The discrete Fourier transform (DFT) underpins many classical algorithms and is a fundamental unitary operator for quantum information processing. Implementing the N-dimensional DFT in photonic integrated circuits (PICs) is limited by the cascades of Mach-Zehnder interferometers that current architectures require. Here we propose bosonic Hamiltonians that realize the N-dimensional DFT through a single stage of multimode evolution, complemented only by phase shifters before and after the interaction region, in a geometry suited to 3D waveguides. Modeling the system as a graph, where edges correspond to couplings and the vertices are the waveguides, we obtain analytical solutions for complete graphs up to N=6 and numerical solutions up to N=31. For non-complete graphs, different propagation constants are required in the Hamiltonian. We report all solutions for N≤ 8, partial exploration for N=9, and selected cases for N=10, together with three conjectures that guide the numerical search for N ≥ 11. These configurations circumvent the vanishing evanescent coupling strength imposed by the waveguide separation, and a closed-form sensitivity criterion selects those that are admissible as a waveguide layout and least sensitive to fabrication error. We also uncover the missing non-affine parameters of the 6-dimensional DFT, and show that the scaling law for implementing the N-dimensional DFT with our building blocks is 𝒪(NloglogN). This allows assembling the 2520-dimensional DFT with only 2625 interferometers, in contrast to the ≈ 3× 10^6 of Reck and Clements architectures.

Distributed quantum computing offers a promising approach to scaling quantum devices by networking multiple quantum processors. We present a quantum state tomography protocol tailored for distributed quantum computers that avoids assuming remote entanglement as a primitive resource. The protocol extends projected least-squares (PLS) tomography based on projective 2-designs to systems composed of multiple quantum processors, using only local operations within each processor and classical communication between nodes. Assuming entanglement within each individual quantum processor is trusted, the protocol can be executed using mutually unbiased bases. We derive rigorous, non-asymptotic trace-norm error bounds for the PLS estimator, with explicit exponential dependence on the number of nodes. In addition, we establish certified error bounds for estimating entanglement negativity from the PLS estimator. Numerical simulations for systems of up to seven qubits distributed across several devices validate the theoretical error bounds.

Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a physics-informed deep learning approach based on Physics-Informed Neural Networks to estimate these operators over the full time domain. By incorporating physical constraints such as unitarity and leveraging the second-order Magnus expansion on the evolution operator, the proposed framework enables the estimation of unitary matrices at different time intervals. The model is trained using simulated unitary operators and evaluated on quantum systems ranging from 2 to 6 qubits. For larger many-body systems, specifically those with 7 and 8 qubits, the same methodology is employed to reconstruct an effective time-dependent Hamiltonian, from which the corresponding time-evolution operator is computed over the entire temporal domain. The proposed framework achieves fidelities exceeding 0.92 using a limited number of unitary samples, indicating a potential reduction in measurement and data acquisition costs. These results highlight the effectiveness of the approach for data-driven simulation and identification of quantum dynamical systems, with direct relevance to quantum computing and quantum simulation applications.

In quantum technologies, continuous-variable systems offer advantages over their discrete counterparts. However, continuous-variable tomography suffers from exponentially growing sample complexity. We propose protocols using quantum mirrors to transfer the complete information of incident photonic states onto a control atomic system. This enables full photonic state characterization through measurements on the control atom alone, realized via kernel functions, direct wavefunction reconstruction, and pointwise Wigner function measurements. Our approach overcomes the limitations of conventional photon counting, statistical inference, and inverse transformation, providing a robust framework for benchmarking and verifying non-Gaussian states in continuous-variable quantum optics.

We introduce a quantum circuit that "transcribes" the elements of the process matrix chi of an arbitrary quantum channel onto the state of a pair of ancillary systems. The circuit works for an arbitrary quantum channel acting on a d-dimensional target system and returns as output not only the chi matrix encoded in the d2-dimensional state of the ancilla systems but also the initial state of the target system. We compare the circuit to the well-known Choi circuit that outputs the Choi-Jamio & lstrok;kowski representation of the channel and the lesser-known Choi-Bell circuit that outputs the chi matrix. We show that the Choi-Bell circuit can be modified to transcribe quantum channels and also return the initial target state but requires more nonlocal gates. We briefly discuss some interesting features of the circuit and its eventual application in quantum process tomography and other computational tasks.

Reconfigurable devices capable to implement any unitary operation with a given fidelity are crucial for photonic universal quantum computation, optical neural networks, and boson sampling. Here, we address the problems of approximating with a given infidelity any unitary operation and any pure state using multi-port interferometers, which are of current interest due to the recent availability of multi-core fiber integrated multi-port interferometers. We show that any pure state, in any dimension $d$, can be prepared with infidelity $\le 10^{-15}$ with $3$~layers of $d$-dimensional Fourier transforms and $3$~layers of configurable phase shifters. In contrast, the schemes in [Phys. Rev. Lett. \textbf{73}, 58 (1994) and Optica \textbf{3}, 1460 (2016)], require optical depth $2(d-1)$. We also present numerical evidence that $d+1$~layers of $d$-dimensional Fourier transforms and $d+2$~layers of configurable phase shifters can produce any unitary with infidelity $\le 10^{-14}$, while the scheme in [Phys. Rev. Lett. \textbf{124}, 010501 (2020)] only achieves an infidelity in the order of $10^{-7}$ for block-diagonal unitary transformations

We present two scalable and entanglement-free methods for estimating the collective state of an n-qubit quantum computer. The first method consists of a fixed set of five quantum circuits-regardless of the number of qubits-that avoid the use of entanglement as a measurement resource, relying instead on classical communication between selected pairs of qubits. The second method requires only 2n+1 circuits, each of which applies a single local gate to one of the n qubits during the measurement stage. Unlike traditional estimation methods, our approaches do not require any costly post-processing procedure to estimate a quantum state, enabling scalability to relatively large system sizes. We experimentally compare both methods on freely available IBM quantum processors, and observe how the state estimation varies with increasing number of qubits and shots. We further validated our results by estimating the 4-qubit entangled state of two remote ion-trap quantum processors, demonstrating that the optimized 2n+1 tomographic scheme achieves estimates consistent with standard methods while using exponentially fewer measurements.

In this work, we propose a machine learning (ML)-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a quantum marginal imposition technique with convolutional denoising autoencoders. The loss function is carefully designed to enforce essential physical constraints, including Hermiticity, positivity, and normalization. Through extensive numerical simulations, we demonstrate the effectiveness of our approach, achieving high success rates and accuracy. Furthermore, we show that, in many cases, our model offers a faster alternative to state-of-the-art semidefinite programming solvers without compromising solution quality. These results highlight the potential of ML techniques for solving complex problems in quantum mechanics.

We propose an estimation procedure for d-dimensional unitary transformations. For d>2, the unitary transformations close to the identity are estimated saturating the quantum Cramér-Rao bound. For d=2, the estimation of all unitary transformations is also optimal with some prior information. We show through numerical simulations that, even in the absence of prior information, two-dimensional unitary transformations can be estimated with greater precision than by means of standard quantum process tomography.

We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two bases are insufficient to construct an informationally complete positive operator-valued measurement (IC-POVM) for pure states. We demonstrate our method using a binary tree structure, providing an algorithmic path for implementation. The performance of the method is evaluated through numerical simulations, showcasing its effectiveness for quantum state estimation.

We revisit the discussion of the quantum resources required to perform optimal unambiguous discrimination between two nonorthogonal quantum states when the protocol is assisted by an auxiliary system (ancilla). Initially, the formulation of the problem led to the assumption that entanglement between the main system and the ancilla was the key resource for the task. However, it was later shown that entanglement is not necessary at all, while quantum dissonance may or may not be required, depending on the relationship between the overlap and the a priori probabilities of the inputs [Zhang, Sci. Rep. 3, 2134 (2013)]. Here, we show that, regardless of this relationship, coherence and purity are required resources for the task and thus more fundamental than dissonance. Coherence is analyzed based on its generalized resource theory, which allowed us to find the scenario that generates the maximal cryptographic randomness gain in the protocol. Purity, on the other hand, is shown to be greater than coherence when both measures are defined via the same distance, including the extreme cases of orthogonal and parallel states, where the latter is zero. Therefore, we conclude that purity is the most fundamental resource for assisted optimal state discrimination.

We present analytic solutions to the evolution in generalized tight-binding models, which consider complex first-neighbor couplings with equal amplitude and arbitrary phases. Our findings provide a powerful tool to efficiently calculate expectation values and correlations within the system, which are otherwise difficult to compute numerically. We apply our results to relevant examples in quantum light manipulation using -port linear couplers, describing the evolution of single (multi)-mode squeezing, single-photon added (subtracted) Gaussian states, and second-order site-to-site photon correlations. Significantly, our analytic results outperform standard numerical calculations. Our study paves the way for a comprehensive mathematical framework describing the spatial evolution of quantum states across a wide range of physical systems governed by the tight-binding model. Published by the American Physical Society 2024

Optical nonlinearities are fundamental in several types of optical information processing protocols. However, the high laser intensities needed for implementing phase nonlinearities using conventional optical materials represent a challenge for nonlinear optics in the few-photon regime. We introduce an infrared cavity quantum electrodynamics (QED) approach for imprinting nonlinear phase shifts on individual THz pulses in reflection setups, conditional on the input power. Power-dependent phase shifts on the order of $ 0.1\, \pi$ can be achieved with femtosecond pulses of only a few $\mu$W input power. The proposed scheme involves a small number of intersubband quantum well transition dipoles evanescently coupled to the near field of an infrared resonator. The field evolution is nonlinear due to the dynamical transfer of spectral anharmonicity from material dipoles to the infrared vacuum, through an effective dipolar chirping mechanism that transiently detunes the quantum well transitions from the vacuum field, leading to photon blockade. We develop analytical theory that describes the dependence of the imprinted nonlinear phase shift on relevant physical parameters. For a pair of quantum well dipoles, the phase control scheme is shown to be robust with respect to inhomogeneities in the dipole transition frequencies and relaxation rates. Numerical results based on the Lindblad quantum master equation validate the theory in the regime where the material dipoles are populated up to the second excitation manifold. In contrast with conventional QED schemes for phase control that require strong light-matter interaction, the proposed phase nonlinearity works best in weak coupling, increasing the prospects for its experimental realization using current nanophotonic technology.

The barren plateau phenomenon is one of the main obstacles to implementing variational quantum algorithms in the current generation of quantum processors. Here, we introduce a method capable of avoiding the barren plateau phenomenon in the variational determination of the geometric measure of entanglement for a large number of qubits. The method is based on measuring compatible two-qubit local functions whose optimization allows for achieving a well-suited initial condition, from which a global function can be further optimized without encountering a barren plateau. We analytically demonstrate that the local functions can be efficiently estimated and optimized. Numerical simulations up to 18-qubit GHZ and W states demonstrate that the method converges to the exact value. In particular, the method allows for escaping from barren plateaus induced by hardware noise or global functions defined on high-dimensional systems. Numerical simulations with noise are in agreement with experiments carried out on IBM's quantum processors for 7 qubits.

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 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.

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.

In a general optimized measurement scheme for discriminating between nonorthogonal quantum states, the error rate is minimized under the constraint of a fixed rate of inconclusive outcomes (FRIO). This so-called optimal FRIO measurement encompasses the standard and well-known minimum-error and optimal unambiguous (or maximum-confidence) discrimination strategies as particular cases. Here, we experimentally demonstrate the optimal FRIO discrimination between $N=2,3,5$, and 7 equally likely symmetric states of a qubit encoded in photonic path modes. Our implementation consists of applying a probabilistic quantum map which increases the distinguishability between the inputs in a controlled way, followed by a minimum-error measurement on the successfully transformed outputs. The results obtained corroborate this two-step approach and, in our experimental scheme, can be straightforwardly extended to higher dimensions. The optimized measurement demonstrated here will be useful for quantum communication scenarios where the error rate and inconclusive rate must be kept below the levels provided by the respective standard strategies.

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 strategy 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 phase flip channel reaching an accurate value of the optimal error probability.

The quantum switch is a quantum computational primitive that provides computational advantage by applying operations in a superposition of orders. In particular, it can reduce the number of gate queries required for solving promise problems where the goal is to discriminate between a set of properties of a given set of unitary gates. In this work, we use Complex Hadamard matrices to introduce more general promise problems, which reduce to the known Fourier and Hadamard promise problems as limiting cases. Our generalization loosens the restrictions on the size of the matrices, number of gates and dimension of the quantum systems, providing more parameters to explore. In addition, it leads to the conclusion that a continuous variable system is necessary to implement the most general promise problem. In the finite dimensional case, the family of matrices is restricted to the so-called Butson-Hadamard type, and the complexity of the matrix enters as a constraint. We introduce the ``query per gate'' parameter and use it to prove that the quantum switch provides computational advantage for both the continuous and discrete cases. Our results should inspire implementations of promise problems using the quantum switch where parameters and therefore experimental setups can be chosen much more freely.

Considering pure quantum states, entanglement concentration is the procedure where, from N copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for N=1. However, the associated success probability can be extremely low when increasing the system’s dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for N=1, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function Q considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of Q. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states.