arXiv subjects

Khaldoon Ghanem

Publications and source records attributed to Khaldoon Ghanem.

13 recordsLinked to original sources

arXiv2024

Experimental Demonstration of Break-Even for the Compact Fermionic Encoding

The utility of solving the Fermi-Hubbard model has been estimated in the billions of dollars. Digital quantum computers can in principle address this task, but have so far been limited to quasi one-dimensional models. This is because of exponential overheads caused by the interplay of noise and the non-locality of the mapping between fermions and qubits. Here, we show experimentally that a recently developed local encoding can overcome this problem. We develop a new compilation scheme, called "corner hopping", that reduces the cost of simulating fermionic hopping by 42% which allows us to conduct the largest digital quantum simulations of a fermionic model to date, using a trapped ion quantum computer to prepare adiabatically the ground state of a 6 x 6 spinless Fermi-Hubbard model encoded in 48 physical qubits. We also develop two new error mitigation schemes for systems with conserved quantities, one based on local postselection and one on extrapolation of local observables. Our results suggest that Fermi-Hubbard models beyond classical simulability can be addressed by digital quantum computers without large increases in gate fidelity.

quant-ph↗

arXiv2024

Practicality of quantum adiabatic algorithm for chemistry applications

Despite its simplicity and strong theoretical guarantees, adiabatic state preparation has received considerably less interest than variational approaches for the preparation of low-energy electronic structure states. Two major reasons for this are the large number of gates required for Trotterising time-dependent electronic structure Hamiltonians, as well as discretisation errors heating the state. We show that a recently proposed randomized algorithm, which implements exact adiabatic evolution without heating and with far fewer gates than Trotterisation, can overcome this problem. We develop three methods for measuring the energy of the prepared state in an efficient and noise-resilient manner, yielding chemically accurate results on a 4-qubit molecule in the presence of realistic gate noise, without the need for error mitigation. These findings suggest that adiabatic approaches to state preparation could play a key role in quantum chemistry simulations both in the era of noisy as well as error-corrected quantum computers.

quant-ph↗

arXiv2023

Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers

Simulating properties of quantum materials is one of the most promising applications of quantum computation, both near- and long-term. While real-time dynamics can be straightforwardly implemented, the finite temperature ensemble involves non-unitary operators that render an implementation on a near-term quantum computer extremely challenging. Recently, [Lu, Bañuls and Cirac, PRX Quantum 2, 020321 (2021)] suggested a "time-series quantum Monte Carlo method" which circumvents this problem by extracting finite temperature properties from real-time simulations via Wick's rotation and Monte Carlo sampling of easily preparable states. In this paper, we address the challenges associated with the practical applications of this method, using the two-dimensional transverse field Ising model as a testbed. We demonstrate that estimating Boltzmann weights via Wick's rotation is very sensitive to time-domain truncation and statistical shot noise. To alleviate this problem, we introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. In addition, we show how to reduce the statistical errors of Monte Carlo sampling via a reweighted version of the Wolff cluster algorithm. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems.

quant-ph↗

arXiv2023

Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer

Calculating the equilibrium properties of condensed matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude $\langle \psi| e^{-i \hat H t}|\psi \rangle$ from initial states $|\psi\rangle$ and a time evolution under the Hamiltonian $\hat H$ up to short times $t$. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm.

quant-ph↗

arXiv2023

Generalized Maximum Entropy Methods as Limits of the Average Spectrum Method

We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing Rényi entropies of order $η$, of which Shannon entropy is the special case $η=1$. The order of Rényi entropy is determined by the way the spectra are sampled. Our derivation also suggests a modification of Rényi entropy, giving it a non-trivial $η\to0$ limit. We show that the sharper peaks generally obtained in ASM are associated with entropies of order $η<1$. Our work provides a generalization of the maximum entropy method that enables extracting more structure than the traditional method.

cond-mat.str-el↗

arXiv2022

Connecting Tikhonov regularization to the maximum entropy method for the analytic continuation of quantum Monte Carlo data

Analytic continuation is an essential step in extracting information about the dynamical properties of physical systems from quantum Monte Carlo (QMC) simulations. Different methods for analytic continuation have been proposed and are still being developed. This paper explores a regularization method based on the repeated application of Tikhonov regularization under the discrepancy principle. The method can be readily implemented in any linear algebra package and gives results surprisingly close to the maximum entropy method (MaxEnt). We analyze the method in detail and demonstrate its connection to MaxEnt. In addition, we provide a straightforward method for estimating the noise level of QMC data, which is helpful for practical applications of the discrepancy principle when the noise level is not known reliably.

physics.comp-ph↗

arXiv2021

Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo

Population control is an essential component of any projector Monte Carlo algorithm. This control mechanism usually introduces a bias in the sampled quantities that is inversely proportional to the population size. In this paper, we investigate the population control bias in the full configuration interaction quantum Monte Carlo method. We identify the precise origin of this bias and quantify it in general. We show that it has different effects on different estimators and that the shift estimator is particularly susceptible. We derive a re-weighting technique, similar to the one used in diffusion Monte Carlo, for correcting this bias and apply it to the shift estimator. We also show that by using importance sampling, the bias can be reduced substantially. We demonstrate the necessity and the effectiveness of applying these techniques for sign-problem-free systems where this bias is especially notable. Specifically, we show results for large one-dimensional Hubbard models and the two-dimensional Heisenberg model, where corrected FCIQMC results are comparable to the other high-accuracy results.

physics.comp-ph↗

arXiv2020

The Adaptive Shift Method in Full Configuration Interaction Quantum Monte Carlo: Development and Applications

In a recent paper, we proposed the adaptive shift method for correcting the undersampling bias of the initiator-FCIQMC. The method allows faster convergence with the number of walkers to the FCI limit than the normal initiator method, particularly for large systems. In its application to strongly correlated molecules, however, the method is prone to overshooting the FCI energy at intermediate walker numbers, with convergence to the FCI limit from below. In this paper, we present a solution to the overshooting problem in strongly correlated molecules, as well as further accelerating convergence to the FCI energy. This is achieved by offsetting the reference energy to a value typically below the Hartree-Fock energy but above the exact energy. This offsetting procedure does not change the exactness property of the algorithm, namely convergence to the exact FCI solution in the large-walker limit, but at its optimal value greatly accelerates convergence. There is no overhead cost associated with this offsetting procedure, and is therefore a pure and substantial computational gain. We illustrate the behavior of this offset adaptive shift method by applying it to the N$_2$ molecule, the ozone molecule at three different geometries (equilibrium open minimum, a hypothetical ring minimum, and a transition state) in three basis sets (cc-pV$X$Z, $X$=D,T,Q), and the chromium dimer in cc-pVDZ basis set, correlating 28 electrons in 76 orbitals. We show that in most cases the offset adaptive shift method converges much faster than both the normal initiator method and the original adaptive shift method.

physics.comp-ph↗

arXiv2020

The Ground State Electronic Energy of Benzene

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$ζ$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 m$E_{\text{H}}$), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

physics.chem-ph↗

arXiv2020

NECI: N-Electron Configuration Interaction with emphasis on state-of-the-art stochastic methods

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24000 CPU cores. In this paper, we describe the core functionalities of NECI and recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs and it is licensed under GPL-3.0.

physics.comp-ph↗

arXiv2020

Extending the average spectrum method: Grid points sampling and density averaging

Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating over all non-negative spectra weighted by how well they fit the data. In a recent paper, we found that discretizing the functional integral as in Feynman's path-integrals, does not have a well-defined continuum limit. Instead, the limit depends on the discretization grid whose choice may strongly bias the results. In this paper, we demonstrate that sampling the grid points, instead of keeping them fixed, also changes the functional integral limit and rather helps to overcome the bias considerably. We provide an efficient algorithm for doing the sampling and show how the density of the grid points acts now as a default model with a significantly reduced biasing effect. The remaining bias depends mainly on the width of the grid density, so we go one step further and average also over densities of different widths. For a certain class of densities, including Gaussian and exponential ones, this width averaging can be done analytically, eliminating the need to specify this parameter without introducing any computational overhead.

physics.comp-ph↗

arXiv2019

The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid

The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible spectral functions, weighted by how well they fit the data. Its main advantage is the apparent lack of adjustable parameters and smoothness constraints, using instead the information on the statistical noise in the data. Its main disadvantage is the enormous computational cost of performing the functional integral. Here we introduce an efficient implementation, based on the singular value decomposition of the integral kernel, eliminating this problem. It allows us to analyze the behavior of the average spectrum method in detail. We find that the discretization of the real-frequency grid, on which the spectral function is represented, biases the results. The distribution of the grid points plays the role of a default model while the number of grid points acts as a regularization parameter. We give a quantitative explanation for this behavior, point out the crucial role of the default model and provide a practical method for choosing it, making the average spectrum method a reliable and efficient technique for analytic continuation.

cond-mat.str-el↗

arXiv2019

Unbiasing the initiator approximation in Full Configuration Interaction Quantum Monte Carlo

We identify and rectify a crucial source of bias in the initiator FCIQMC algorithm. Non-initiator determinants (i.e. determinants whose population is below the initiator threshold) are subject to a systematic {\em undersampling} bias, which in large systems leads to a bias in the energy when an insufficient number of walkers is used. We show that the acceptance probability ($p_{acc}$), that a non-initiator determinant has its spawns accepted, can be used to unbias the initiator bias, in a simple and accurate manner, by reducing the applied shift to the non-initiator proportionately to $p_{acc}$. This modification preserves the property that in the large walker limit, when $p_{acc}\rightarrow1$, the unbiasing procedure disappears, and the initiator approximation becomes exact. We demonstrate that this algorithm shows rapid convergence to the FCI limit with respect to walker number, and furthermore largely removes the dependence of the algorithm on the initiator threshold, enabling highly accurate results to be obtained even with large values of the threshold. This is exemplified in the case of butadiene/ANO-L-pVDZ and benzene/cc-pVDZ, correlating 22 and 30 electrons in 82 and 108 orbitals respectively. In butadiene $5\times 10^7$ and in benzene $10^8$ walkers suffice to obtain an energy to within a milli-Hartree of the CCSDT(Q) result, in Hilbert spaces of $10^{26}$ and $10^{35}$ respectively. Essentially converged results require $\sim 10^8$ walkers for butadiene and $\sim 10^9$ walkers for benzene, and lie slightly lower than CCSDT(Q). Owing to large-scale parallelisability, these calculations can be executed in a matter of hours on a few hundred processors. The present method largely solves the initiator-bias problems that the initiator method suffered from when applied to medium-sized molecules.

physics.comp-ph↗