arXiv subjects

Gumaro Rendon

Publications and source records attributed to Gumaro Rendon.

At least 19 recordsLinked to original sources

arXiv2026

Exponentially Fast Solution State Preparation for the Heat Equation and its use for Option Pricing

In this work, we present the methods necessary to price an important set of derivatives on a quantum device while offering an advantage over existing classical methods. The methods developed here, in conjunction with ~\cite{GumaroS2026}, also provide an exponential advantage in requirement of qubits when pricing some option contracts with path-dependent payoff compared to state-of-the-art quantum Monte Carlo methods.

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arXiv2026

Agnostic Dynamical Decoupling for Single-Qubit Gates

We introduce a method for designing smooth single-qubit control pulses that implement a desired gate while suppressing the effect of unknown static error sources to first order. Unlike dynamically corrected gate constructions that require prior knowledge of the noise model, the present approach is agnostic to the detailed form of the target-bath interaction. The method parametrizes the control propagator through an auxiliary matrix expansion over orthogonal basis functions and enforces decoupling through algebraic orthogonality and equal-norm constraints on the expansion coefficients. These conditions guarantee that the leading Magnus contribution of an arbitrary static interaction reduces to a term proportional to the identity on the target system, thereby cancelling first-order error effects independently of the microscopic origin of the noise. We further show that the same construction suppresses, to first order, mediated couplings between simultaneously controlled qubits when their interaction occurs through intermediate environmental degrees of freedom, yielding effective second-order decoupling of the induced inter-qubit interaction. By using a discrete cosine transform parametrization, the pulse-synthesis problem is cast into a numerically stable constrained optimization with a minimal number of free parameters. Numerical examples for $R_z$ rotations and random single-qubit unitaries demonstrate smooth control fields that realize the target gates while remaining robust against arbitrary static single-qubit noise and mediated multi-qubit couplings. These results provide a hardware-friendly route toward noise-agnostic dynamically corrected single-qubit gates.

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arXiv2026

Preconditioned Multivariate Quantum Solution Extraction

Numerically solving partial differential equations is a ubiquitous computational task with broad applications in many fields of science. Quantum computers can potentially provide high-degree polynomial speed-ups for solving PDEs, however many algorithms simply end with preparing the quantum state encoding the solution in its amplitudes. Trying to access explicit properties of the solution naively with quantum amplitude estimation can subsequently diminish the potential speed-up. In this work, we present a technique for extracting a smooth positive function encoded in the amplitudes of a quantum state, which achieves the Heisenberg limit scaling. We improve upon previous methods by allowing higher dimensional functions, by significantly reducing the quantum complexity with respect to the number of qubits encoding the function, and by removing the dependency on the minimum of the function using preconditioning. Our technique works by sampling the cumulative distribution of the given function, fitting it with Chebyshev polynomials, and subsequently extracting a representation of the whole encoded function. Finally, we trial our method by carrying out small scale numerical simulations.

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arXiv2025

Exponentially Improved Constant in Quantum Solution Extraction

We have provided an algorithm to extract a smooth and positive definite function $\psi(x)$ encoded in quantum memory of size $2^n$ without running into the problem of exponentially suppressed sub-normalization. Through this, we remove an important bottleneck of solution information extraction, the last step, in fully solving an important class of differential equations on quantum computers. This class of problems includes solutions to the heat equation or other diffusive equations in fluid dynamics and finance.

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arXiv2025

Canonical Partition Function on a Quantum Computer through Trotter Interpolation

In this work, we present a Gibbs state observable estimation algorithm based on Trotter interpolation, which reaches a state-of-the-art quantum computational cost of $ \tilde{O}(\beta \log{1/\epsilon})$. Our approach saves $\log(\Gamma)$ ancilla qubits compared with the qubitization-based methods for Hamiltonian with $\Gamma$ stages. To provide a robust assessment of our approach, we benchmark our results against state-of-the-art methodology using the SYK model as a testbed. Our method provides an efficient alternative method for Gibbs-state accessing based on Trotterization in the context of quantum state preparation and estimation of thermal observables.

quant-ph↗

arXiv2025

Exponential Improvement on Asian Option Pricing Through Quantum Preconditioning Methods

In this work, we present a quantum algorithm designed to solve the differential equation used in the pricing of Asian options, in the framework of the Black-Scholes model. Our approach modifies an existing quantum pre-conditioning method (different from classical methods) for the problem of Asian option pricing such that we remove the dependence on the original condition number of discretized differential equation (system of linear equations). This was possible with new fast-forwardable discretizations of the first and second derivatives with respect to the underlying asset value ratio (value over average). We determine that these discretizations handle well kinks in the initial/terminal conditions. We also introduce a new circuit construction for the discretized time-derivative operator with Dirichlet boundary conditions which avoids the oracle workspace needed for the general sparse matrix implementation. Here, we also devised a new method probability integral estimation from which we extract the solution, achieving $\tilde{O}({\rm polylog}\left(1/\epsilon)\right)$, which is an exponential improvement over other quantum methods when it comes to solution information extraction from the solution state.

quant-ph↗

arXiv2024

Lattice outlook on $B\toρ\ell\barν$ and $B\to K^\star \ell \ell$

Lattice Quantum Chromodynamics (QCD) has significantly contributed to our understanding of the CKM matrix through precise determinations of hadronic matrix elements. With advancements in theoretical methodologies and computational resources, investigations can now extend to processes involving QCD-unstable hadrons such as the $ρ$ and $K^\star(892)$. These resonances play vital roles in processes such as weak decays of $B$ mesons, opening new avenues for exploration. Finite-volume lattice QCD techniques involving complex computational methods are used to determine the transition amplitudes. Here, we present preliminary results for $B\toρ\ell\barν$.

hep-lat↗

arXiv2024

Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation

Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause deviations from this fundamental limit. In this work, we show how algorithmic errors due to Trotterized time evolution can be mitigated through the use of standard polynomial interpolation techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors. We perform a rigorous error analysis of the interpolation approach for estimating eigenvalues and time-evolved expectation values, and show that the Heisenberg limit is achieved up to polylogarithmic factors in the error. Our work suggests that accuracies approaching those of state-of-the-art simulation algorithms may be achieved using Trotter and classical resources alone for a number of relevant algorithmic tasks.

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arXiv2023

All you need is Trotter

The work here enables linear cost-scaling with evolution time $t$ while keeping ${\rm polylog} (1/\epsilon)$ scaling and no extra block-encoding qubits, where $\epsilon$ is the algorithmic error. This is achieved through product formulas, stable interpolation (Chebyshev), and to calculate the needed fractional queries, cardinal sine interpolation is used.

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arXiv2023

Low-depth Gaussian State Energy Estimation

Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and limitations. Motivated by this, recent work has developed low-depth quantum algorithms for ground state energy estimation (GSEE), an important subroutine in quantum chemistry and materials. We detail a new GSEE algorithm which, like recent work, uses a number of operations scaling as $O(1/Δ)$ as opposed to the typical $O(1/ε)$, at the cost of an increase in the number of circuit repetitions from $O(1)$ to $O(1/ε^2)$. The relevant features of this algorithm come about from using a Gaussian window, which exponentially reduces contamination from excited states over the simplest GSEE algorithm based on the Quantum Fourier Transform (QFT). We adapt this algorithm to interpolate between the low-depth and full-depth regime by replacing $Δ$ with anything between $Δ$ and $ε$. At the cost of increasing the number of ancilla qubits from $1$ to $O(\logΔ)$, our method reduces the upper bound on the number of circuit repetitions by a factor of four compared to previous methods.

quant-ph↗

arXiv2023

A lattice QCD study of the $B \to ππ\ell \barν$ transition

$V_{ub}$ is the smallest and least known of all CKM matrix elements; the community currently determines its magnitude primarily through the exclusive process $B\toπ\ell\barν$. Here we present our progress toward a lattice QCD determination of the $V_{ub}$ matrix element from a novel transition -- $B\toππ\ell\barν$ process, where the $ππ$ system is in a $P$ wave and scattering features the $ρ(770)$ resonance as an enhancement. We perform our calculation on $N_f=2+1$ isotropic clover fermions on a lattice of $L\approx 3.6$ fm and a pion mass of $\approx 320$ MeV; for the $b$-quark we use the anisotropic clover action. After a brief overview of the theoretical framework, we will discuss some preliminary results.

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arXiv2023

Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers

A major thrust in quantum algorithm development over the past decade has been the search for the quantum algorithms that will deliver practical quantum advantage first. Today's quantum computers - and even early fault-tolerant quantum computers - are limited in the number of operations they can implement per circuit. We introduce quantum algorithms for ground-state energy estimation (GSEE) that accommodate this design constraint. The first algorithm estimates ground-state energies, offering a quadratic improvement on the ground state overlap parameter compared to other methods in this regime. The second algorithm certifies that the estimated ground-state energy is within a specified error tolerance of the true ground-state energy, addressing the issue of gap estimation that beleaguers several ground state preparation and energy estimation algorithms. We note, however, that the scaling of this certification technique is currently less favorable than that of the GSEE algorithm. To develop the certification algorithm, we propose a novel use of quantum computers to facilitate rejection sampling. After a classical computer generates initial samples, the quantum computer is used to accept or reject these samples, resulting in a set of accepted samples that approximate draws from a target distribution. Although we apply this technique specifically for ground-state energy certification, it may find broader applications. Our work pushes the boundaries of what operation-limited quantum computers can achieve, bringing the prospect of quantum advantage closer to realization.

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arXiv2022

$Λ_c \to Λ^(1520)$ form factors from lattice QCD and improved analysis of the $Λ_b \to Λ^(1520)$ and $Λ_b \to Λ_c^*(2595,2625)$ form factors

We present the first lattice-QCD calculation of the form factors governing the charm-baryon semileptonic decays $Λ_c \to Λ^*(1520)\ell^+ν_\ell$. As in our previous calculation of the $Λ_b \to Λ^*(1520)$ form factors, we work in the $Λ^*(1520)$ rest frame, but here we use four different heavy-baryon momenta instead of just two. Because of the lower mass of the $Λ_c$, the moderately-sized momenta used here are sufficient to determine the form factors in the full kinematic range of the semileptonic decay. We also update the analysis of our lattice results for the $Λ_b \to Λ^*(1520)$ and $Λ_b \to Λ_c^*(2595,2625)$ form factors by imposing exact relations among the different form factors at zero recoil that follow from rotational symmetry. Imposing these relations ensures the correct behavior of the angular observables near the endpoint.

hep-lat↗

arXiv2022

Charm-baryon semileptonic decays and the strange $Λ^*$ resonances: New insights from lattice QCD

Understanding the properties of the strange $Λ^*$ baryon resonances is a long-standing and fascinating problem. $Λ_c$ charm-baryon semileptonic weak decays to these resonances are highly sensitive to their internal structure and can be used to test theoretical models. We have performed the first lattice-QCD computation of the form factors governing $Λ_c$ semileptonic decays to a $Λ^*$ resonance: the $Λ^*(1520)$, which has negative parity and spin $3/2$. Here we present the resulting Standard-Model predictions of the $Λ_c\toΛ^*(1520)\ell^+ν_\ell$ differential and integrated decay rates as well as angular observables. Furthermore, by combining the recent BESIII measurement of the $Λ_c \to X e^+ ν_e$ inclusive semipositronic branching fraction [Phys. Rev. Lett. 121, 251801 (2018)] with lattice-QCD predictions of the $Λ_c \to Λe^+ ν_e$, $Λ_c \to n e^+ ν_e$, and $Λ_c \to Λ^*(1520) e^+ ν_e$ decay rates, we obtain an upper limit on the sum of the branching fractions to all other semipositronic final states. In particular, this upper limit constrains the $Λ_c\toΛ^*(1405)e^+ ν_e$ branching fraction to be very small, which may be another hint for a molecular structure of the $Λ^*(1405)$.

hep-ph↗

arXiv2022

The $πγ\to ππ$ transition and the $ρ$ radiative decay width from lattice QCD

We report a lattice QCD determination of the $πγ\to ππ$ transition amplitude for the $P$-wave, $I=1$ two-pion final state, as a function of the photon virtuality and $ππ$ invariant mass. The calculation was performed with $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV, on a $32^3 \times 96$ lattice with $L\approx 3.6$ fm. We construct the necessary correlation functions using a combination of smeared forward, sequential and stochastic propagators, and determine the finite-volume matrix elements for all $ππ$ momenta up to $|\vec{P}|= \sqrt{3} \frac{2π}{L}$ and all associated irreducible representations. In the mapping of the finite-volume to infinite-volume matrix elements using the Lellouch-Lüscher factor, we consider two different parametrizations of the $ππ$ scattering phase shift. We fit the $q^2$ and $s$ dependence of the infinite-volume transition amplitude in a model-independent way using series expansions, and compare multiple different truncations of this series. Through analytic continuation to the $ρ$ resonance pole, we also determine the $πγ\to ρ$ resonant transition form factor and the $ρ$ meson photocoupling, and obtain $|G_{ρπγ}| = 0.0802(32)(20)$.

hep-lat↗

arXiv2021

Effects of Cosine Tapering Window on Quantum Phase Estimation

We provide a modification to the quantum phase estimation algorithm (QPEA) inspired on classical windowing methods for spectral density estimation. From this modification we obtain an upper bound in the cost that implies a cubic improvement with respect to the algorithm's error rate. Numerical evaluation of the costs also demonstrates an improvement. Moreover, with similar techniques, we detail an iterative projective measurement method for ground state preparation that gives an exponential improvement over previous bounds using QPEA. Numerical tests that confirm the expected scaling behavior are also obtained. For these numerical tests we have used a Lattice Thirring model as testing ground. Using well-known perturbation theory results, we also show how to more appropriately estimate the cost scaling with respect to state error instead of evolution operator error.

quant-ph↗

arXiv2021

$Λ_b \to Λ_c^*(2595,2625)\ell^-\barν$ form factors from lattice QCD

We present the first lattice-QCD determination of the form factors describing the semileptonic decays $Λ_b \to Λ_c^*(2595)\ell^-\barν$ and $Λ_b \to Λ_c^*(2625)\ell^-\barν$, where the $Λ_c^*(2595)$ and $Λ_c^*(2625)$ are the lightest charm baryons with $J^P=\frac12^-$ and $J^P=\frac32^-$, respectively. These decay modes provide new opportunities to test lepton flavor universality and also play an important role in global analyses of the strong interactions in $b\to c$ semileptonic decays. We determine the full set of vector, axial vector, and tensor form factors for both decays, but only in a small kinematic region near the zero-recoil point. The lattice calculation uses three different ensembles of gauge-field configurations with $2+1$ flavors of domain-wall fermions, and we perform extrapolations of the form factors to the continuum limit and physical pion mass. We present Standard-Model predictions for the differential decay rates and angular observables. In the kinematic region considered, the differential decay rate for the $\frac12^-$ final state is found to be approximately 2.5 times larger than the rate for the $\frac32^-$ final state. We also test the compatibility of our form-factor results with zero-recoil sum rules.

hep-lat↗

arXiv2021

P-wave nucleon-pion scattering amplitude in the $Δ(1232)$ channel from lattice QCD

We determine the $Δ(1232)$ resonance parameters using lattice QCD and the Lüscher method. The resonance occurs in elastic pion-nucleon scattering with $J^P=3/2^+$ in the isospin $I = 3/2$, $P$-wave channel. Our calculation is performed with $N_f=2+1$ flavors of clover fermions on a lattice with $L\approx 2.8$ fm. The pion and nucleon masses are $m_π=255.4(1.6)$ MeV and $m_N=1073(5)$ MeV, and the strong decay channel $Δ\rightarrow πN$ is found to be above the threshold. To thoroughly map out the energy-dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to $\vec{P}=\frac{2π}{L}(1,1,1)$, including irreps that mix $S$ and $P$ waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the $P$-wave phase shift and the effective-range expansion for the $S$-wave phase shift. From the location of the pole in the $P$-wave scattering amplitude, we obtain the resonance mass $m_Δ=1378(7)(9)$ MeV and the coupling $g_{Δ\text{-}πN}=23.8(2.7)(0.9)$.

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