arXiv subjects

Thiago O. Maciel

Publications and source records attributed to Thiago O. Maciel.

At least 19 recordsLinked to original sources

arXiv2026

A competitive NISQ and qubit-efficient solver for the LABS problem

Pauli Correlation Encoding (PCE) is as a qubit-efficient variational approach to combinatorial optimization problems. The method offers a polynomial reduction in qubit count and a super-polynomial suppression of barren plateaus. Here, we extend the PCE-based framework to solve the Low Autocorrelation Binary Sequences (LABS) problem, a notoriously hard problem often used as a benchmark for classical and quantum solvers. To illustrate this,we simulate two variants of the PCE quantum solver for LABS instances of up to $N=45$ binary variables: one with commuting and one with maximally non-commuting sets of Pauli operators. The simulations use $4$ qubits and a circuit Ansatz with a total of $30$ two-qubit gates. We benchmark our method against the state-of-the-art classical solver and other quantum schemes. We observe improved scaling in the total time to reach the exact solution, outperforming the best-performing classical heuristic while using only a fraction of the quantum resources required by other quantum approaches. In addition, we perform proof-of-principle demonstrations on IonQ's Forte quantum processor, showing that the final solution is resilient to noise. Our findings point at PCE-based solvers as a promising quantum-inspired classical heuristic for hard problems as well as a tool to reduce the resource requirements for actual quantum algorithms.

quant-ph↗

arXiv2026

Quantum optimization with exact geodesic transport

We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes known quantum natural gradient methods by removing expensive estimations of the metric tensor and provably reducing gradient estimation costs by $62.5\%$. Moreover, the framework also naturally incorporates conjugate gradients as a built-in feature, giving an accelerated descent method with convergence guarantees that we dub exact geodesic transport with conjugate gradients. Numerical benchmarks against state-of-the-art variational methods for ground-state preparation of molecular Hamiltonians or $1$-dimensional spin chains (both with and without particle-number conservation) up to $n=16$ qubits show reductions of over one order of magnitude in the number of optimization steps, with global convergence even for degenerate cases and competitive quantum-resource scalings. In addition, we perform proof-of-principle demonstrations on IonQ's Forte quantum processor, showcasing deployment of pre-trained circuits for the $H_{3}^{+}$ molecule and experimental training for $H_{2}$. Our work enables quantum machine learning applications with shorter training runtime, with implications at the interface of quantum simulation, differential geometry, and optimal control theory.

quant-ph↗

arXiv2026

Compilation-informed probabilistic logical-error cancellation

The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction (QEC) offers a clear path towards fault tolerance, overcoming the scalability issues will take time. Early applications will likely rely on QEC combined with quantum error mitigation (QEM). We introduce a QEM scheme against both compilation errors and logical-gate noise that is circuit-, QEC code-, and compiler-agnostic. The scheme builds on quasi-probability methods and uses information about the circuit's gates' compilations to attain an unbiased estimation of noiseless expectation values incurring a constant sample-complexity overhead. Moreover, it features maximal circuit size and code distance both independent of the target precision, in contrast to strategies based on QEC alone. We formulate the mitigation procedure as a linear program, demonstrate its efficacy through numerical simulations, and illustrate it for estimating the Jones polynomials of knots. Our method significantly reduces quantum resource requirements for high-precision estimations, offering a practical route towards fault-tolerant quantum computation with precision-independent overheads for fixed circuit complexity and code distance.

quant-ph↗

arXiv2025

Quantum encoder for fixed Hamming-weight subspaces

We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression of degree $k$. The circuit is optimal in that it expresses an arbitrary data vector using only $d-1$ (controlled) Reconfigurable Beam Splitter (RBS) gates and is constructed by an efficient classical algorithm that sequentially generates all bitstrings of weight $k$ and identifies the gates that superpose the corresponding states with the correct amplitudes. An explicit compilation into CNOTs and single-qubit gates is presented, with the total CNOT-gate count of $\mathcal{O}(k\, d)$ provided in analytical form. In addition, we show how to load data in the binary basis by sequentially stacking encoders of different Hamming weights using $\mathcal{O}(d\,\log(d))$ CNOT gates. Moreover, using generalized RBS gates that mix states of different Hamming weights, we extend the construction to efficiently encode arbitrary sparse vectors. Experimentally, we perform a proof-of-principle demonstration of our scheme on a commercial trapped-ion quantum computer. We successfully upload a $q$-Gaussian probability distribution in the non-log-concave regime with $n = 6$ and $k = 2$. We also showcase how the effect of hardware noise can be alleviated by quantum error mitigation. Numerically, we show how our encoder can improve the performance of variational quantum algorithms for problems that include particle-preserving symmetries. Our results constitute a versatile framework for quantum data compression with various potential applications in fields such as quantum chemistry, quantum machine learning, and constrained combinatorial optimizations.

quant-ph↗

arXiv2022

Grand Unification of continuous-variable codes

Quantum error correction codes in continuous variables (also called CV codes, or single-mode bosonic codes) have recently been identified to be a technologically viable option for building fault-tolerant quantum computers. The best-known examples are the GKP code and the cat-code, both of which were shown to have some advantageous properties over any discrete-variable, or qubit codes. It was recently shown that the cat-code, as well as other kinds of CV codes, belong to a set of codes with common properties called rotation-symmetric codes. We expand this result by giving a general description of sets of codes with common properties, and rules by which they can be mapped into one another, effectively creating a unified description of continuous-variable codes. We prove that the properties of all of these sets of codes can be obtained from the properties of the GKP code. We also show explicitly how this construction works in the case of rotation-symmetric codes, re-deriving known properties and finding new ones.

quant-ph↗

arXiv2022

Genuine Multipartite Correlations in a Boundary Time Crystal

In this work we study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC). Boundary time crystals are nonequilibrium quantum phases of matter in contact to an environment, for which a macroscopic fraction of the many-body system breaks the time-translation symmetry. We analyze both (i) the structure (orders) of GMC's among the subsystems, as well as (ii) their build-up dynamics for an initially uncorrelated state. We find that, in the thermodynamic limit (and only in such a limit), multipartite correlations of all orders grow indefinitely in time in the BTC phase, further displaying a persistent oscillatory behavior around their mean growth. The orders of the correlations show a power-law decaying hierarchy among its $k$-partitions. Moreover, in the long-time limit the GMC's are shown extensive with the system size, contrasting to the subextensive scaling in the non time-crystal (ferromagnetic) phase of the model. We also discuss the classical and quantum nature of these correlations with basis on multipartite entanglement witnesses, specifically, the analysis of the Quantum Fisher Information (QFI). Both GMC and QFI are able to capture and distinguish the different phases of the model. Our work highlights the genuine many-body properties of these peculiar non-equilibrium phases of matter.

quant-ph↗

arXiv2022

Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model

We study the ground state properties of the one-dimensional extended Hubbard model at half-filling from the perspective of its particle reduced density matrix. We focus on the reduced density matrix of $2$ fermions and perform an analysis of its quantum correlations and coherence along the different phases of the model. Specifically, we study its (i) entanglement entropy, (ii) $\ell_1$ norm of coherence, (iii) irreducible two-body cumulant matrix and (iv) entanglement spectrum. Our results show that these different properties are complementary to each other depending on the phase of the system, exhibiting peculiar behaviors such as discontinuities, maximum or minimum values at the quantum phase transitions, thus providing a qualitative view of the phase diagram of the model. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system. Moreover, from the analysis of the dominant eigenvector in the reduced state, we can relate the SS-TS transition to the spatial separation between the fermion pairs in the two different pairing orderings. The entanglement gap is also able to highlight a transition - at a few-body level - in the groundstate wavefunction, not discussed previously in the literature. While other quantifiers are less sensitive to few-body defects in the wavefunction, the entanglement gap can work as a magnifying glass for these, capturing such small fluctuations.

cond-mat.str-el↗

arXiv2021

Simple and maximally robust processes with no classical common-cause or direct-cause explanation

Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and applying the identity quantum channel, thus not requiring an explicit coherent mixture of common-cause and direct-cause, exploiting the possibility of a process to have both relations simultaneously. We then prove that, although all bipartite direct-cause processes are bipartite separable operators, there exist bipartite separable processes which are not direct-cause. This shows that the problem of deciding weather a process is direct-cause process is not equivalent to entanglement certification and points out the limitations of entanglement methods to detect non-classical CCDC processes. We also present a semi-definite programming hierarchy that can detect and quantify the non-classical CCDC robustnesses of every non-classical CCDC process. Among other results, our numerical methods allow us to show that the simple processes presented here are likely to be also the maximally robust against white noise. Finally, we explore the equivalence between bipartite direct-cause processes and bipartite processes without quantum memory, to present a separable process which cannot be realized as a process without quantum memory.

quant-ph↗

arXiv2021

QBoost for regression problems: solving partial differential equations

A hybrid algorithm based on machine learning and quantum ensemble learning is proposed that is capable of finding a solution to a partial differential equation with good precision and favorable scaling in the required number of qubits. The classical part is composed by training several regressors (weak-learners), capable of solving a partial differential equation using machine learning. The quantum part consists of adapting the QBoost algorithm to solve regression problems. We have successfully applied our framework to solve the 1D Burgers' equation with viscosity, showing that the quantum ensemble method really improves the solutions produced by weak-learners. We also implemented the algorithm on the D-Wave Systems, confirming the best performance of the quantum solution compared to the simulated annealing and exact solver methods, given the memory limitations of our classical computer used in the comparison.

quant-ph↗

arXiv2021

A hybrid classical-quantum approach to solve the heat equation using quantum annealers

The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate subject to fixed temperatures at the edges and random heat sources and sinks within the domain. The hybrid classical-quantum approach consists in the solution on a quantum computer of the coupled linear system of equations that result from the discretization step. Owing to the limitations in the number of qubits and their connectivity, we use the Gauss-Seidel method to divide the full system of linear equations into subsystems, which are solved iteratively in block fashion. Each of the linear subsystems were solved using 2000Q and Advantage quantum computers developed by D-Wave Systems Inc. By comparing classical numerical and quantum solutions, we observe that the errors and chain break fraction are, on average, greater on the 2000Q system. Unlike the classical Gauss-Seidel method, the errors of the quantum solutions level off after a few iterations of our algorithm. This is partly a result of the span of the real number line available from the mapping of the chosen size of the set of qubit states. We verified this by using techniques to progressively shrink the range mapped by the set of qubit states at each iteration (increasing floating-point accuracy). As a result, no leveling off is observed. However, an increase in qubits does not translate to an overall lower error. This is believed to be indicative of the increasing length of chains required for the mapping to real numbers and the ensuing limitations of hardware.

quant-ph↗

arXiv2020

Promoting quantum correlations in DQC1 model via post-selection

The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work we analyse the quantum correlations named entanglement, Bell's nonlocality, quantum discord, and coherence generated by the DQC1 circuit considering only two qubits (auxiliary and control). For the standard DQC1 model only quantum discord and coherence appear. By introducing a filter in the circuit we purify the auxiliary qubit taking it out from the totally mixed state and consequently promoting other quantum correlations between the qubits, such as entanglement and Bell's nonlocality. Through the optimization of the purification process we conclude that even a small purification is enough to generate entanglement and Bell's nonlocality. We obtain, in average, that applying the purification process repeatedly by twelve times the auxiliary qubit becomes 99% pure. In this situation, almost maximally entangled states are achieved, which by its turn, almost maximally violate the Bell's inequality. This result suggests that with a simple modification the DQC1 model can be promoted to a universal model of quantum computing.

quant-ph↗

arXiv2020

Genuine Multipartite Correlations Distribution in the Criticality of Lipkin-Meshkov-Glick Model

Correlations play a key role in critical phenomena. Quantities such as the entanglement entropy, for instance, provide key insights into the mechanisms underlying quantum criticality. Almost all of our present knowledge, however, is restricted to bipartite correlations. Some questions still remain unanswered, such as: What parcel of the total correlations are genuinely k-partite? With the goal of shedding light on this difficult question, in this paper we put forth a detailed study of the behavior of genuine multipartite correlations (GMC) of arbitrary orders in the Lipkin-Meshkov-Glick model. We find that GMC of all orders serve to signal the second order quantum phase transition presented in the model. Applying finite-size scaling methods, we also find the critical exponents for some orders of correlations.

quant-ph↗

arXiv2020

Automated Machine Learning can Classify Bound Entangled States with Tomograms

For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning approach to classify random states of two qutrits as separable or entangled using enough data to perform a quantum state tomography, without any direct measurement of its entanglement. We could successfully apply our framework even when the Peres-Horodecki criterion fails. In addition, we could also estimate the Generalized Robustness of Entanglement with regression techniques and use it to validate our classifiers.

quant-ph↗

arXiv2020

Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions

We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase transitions, or abrupt variations in the correlation distributions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.

quant-ph↗

arXiv2019

Probing Genuine Multipartite Entanglement in Large Systems

We introduce a new kind of Entanglement Witness which is appropriate for studying genuine multipartite entanglement in large systems. The witness operator has a form that fits naturally to quantum states represented by tensor networks. It opens up novel routes for investigating properties of condensed matter systems, and gives a new perspective to understand many-body quantum correlations. We illustrate the potential of this new operator with a GHZ state, and apply the method to a transverse Ising model with the well-known approach of Matrix Product States and Matrix Product Operators for a hundred spins.

quant-ph↗

arXiv2017

Most incompatible measurements for robust steering tests

We address the problem of characterizing the steerability of quantum states under restrictive measurement scenarios, i.e., the problem of determining whether a quantum state can demonstrate steering when subjected to $N$ measurements of $k$ outcomes. We consider the cases of either general positive operator-valued measures (POVMs) or specific kinds of measurements (e.g., projective or symmetric). We propose general methods to calculate lower and upper bounds for the white-noise robustness of a $d$-dimensional quantum state under different measurement scenarios that are also applicable to the study of the noise robustness of the incompatibility of sets of unknown qudit measurements. We show that some mutually unbiased bases, symmetric informationally complete measurements, and other symmetric choices of measurements are not optimal for steering isotropic states and provide candidates to the most incompatible sets of measurements in each case. Finally, we provide numerical evidence that nonprojective POVMs do not improve over projective ones for this task.

quant-ph↗

arXiv2017

Error regions in quantum state tomography: computational complexity caused by geometry of quantum states

The outcomes of quantum mechanical experiments are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the particularly relevant task of quantum state estimation, it has been shown that a significant reduction in uncertainty can be achieved by taking the positivity of quantum states into account. However -- the large number of partial results and heuristics notwithstanding -- no efficient general algorithm is known that produces an optimal uncertainty region from experimental data and the prior constraint of positivity. Here, we make this problem precise and show that the general case is NP-hard. Our result leaves room for the existence of efficient approximate solutions, and therefore does not yet imply that the practical task of quantum uncertainty quantification is intractable. However, it does show that there exists a non-trivial trade-off between optimality and computational efficiency for error regions. We prove two versions of the result: One for frequentist and one for Bayesian statistics.

quant-ph↗

arXiv2017

Dynamical matrix for arbitrary quadratic fermionic bath Hamiltonians and non-Markovian dynamics of one and two qubits in an Ising model environment

We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.

quant-ph↗