arXiv subjects

Jerimiah Wright

Publications and source records attributed to Jerimiah Wright.

5 recordsLinked to original sources

arXiv2026

Benchmarking Quantum Simulations of the Lipkin-Meshkov-Glick Model Using Large Tensor Networks

As quantum computing matures, it is critical to benchmark its real-world problem solving performance against competitive classical methods, such as tensor networks. In this work, we leverage the Density Matrix Renormalization Group (DMRG) algorithm to compute ground state energies of the Lipkin Meshkov Glick (LMG) model as a comparative benchmark against popular noisy intermediate-scale (NISQ) algorithms like the Variational Quantum Eigensolver (VQE) and Sample-Based Quantum Diagonalization (SQD) method. By running DMRG on the NERSC Perlmutter supercomputer, we provide one of the largest LMG ground state energy datasets in literature, containing accurate ground state energies for systems up to 1400 particles. We compare these results with VQE and SQD implementations on an IBM Eagle quantum computer for comparison. VQE achieved results within 1 percent error for 6 particles, while exceeding that threshold for all other values while SQD extended that range to 17 particles, suggesting that in a noisy intermediate scale quantum era, subspace-based approaches may strike the best balance between accuracy, circuit depth, and noise resilience.

quant-ph↗

arXiv2024

Logical Error Rates for a [[4,2,2]]-Encoded Variational Quantum Eigensolver Ansatz

Quantum computing offers a potential for algorithmic speedups for applications, such as large-scale simulations in chemistry and physics. However, these speedups must yield results that are sufficiently accurate to predict realistic outcomes of experiments precisely. Delivering on the promise of high accuracy and precision requires methods to evaluate the computational accuracy of the quantum computing devices. We develop a framework to estimate the computational accuracy of near-term noisy, intermediate scale quantum (NISQ) computing devices using a quantum chemistry application. Application benchmarks that run on NISQ devices require techniques for mitigating errors to improve accuracy and precision. We use device agnostic error-mitigation schemes, quantum error detection and readout error detection, with post-selection to mitigate the dominant sources of noise. We evaluate the framework by simulating the ground state of molecular hydrogen with the variational quantum eigensolver (VQE) algorithm, estimating the energy and calculating the precision of the estimate using numerical simulations with realistic noise models. We first quantify the improvement in the logical error rate and state fidelity of the VQE application when encoded with the [[4,2,2]] quantum error detection code. When additionally encoded with readout error detection, we show that compared to the unencoded simulation, the encoded simulation yields a more accurate estimate by more than 1 mHa (0.027 eV) with comparable precision and higher state fidelity. Additionally, unlike the best estimate from the unencoded simulations, the results from the encoded simulation fall within the chemical accuracy threshold of 1.6 mHa of the exact energy. The estimated accuracy and precision indicate that current quantum computers can achieve error rates that yield useful outcomes for chemical applications.

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arXiv2022

Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry

The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the behavior of these noisy quantum circuits using numerical simulations to estimate the accuracy and fidelity of the prepared quantum states relative to the ground truth obtained by conventional means. We implement several different types of ansatz circuits derived from unitary coupled cluster theory for the purposes of estimating the ground-state energy of Sodium Hydride using the variational quantum eigensolver algorithm. We show how relative error in the energy and the fidelity scale with the levels of gate-based noise, the inter-molecular configuration, the ansatz circuit depth, and the parameter optimization methods.

quant-ph↗

arXiv2020

Benchmarking adaptive variational quantum eigensolvers

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H$_2$, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

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arXiv2019

Computational Chemistry on Quantum Computers

The purpose of this experiment was to use the known analytical techniques to study the creation, simulation, and measurements of molecular Hamiltonians. The techniques used consisted of the Linear Combination of Atomic Orbitals (LCAO), the Linear Combination of Unitaries (LCU), and the Phase Estimation Algorithm (PEA). The molecules studied were $H_2$ with and without spin, as well as $He_2$ without spin. Hamiltonians were created under the LCAO basis, and reconstructed using the Jordan-Winger transform in order to create a linear combination of Pauli spin operators. The lengths of each molecular Hamiltonian greatly increased from the $H_2$ without spin, to $He_2$. This resulted in a reduced ability to simulate the Hamiltonians under ideal conditions. Thus, only low orders of l = 1 and l = 2 were used when expanding the Hamiltonian in accordance to the LCU method of simulation. The resulting Hamiltonians were measured using PEA, and plotted against function of $\frac{2π(K)}{N}$ and the probability distribution of each register. The resolution of the graph was dependent on the amount of registers, N, being used. However, the reduction of order hardly changed the image of the $H_2$ graphs. Qualitative comparisons between the three molecules were drawn.

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