arXiv subjects

Almudena Carrera Vazquez

Publications and source records attributed to Almudena Carrera Vazquez.

9 recordsLinked to original sources

arXiv2026

Quantum chemistry with provable convergence via randomized sample-based Krylov quantum diagonalization

Quantum algorithms based on classical processing of individual samples have recently emerged as a promising route to perform large-scale quantum-chemical calculations on pre-fault-tolerant and early-fault-tolerant quantum devices. In these algorithms, the quantum computer acts as a sampling engine that generates the subspace in which the Hamiltonian is classically diagonalized. The recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) uses quantum Krylov states as circuits from which samples are collected. Convergence guarantees can be derived for SKQD under assumptions similar to those of quantum phase estimation -- namely, a sufficiently large overlap between the reference and the target ground state -- with the additional requirement that the ground-state wave function be well approximated by a polynomial subset of the full Hilbert space. However, implementations of SKQD for complex many-body Hamiltonians, such as quantum chemistry ones, are limited by the depths of time-evolution circuits needed to generate Krylov vectors. In this work, we introduce a method that combines SKQD with a qDRIFT randomized compilation of the Hamiltonian propagator. The resulting algorithm, termed SqDRIFT, enables executing quantum chemistry experiments on present-day quantum processors while retaining provable convergence guarantees, which we extend to account for the error of the randomized compilation and of finite sampling. We demonstrate its viability by applying SqDRIFT to calculate the electronic ground-state energy of several polycyclic aromatic hydrocarbons, up to system sizes beyond the reach of exact diagonalization.

quant-ph↗

arXiv2026

Efficient Fourier-Based Linear Combination of Unitaries and Applications in Quantum Optimization

We investigate ancilla-free linear combination of unitaries (LCU) as a framework for approximating complex quantum circuits. This is particularly effective for quantum optimization algorithms, where candidate solutions can be evaluated classically and the task is to sample high-quality bitstrings rather than reproduce the full output distribution. We show that Fourier-based LCU constructions efficiently decompose broad classes of diagonal and non-diagonal unitaries, replacing highly connected qubit interactions with single-qubit gate layers or significantly simpler structures at the cost of a polynomial sampling overhead. Applied to algorithms such as QAOA, this yields efficient, hardware-friendly decompositions of, for instance, cardinality-constraint penalties and the fully connected XY-mixer, while maintaining rigorous performance guarantees compared to fully coherent implementations. Furthermore, we establish a formal connection between Fourier-based quantum penalties and Lagrangian relaxation, offering a unified perspective on constraint handling. We validate our approach using exact statevector simulations of 12-qubit circuits and large-scale experiments on 106 superconducting qubits. Our results illustrate how approximate sampling via an LCU systematically trades circuit complexity for sampling overhead, extending the practical reach of near-term quantum optimization.

quant-ph↗

arXiv2026

Mitigating errors in state preparation and measurement with noncomputational states

Error mitigation has enabled quantum computing applications with over one hundred qubits and deep circuits. Many error mitigation methods are noise-aware, relying on a faithful characterization of the noise channels of the hardware. However, fundamental limitations lead to unlearnable degrees of freedom of the underlying noise models when considering qubits. Here, we show how to leverage non-computational states as an additional resource to learn state-preparation errors in superconducting qubits. This allows one to fully constrain the noise models. We can thus independently and accurately mitigate state-preparation errors, gate errors and measurement errors. Our proposed method is also applicable to dynamic circuits with mid-circuit measurements. This work opens the door to improved error mitigation for measurements, both at the end of the circuit and mid-circuit.

quant-ph↗

arXiv2026

Spectral Gaps with Quantum Counting Queries and Oblivious State Preparation

Approximating the $k$-th spectral gap $Δ_k=|λ_k-λ_{k+1}|$ and the corresponding midpoint $μ_k=\frac{λ_k+λ_{k+1}}{2}$ of an $N\times N$ Hermitian matrix with eigenvalues $λ_1\geqλ_2\geq\ldots\geqλ_N$, is an important special case of the eigenproblem with numerous applications in science and engineering. In this work, we present a quantum algorithm which approximates these values up to additive error $εΔ_k$ using a logarithmic number of qubits. Notably, in the QRAM model, its total complexity (queries and gates) is bounded by $O\left( \frac{N^2}{ε^{2}Δ_k^2}\mathrm{polylog}\left( N,\frac{1}{Δ_k},\frac{1}ε,\frac{1}δ\right)\right)$, where $ε,δ\in(0,1)$ are the accuracy and the failure probability, respectively. For large gaps $Δ_k$, this provides a speed-up against the best-known complexities of classical algorithms, namely, $O \left( N^ω\mathrm{polylog} \left( N,\frac{1}{Δ_k},\frac{1}ε\right)\right)$, where $ω\lesssim 2.371$ is the matrix multiplication exponent. A key technical step in the analysis is the preparation of a suitable random initial state, which ultimately allows us to efficiently count the number of eigenvalues that are smaller than a threshold, while maintaining a quadratic complexity in $N$. In the black-box access model, we also report an $Ω(N^2)$ query lower bound for deciding the existence of a spectral gap in a binary (albeit non-symmetric) matrix.

quant-ph↗

arXiv2025

Combining quantum processors with real-time classical communication

Quantum computers process information with the laws of quantum mechanics. Current quantum hardware is noisy, can only store information for a short time, and is limited to a few quantum bits, i.e., qubits, typically arranged in a planar connectivity. However, many applications of quantum computing require more connectivity than the planar lattice offered by the hardware on more qubits than is available on a single quantum processing unit (QPU). Here we overcome these limitations with error mitigated dynamic circuits and circuit-cutting to create quantum states requiring a periodic connectivity employing up to 142 qubits spanning multiple QPUs connected in real-time with a classical link. In a dynamic circuit, quantum gates can be classically controlled by the outcomes of mid-circuit measurements within run-time, i.e., within a fraction of the coherence time of the qubits. Our real-time classical link allows us to apply a quantum gate on one QPU conditioned on the outcome of a measurement on another QPU which enables a modular scaling of quantum hardware. Furthermore, the error mitigated control-flow enhances qubit connectivity and the instruction set of the hardware thus increasing the versatility of our quantum computers. Dynamic circuits and quantum modularity are thus key to scale quantum computers and make them useful.

quant-ph↗

arXiv2023

Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation

Simulating the time-evolution of a Hamiltonian is one of the most promising applications of quantum computers. Multi-Product Formulas (MPFs) are well suited to replace standard product formulas since they scale better with respect to time and approximation errors. Hamiltonian simulation with MPFs was first proposed in a fully quantum setting using a linear combination of unitaries. Here, we analyze and demonstrate a hybrid quantum-classical approach to MPFs that classically combines expectation values evaluated with a quantum computer. This has the same approximation bounds as the fully quantum MPFs, but, in contrast, requires no additional qubits, no controlled operations, and is not probabilistic. We show how to design MPFs that do not amplify the hardware and sampling errors, and demonstrate their performance. In particular, we illustrate the potential of our work by theoretically analyzing the benefits when applied to a classically intractable spin-boson model, and by computing the dynamics of the transverse field Ising model using a classical simulator as well as quantum hardware. We observe an error reduction of up to an order of magnitude when compared to a product formula approach by suppressing hardware noise with Pauli Twirling, pulse efficient transpilation, and a novel zero-noise extrapolation based on scaled cross-resonance pulses. The MPF methodology reduces the circuit depth and may therefore represent an important step towards quantum advantage for Hamiltonian simulation on noisy hardware.

quant-ph↗

arXiv2021

Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation

We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity of $poly(\log(κ), 1/\sqrtε, \log(N))$, where $N$ denotes the number of equations, $ε$ is the accuracy, and $κ$ the condition number. The \emph{repeat-until-success} algorithm has to be run $\mathcal{O}\left(κ/(1-ε)\right)$ times to succeed, leveraging amplitude amplification, and sampled $\mathcal{O}(1/ε^2)$ times. Thus, the algorithm achieves an exponential improvement with respect to $N$ over classical methods. In particular, we present efficient oracles for state preparation, Hamiltonian simulation and a set of observables together with the corresponding error and complexity analyses. As the main result of this work, we show how to use Richardson extrapolation to enhance Hamiltonian simulation, resulting in an implementation of Quantum Phase Estimation (QPE) within the algorithm with $1/\sqrtε$ circuit complexity instead of $1/ε$ and which can be parallelized. Furthermore, we analyze necessary conditions for the overall algorithm to achieve an exponential speedup compared to classical methods. Our approach is not limited to the considered setting and can be applied to more general problems where Hamiltonian simulation is approximated via product formulae, although, our theoretical results would need to be extended accordingly. All the procedures presented are implemented with Qiskit and tested for small systems using classical simulation as well as using real quantum devices available through the IBM Quantum Experience.

quant-ph↗

arXiv2020

Teaching quantum computing with an interactive textbook

Quantum computing is a technology that promises to offer significant advantages during the coming decades. Though the technology is still in a prototype stage, the last few years have seen many of these prototype devices become accessible to the public. This has been accompanied by the open-source development of the software required to use and test quantum hardware in increasingly sophisticated ways. Such tools provide new education opportunities, not just for quantum computing specifically, but also more broadly for quantum information science and even quantum physics as a whole. In this paper we present a case study of one education resource which aims to take advantage of the opportunities: the open-source online textbook `Learn Quantum Computation using Qiskit'. An overview of the topics covered is given, as well as an explanation of the approach taken for each.

physics.ed-ph↗

arXiv2020

Efficient State Preparation for Quantum Amplitude Estimation

Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If state preparation is too expensive, it can diminish the quantum advantage. Preparing arbitrary quantum states has exponential complexity with respect to the number of qubits, thus, is not applicable. Currently known efficient techniques require problems based on log-concave probability distributions, involve learning an unknown distribution from empirical data, or fully rely on quantum arithmetic. In this paper, we introduce an approach to simplify state preparation, together with a circuit optimization technique, both of which can help reduce the circuit complexity for QAE state preparation significantly. We demonstrate the introduced techniques for a numerical integration example on real quantum hardware, as well as for option pricing under the Heston model, i.e., based on a stochastic volatility process, using simulation.

quant-ph↗