arXiv subjects

Júlia Barberà-Rodríguez

Publications and source records attributed to Júlia Barberà-Rodríguez.

6 recordsLinked to original sources

arXiv2026

Direct fidelity estimation through joint fiducial grouping

Fault-tolerant quantum computation hinges on the requirement for low physical error rates. Reaching below threshold regime requires the accounting of circuit dependent noise, that is inherent to the execution context in which a quantum gate is usually embedded. Direct fidelity estimation is a technique that offers natural context preservation as it solely requires the insertion of local Pauli preparation and measurement fiducials around the window of interest. However, each sampled input-output Pauli pair demands its own preparation and measurement setting, an overhead that grows rapidly once the target gate is no longer Clifford. We introduce joint fiducial grouping, which partitions Pauli pairs into sets with commuting input and output operators, allowing several Pauli-transfer coefficients to be estimated within the same preparation-measurement setting. We derive an unbiased grouped estimator and finite-sample guarantees showing that grouping always reduces the number of distinct input-output settings and can also reduce the required channel uses when the target weight is concentrated within compatible groups. We characterize these gains for the parametric two-qubit gate $\mathrm{fSim}(θ,φ)$, and use the grouped estimator as a context-sensitive reward for reinforcement-learning-based gate calibration. Our results provide a practical route to lower-overhead, context-preserving fidelity estimation for continuously parameterized quantum gates.

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arXiv2026

Strong unitary designs in optimal depth and space

Unitary designs provide finite-moment approximations to Haar-random unitaries, with wide-ranging applications across physics and quantum information, from scrambling and black-hole dynamics to foundational primitives in quantum algorithms. Strong unitary designs capture a more demanding operational notion of approximation, requiring indistinguishability from Haar randomness even for quantum algorithms that may access a unitary not only in the forward direction, but also through its inverse, transpose, and complex conjugate. Motivated by the physical requirement that scrambling arise within the system itself, Schuster, Ma, Lombardi, Brandão, and Huang (arXiv:2509.26310) left open whether strong unitary designs can be generated in logarithmic depth using only the system qubits. For every fixed design order $k$ and measurable-error tolerance, we construct strong approximate unitary $k$-designs in optimal $Θ(\log n)$ all-to-all circuit depth using only the $n$ original system qubits. Our new ingredient is a logarithmic-depth Pauli-mixing bound for the perfect-matching ensemble, whose layers pair the qubits uniformly at random and apply independent random two-qubit gates. This bound controls the mixed forward-reverse two-query case, which we combine with existing design and gluing results to obtain strong unitary designs of arbitrary fixed order.

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arXiv2026

Beyond Ground States: Physics-Inspired Optimization of Excited States of Classical Hamiltonians

We introduce excited local quantum annealing (ExcLQA), a classical, physics-inspired algorithm that extends local quantum annealing (LQA) to identify excited states of classical Ising Hamiltonians. LQA simulates quantum annealing while constraining the quantum state to remain in a product state and uses a gradient-based approach to find approximate solutions to large-scale quadratic unconstrained binary optimization problems. ExcLQA extends this framework by adding a penalty term in the cost function to target excited states, with a single hyperparameter that can be tuned via binary search to set the desired penalization level. We benchmark ExcLQA on fully connected Ising models with random interactions and on the shortest vector problem (SVP). The latter is a fundamental lattice problem underlying the security of many post-quantum cryptographic schemes, and its solution can be mapped to the first excited state of an Ising Hamiltonian. For the fully connected Ising models, we show that, on the tested instances, ExcLQA outperforms both a matrix-product-state-based method and simulated annealing. Notably, even when only a lower bound on the ground-state energy is provided, rather than the exact ground-state information required by these competing methods, ExcLQA still achieves superior performance. For the SVP, ExcLQA finds exact solutions for instances up to rank 46, and outperforms the Metropolis-Hastings algorithm in terms of solved ratio, number of shots, and approximation factor on the tested instances.

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arXiv2025

Sampling Groups of Pauli Operators to Enhance Direct Fidelity Estimation

Direct fidelity estimation is a protocol that estimates the fidelity between an experimental quantum state and a target pure state. By measuring the expectation values of Pauli operators selected through importance sampling, the method is exponentially faster than full quantum state tomography. We propose an enhanced direct fidelity estimation protocol that uses fewer copies of the experimental state by grouping Pauli operators before the sampling process. We derive analytical bounds on the measurement cost and estimator variance, showing improvements over the standard method. Numerical simulations validate our approach, demonstrating that for 8-qubit Haar-random states, our method achieves a one-third reduction in the required number of copies and reduces variance by an order of magnitude using only local measurements. These results underscore the potential of our protocol to enhance the efficiency of fidelity estimation in current quantum devices.

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arXiv2025

Boosting projective methods for quantum process and detector tomography

We introduce two methods for quantum process and detector tomography. In the quantum process tomography method, we develop an analytical procedure for projecting the linear inversion estimation of a quantum channel onto the set of completely positive trace-preserving matrices. By integrating this method with alternate projection techniques, we achieve a three-order-of-magnitude improvement in approximating the closest quantum channel to an arbitrary Hermitian matrix compared to existing methods without compromising computational efficiency. Our second method extends this approach to quantum detector tomography, demonstrating superior efficiency compared to current techniques. Through numerical simulations, we evaluate our protocols across channels of up to four qubits in quantum process tomography and systems of up to six qubits in quantum detector tomography, showcasing superior precision and efficiency.

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arXiv2024

Finding dense sub-lattices as low-energy states of a Hamiltonian

Lattice-based cryptography has emerged as one of the most prominent candidates for post-quantum cryptography, projected to be secure against the imminent threat of large-scale fault-tolerant quantum computers. The Shortest Vector Problem (SVP) is to find the shortest non-zero vector in a given lattice. It is fundamental to lattice-based cryptography and believed to be hard even for quantum computers. We study a natural generalization of the SVP known as the $K$-Densest Sub-lattice Problem ($K$-DSP): to find the densest $K$-dimensional sub-lattice of a given lattice. We formulate $K$-DSP as finding the first excited state of a Z-basis Hamiltonian, making $K$-DSP amenable to investigation via an array of quantum algorithms, including Grover search, quantum Gibbs sampling, adiabatic, and Variational Quantum Algorithms. The complexity of the algorithms depends on the basis through which the input lattice is presented. We present a classical polynomial-time algorithm that takes an arbitrary input basis and preprocesses it into inputs suited to quantum algorithms. With preprocessing, we prove that $O(KN^2)$ qubits suffice for solving $K$-DSP for $N$ dimensional input lattices. We empirically demonstrate the performance of a Quantum Approximate Optimization Algorithm $K$-DSP solver for low dimensions, highlighting the influence of a good preprocessed input basis. We then discuss the hardness of $K$-DSP in relation to the SVP, to see if there is reason to build post-quantum cryptography on $K$-DSP. We devise a quantum algorithm that solves $K$-DSP with run-time exponent $(5KN\log{N})/2$. Therefore, for fixed $K$, $K$-DSP is no more than polynomially harder than the SVP.

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