arXiv subjects

Teodor Parella-Dilmé

Publications and source records attributed to Teodor Parella-Dilmé.

4 recordsLinked to original sources

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

Swap Network Augmented Ansätze on Arbitrary Connectivity

Efficient parametrizations of quantum states are essential for trainable hybrid classical-quantum algorithms. A key challenge in their design consists in adapting to the available qubit connectivity of the quantum processor, which limits the capacity to generate correlations between distant qubits in a resource-efficient and trainable manner. In this work we first introduce an algorithm that optimizes qubit routing for arbitrary connectivity graphs, resulting in a swap network that enables direct interactions between any pair of qubits. We then propose a co-design of circuit layers and qubit routing by embedding the derived swap networks within layered, connectivity-aware ansätze. This construction significantly improves the trainability of the ansatz, leading to enhanced performance with reduced resources. We showcase these improvements through ground-state simulations of strongly correlated systems, including spin-glass and molecular electronic structure models. Across exemplified connectivities, the swap-enhanced ansatz consistently achieves lower energy errors using fewer entangling gates, shallower circuits, and fewer parameters than standard layered-structured baselines. Our results indicate that swap network augmented ansätze provide enhanced trainability and resource-efficient design to capture complex correlations on devices with constrained qubit connectivity.

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arXiv2026

Certification of quantum properties with imperfect measurements

The accurate characterization of quantum systems is essential for the advancement of quantum technologies. In particular, certifying convex functions of quantum states plays a central role in many applications. We present a certification method for experimentally prepared quantum states that accounts for both shot noise and measurement imperfections in the data-acquisition stage. Building upon previous work, our method extends confidence regions to accommodate imperfect control over measurements. The values of the functions can then be bounded using convex optimization techniques. We provide explicit prescriptions for quantifying the noise contribution from finite statistics and for estimating the effect of measurement imperfections. By jointly incorporating statistical and systematic errors, the method yields a robust certification framework for quantum experiments.

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arXiv2024

Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings

In ab-initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step of the fermionic problem into qubits. This work introduces a physically-inspired method for constructing mappings that significantly simplify entanglement requirements when simulating states of interest. The presence of electronic excitations drives the construction of our mappings, reducing correlations for target states in the qubit space. To benchmark our method, we simulate ground states of small molecules and observe an enhanced performance when compared to classical and quantum variational approaches from prior research employing conventional mappings. In particular, on the quantum side, our mappings require a reduced number of entangling layers to achieve accuracy for $LiH$, $H_2$, $(H_2)_2$, the $H_4$ stretching and benzene's π system using the RY hardware efficient ansatz. In addition, our mappings also provide an enhanced ground state simulation performance in the density matrix renormalization group algorithm for the $N_2$ molecule.

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