arXiv subjects

Alessandro Roggero

Publications and source records attributed to Alessandro Roggero.

At least 37 records · Page 2Linked to original sources

arXiv2024

Time Dependent Hamiltonian Simulation Using Discrete Clock Constructions

Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty prevents a direct adaptation of time independent simulation algorithms for time dependent simulation. However, there exists a framework within the theory of dynamical systems which eliminates time ordering by adding a "clock" degree of freedom. In this work, we provide a computational framework, based on this reduction, for encoding time dependent dynamics as time independent systems. As a result, we make two advances in digital Hamiltonian simulation. First, we create a time dependent simulation algorithm based on performing qubitization on the augmented clock system, and in doing so, provide the first qubitization-based approach to time dependent Hamiltonians that goes beyond Trotterization of the ordered exponential. Second, we define a natural generalization of multiproduct formulas for time-ordered exponentials, then propose and analyze an algorithm based on these formulas. Unlike other algorithms of similar accuracy, the multiproduct approach achieves commutator scaling, meaning that this method outperforms existing methods for physically-local time dependent Hamiltonians. Our work reduces the disparity between time dependent and time independent simulation and indicates a step towards optimal quantum simulation of time dependent Hamiltonians.

quant-ph↗

arXiv2024

Time Scales in Many-Body Fast Neutrino Flavor Conversion

Time scales associated with many-body fast neutrino flavor conversions in core-collapse supernova are explored in the context of an effective two-flavor model with axial symmetry. We present a preliminary study of time scales obtained from a linear stability analysis and from the distributions of Loschmidt echo crossing times (intimately connected to dynamical phase transitions in non-equilibrium systems) determined by time evolution with the exact many-body Hamiltonian. Starting from a tensor-product initial state describing systems of $N$ neutrinos, with $N/2$ electron-type and $N/2$ heavy-type, with uniform angular distributions, the Loschmidt echo crossing times, $t_{\mathcal{L}_{\times}}$, are found to exhibit two distinct time scales that are exponentially separated. The second peak structure at longer times, effectively absent for $N=4$, develops with increasing $N$. When re-scaled in terms of $\log t_{\mathcal{L}_{\times}}$, the distributions are found to become increasingly well described by the sum of two stable distributions. The distribution of Loschmidt echo crossing times differs somewhat from the results of the (numerical) linear stability analysis, which exhibits a peak at finite frequency and a second peak consistent with zero frequency. The exact analysis suggests that the zero-frequency instability manifests itself as a modest flavor-conversion time scale.

nucl-th↗

arXiv2024

Quantum error mitigation for Fourier moment computation

Hamiltonian moments in Fourier space - expectation values of the unitary evolution operator under a Hamiltonian at different times - provide a convenient framework to understand quantum systems. They offer insights into the energy distribution, higher-order dynamics, response functions, correlation information and physical properties. This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 CNOT gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices.

quant-ph↗

arXiv2023

Enhancing Qubit Readout with Autoencoders

In addition to the need for stable and precisely controllable qubits, quantum computers take advantage of good readout schemes. Superconducting qubit states can be inferred from the readout signal transmitted through a dispersively coupled resonator. This work proposes a novel readout classification method for superconducting qubits based on a neural network pre-trained with an autoencoder approach. A neural network is pre-trained with qubit readout signals as autoencoders in order to extract relevant features from the data set. Afterwards, the pre-trained network inner layer values are used to perform a classification of the inputs in a supervised manner. We demonstrate that this method can enhance classification performance, particularly for short and long time measurements where more traditional methods present lower performance.

quant-ph↗

arXiv2023

Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group

Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage, namely a significant (in some cases exponential) speed-up of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models which are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this roadmap paper, led by CERN, DESY and IBM, we provide the status of high-energy physics quantum computations and give examples for theoretical and experimental target benchmark applications, which can be addressed in the near future. Having the IBM 100 x 100 challenge in mind, where possible, we also provide resource estimates for the examples given using error mitigated quantum computing.

quant-ph↗

arXiv2023

Importance sampling for stochastic quantum simulations

Simulating many-body quantum systems is a promising task for quantum computers. However, the depth of most algorithms, such as product formulas, scales with the number of terms in the Hamiltonian, and can therefore be challenging to implement on near-term, as well as early fault-tolerant quantum devices. An efficient solution is given by the stochastic compilation protocol known as qDrift, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. In this work, we unify the qDrift protocol with importance sampling, allowing us to sample from arbitrary probability distributions, while controlling both the bias, as well as the statistical fluctuations. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Moreover, we incorporate recent work on composite channel and compute rigorous bounds on the bias and variance, showing how to choose the number of samples, experiments, and time steps for a given target accuracy. These results lead to a more efficient implementation of the qDrift protocol, both with and without the use of composite channels. Theoretical results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.

quant-ph↗

arXiv2022

Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations

It is well known that the neutrino flavor in extreme astrophysical environments changes under the effect of three contributions: the vacuum oscillation, the interaction with the surrounding matter, and the collective oscillations due to interactions between different neutrinos. The latter adds a non-linear contribution to the equations of motion, making the description of their dynamics complex. In this work we study various strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. This was achieved by using a pair-neutrino decomposition designed to account for the fact that the flavor Hamiltonian, in the presence of the neutrino-neutrino term, presents an all-to-all interaction that makes the implementation of the evolution dependent on the qubit topology. We analyze the Trotter error caused by the decomposition demonstrating that the complexity of the implementation of time evolution scales polynomially with the number of neutrinos and that the noisy from near-term quantum device simulation can be reduced by optimizing the quantum circuit decomposition and exploiting a full-qubit connectivity. We find that the gate complexity using second order Trotter-Suzuki formulae scales better with system size than with other decomposition methods such as Quantum Signal Processing. We finally present the application and the results of our algorithm on a real quantum device based on trapped-ions qubits.

quant-ph↗

arXiv2022

Quantum Monte Carlo in Configuration Space with Three-Nucleon Forces

Neutron matter, through its connection to neutron stars as well as systems like cold atom gases, is one of the most interesting yet computationally accessible systems in nuclear physics. The Configuration-Interaction Monte Carlo (CIMC) method is a stochastic many-body technique allowing to tackle strongly coupled systems. In contrast to other Quantum Monte Carlo methods employed in nuclear physics, the CIMC method can be formulated directly in momentum space allowing for an efficient use of non-local interactions. In this work we extend CIMC method to include three-nucleon interactions through the normal-ordered two-body approximation. We present results for the equation of state of neutron matter in line with other many-body calculations that employ low resolution chiral interactions, and provide predictions for the momentum distribution and the static structure factor.

nucl-th↗

arXiv2022

Quantum Error Correction with Gauge Symmetries

Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors in order to retain a local Hamiltonian. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss' law constraint to correct one-qubit errors for a $\mathbb{Z}_2$ or truncated U(1) LGT in 1+1 and 2+1 dimensions with a link flux cutoff of $1$. Unlike existing work on detecting violations of Gauss' law, our circuits are fault tolerant and the overall error correction scheme outperforms a naïve application of the $[5,1,3]$ code. The constructions outlined can be extended to LGT systems with larger cutoffs and may be of use in understanding how to hybridize error correction and quantum simulation for LGTs in higher space-time dimensions and with different symmetry groups.

quant-ph↗

arXiv2022

Faster spectral density calculation using energy moments

Accurate predictions of inclusive scattering cross sections in the linear response regime require efficient and controllable methods to calculate the spectral density in a strongly-correlated many-body system. In this work we reformulate the recently proposed Gaussian Integral Transform technique in terms of Fourier moments of the system Hamiltonian which can be computed efficiently on a quantum computer. One of the main advantages of this framework is that it allows for an important reduction of the computational cost by exploiting previous knowledge about the energy moments of the spectral density. For a simple model of medium mass nucleus like $^{40}$Ca and target energy resolution of $1$ MeV we find an expected speed-up of $\approx 125$ times for the calculation of the giant dipole response and of $\approx 50$ times for the simulation of quasi-elastic electron scattering at typical momentum transfers.

quant-ph↗

arXiv2022

Hybridized Methods for Quantum Simulation in the Interaction Picture

Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic advantages for some Hamiltonians, but incurs prohibitive constant factors and is incompatible with methods like qubitization. We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations over known algorithms. These approaches show asymptotic improvements over the individual methods that comprise them and further make interaction picture simulation methods practical in the near term. Physical applications of these hybridized methods yield a gate complexity scaling as $\log^2 Λ$ in the electric cutoff $Λ$ for the Schwinger Model and independent of the electron density for collective neutrino oscillations, outperforming the scaling for all current algorithms with these parameters. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $λ$ used to impose an energy cost on time-evolution into an unphysical subspace.

quant-ph↗

arXiv2022

Quantum Machine Learning with SQUID

In this work we present the Scaled QUantum IDentifier (SQUID), an open-source framework for exploring hybrid Quantum-Classical algorithms for classification problems. The classical infrastructure is based on PyTorch and we provide a standardized design to implement a variety of quantum models with the capability of back-propagation for efficient training. We present the structure of our framework and provide examples of using SQUID in a standard binary classification problem from the popular MNIST dataset. In particular, we highlight the implications for scalability for gradient-based optimization of quantum models on the choice of output for variational quantum models.

quant-ph↗

arXiv2022

Quantum Simulation for High Energy Physics

It is for the first time that Quantum Simulation for High Energy Physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in Quantum Information Sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This community whitepaper is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

quant-ph↗

arXiv2022

Entanglement and correlations in fast collective neutrino flavor oscillations

Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings like supernovae and neutron star binary merger remnants, which are characterized by large neutrino densities. In these settings, simulations in the mean-field approximation show that neutrino-neutrino interactions can overtake vacuum oscillations and give rise to fast collective flavor evolution on time-scales $t\proptoμ^{-1}$, with $μ$ proportional to the local neutrino density. In this work, we study the full out-of-equilibrium flavor dynamics in simple multi-angle geometries displaying fast oscillations in the mean field linear stability analysis. Focusing on simple initial conditions, we analyze the production of pair correlations and entanglement in the complete many-body-dynamics as a function of the number $N$ of neutrinos in the system, for up to thousands of neutrinos. Similarly to simpler geometries with only two neutrino beams, we identify three regimes: stable configurations with vanishing flavor oscillations, marginally unstable configurations with evolution occurring on long time scales $τ\approxμ^{-1}\sqrt{N}$, and unstable configurations showing flavor evolution on short time scales $τ\approxμ^{-1}\log(N)$. We present evidence that these fast collective modes are generated by the same dynamical phase transition which leads to the slow bipolar oscillations, establishing a connection between these two phenomena and explaining the difference in their time scales. We conclude by discussing a semi-classical approximation which reproduces the entanglement entropy at short to medium time scales and can be potentially useful in situations with more complicated geometries where classical simulation methods starts to become inefficient.

astro-ph.HE↗

arXiv2021

Stochastic Dynamics and Bound States of Heavy Impurities in a Fermi Bath

We investigate the dynamics of heavy impurities embedded in an ultra-cold Fermi gas by using a Generalized Langevin equation. The latter -- derived by means of influence functional theory -- describes the stochastic classical dynamics of the impurities and the quantum nature of the fermionic bath manifests in the emergent interaction between the impurities and in the viscosity tensor. By focusing on the two-impurity case, we predict the existence of bound states, in different conditions of coupling and temperature, and whose life-time can be analytically estimated. Our predictions should be testable using cold-gases platforms within current technology.

cond-mat.quant-gas↗

arXiv2021

Entanglement and Many-Body effects in Collective Neutrino Oscillations

Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings, such as supernovae, where the neutrino density is large. In this regime, neutrino-neutrino interactions are important and simulations in the mean-field approximation show evidence for collective oscillations occurring at time scales much larger than those associated with vacuum oscillations. In this work, we study the out-of-equilibrium dynamics of a corresponding spin model using Matrix Product States and show how collective bipolar oscillations can be triggered by many-body correlations if appropriate initial conditions are present. We find entanglement entropies scaling at most logarithmically in the system size suggesting that classical tensor network methods could be efficient in describing collective neutrino dynamics more generally. These observation provide a clear path forward, not only to increase the accuracy of current simulations, but also to elucidate the mechanism behind collective flavor oscillations without resorting to the mean field approximation.

hep-ph↗

arXiv2021

Imaginary Time Propagation on a Quantum Chip

Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems, and the heart of a number of numerical methods that have been used with great success in quantum chemistry, condensed matter and nuclear physics. We propose an algorithm to implement imaginary time propagation on a quantum computer. Our algorithm is devised in the context of an efficient encoding into an optimized gate, drawing on the underlying characteristics of the quantum device, of a unitary operation in an extended Hilbert space. However, we proved that for simple problems it can be successfully applied to standard digital quantum machines. This work paves the way for porting quantum many-body methods based on imaginary-time propagation to near-term quantum devices, enabling the future quantum simulation of the ground states of a broad class of microscopic systems.

quant-ph↗

arXiv2021

Nuclear two point correlation functions on a quantum-computer

The calculation of dynamic response functions is expected to be an early application benefiting from rapidly developing quantum hardware resources. The ability to calculate real-time quantities of strongly-correlated quantum systems is one of the most exciting applications that can easily reach beyond the capabilities of traditional classical hardware. Response functions of fermionic systems at moderate momenta and energies corresponding roughly to the Fermi energy of the system are a potential early application because the relevant operators are nearly local and the energies can be resolved in moderately short real time, reducing the spatial resolution and gate depth required. This is particularly the case in quasielastic electron and neutrino scattering from nuclei, a topic of great interest in the nuclear and particle physics communities and directly related to experiments designed to probe neutrino properties. In this work we use current quantum hardware and error mitigation protocols to calculate response functions for a highly simplified nuclear model through calculations of a 2-point real time correlation function for a modified Fermi-Hubbard model in two dimensions with three distinguishable nucleons on four lattice sites.

quant-ph↗