To overcome this limitation, we introduce an adaptive tomographic method that is characterized by a precision that is better than half that of the Gill-Massar bound for any finite dimension. This provides a new achievable accuracy limit for quantum state estimation. We demonstrate the high-accuracy of our method by estimating the state of 10-dimensional quantum systems. With the advent of new technologies capable of high-dimensional quantum information processing, our results become critically relevant as state reconstruction is an essential tool for certifying the proper operation of quantum devices.

quant-ph↗

arXiv2020

Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency

We analyze the kinematics of electron-positron production in a photon-photon interaction when one has a modification of the special relativistic kinematics as a power expansion in the inverse of a new high-energy scale. We derive the equation for the threshold energy of this reaction to first order in this expansion, including the effects due to a modification of the energy-momentum conservation equation. In contrast with the Lorentz invariance violation case, a scale of the order of a few TeV is found to be compatible with the observations of very high-energy cosmic gamma rays in the case of a modification compatible with the relativity principle.

hep-ph↗

arXiv2020

Estimation of pure states using three measurement bases

We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of $2^{d-1}$ possible states, the likelihood of which is evaluated using the measurement results of the $d$ remaining projectors. The state with the highest likelihood is the estimate of the unknown state. The method estimates all pure states but a null-measure set. The viability of the protocol is experimentally demonstrated using two different and complementary high-dimensional quantum information platforms. First, by exploring the photonic path-encoding strategy, we validate the method on a single 8-dimensional quantum system. Then, we resort to the five superconducting qubit IBM quantum processor to demonstrate the high performance of the method in the multipartite scenario.

quant-ph↗

arXiv2020

Multi-core fiber integrated multi-port beamsplitters for quantum information processing

Multi-port beamsplitters are cornerstone devices for high-dimensional quantum information tasks, which can outperform the two-dimensional ones. Nonetheless, the fabrication of such devices has been proven to be challenging with progress only recently achieved with the advent of integrated photonics. Here, we report on the production of high-quality $N \times N$ (with $N=4,7$) multi-port beamsplitters based on a new scheme for manipulating multi-core optical fibers. By exploring their compatibility with optical fiber components, we create 4-dimensional quantum systems and implement the measurement-device-independent random number generation task with a programmable 4-arm interferometer operating at a 2 MHz repetition rate. Thanks to the high visibilities observed, we surpass the 1-bit limit of binary protocols and attain 1.23 bits of certified private randomness per experimental round. Our result demonstrates that fast switching, low-loss and high optical quality for high-dimensional quantum information can be simultaneously achieved with multi-core fiber technology.

quant-ph↗

arXiv2016

Iterative reconstruction of SiPM light response functions in a square-shaped compact gamma camera

Compact gamma cameras with a square-shaped monolithic scintillator crystal and an array of silicon photomultipliers (SiPMs) are actively being developed for applications in areas such as small animal imaging, cancer diagnostics and radiotracer guided surgery. Statistical methods of position reconstruction, which are potentially superior to the traditional centroid method, require accurate knowledge of the spatial response of each photomultiplier. Using both Monte Carlo simulations and experimental data obtained with a camera prototype, we show that the spatial response of all photomultipliers (light response functions) can be parameterized with axially symmetric functions obtained iteratively from flood field irradiation data. The study was performed with a camera prototype equipped with a 30 x 30 x 2 mm3 LYSO crystal and an 8 x 8 array of SiPMs for 140 keV gamma rays. The simulations demonstrate that the images, reconstructed with the maximum likelihood method using the response obtained with the iterative approach, exhibit only minor distortions: the average difference between the reconstructed and the true positions in X and Y directions does not exceed 0.2 mm in the central area of 22 x 22 mm2 and 0.4 mm at the periphery of the camera. A similar level of image distortions is shown experimentally with the camera prototype.

physics.med-ph↗

arXiv2015

Emulation workbench for position sensitive gaseous scintillation detectors

Position sensitive detectors based on gaseous scintillation proportional counters with Anger-type readout are being used in several research areas such as neutron detection, search for dark matter and neutrinoless double beta decay. Design and optimization of such detectors are complex and time consuming tasks. Simulations, while being a powerful tool, strongly depend on the light transport models and demand accurate knowledge of many parameters, which are often not available. Here we describe an alternative approach based on the experimental evaluation of a detector using an isotropic point-like light source with precisely controllable light emission properties, installed on a 3D positioning system. The results obtained with the developed setup at validation conditions, when the scattered light is strongly suppressed, show good agreement with simulations.

physics.ins-det↗