arXiv subjects

Sean A. Fischer

Publications and source records attributed to Sean A. Fischer.

3 recordsLinked to original sources

arXiv2020

Efficient algorithm for generating Pauli coordinates for an arbitrary linear operator

Several linear algebra routines for quantum computing use a basis of tensor products of identity and Pauli operators to describe linear operators, and obtaining the coordinates for any given linear operator from its matrix representation requires a basis transformation, which for an $\mathrm N\times\mathrm N$ matrix generally involves $\mathcal O(\mathrm N^4)$ arithmetic operations. Herein, we present an efficient algorithm that for our particular basis transformation only involves $\mathcal O(\mathrm N^2\log_2\mathrm N)$ operations. Because this algorithm requires fewer than $\mathcal O(\mathrm N^3)$ operations, for large $\mathrm N$, it could be used as a preprocessing step for quantum computing algorithms for certain applications. As a demonstration, we apply our algorithm to a Hamiltonian describing a system of relativistic interacting spin-zero bosons and calculate the ground-state energy using the variational quantum eigensolver algorithm on a quantum computer.

quant-ph↗

arXiv2019

Symmetry Configuration Mapping for Representing Quantum Systems on Quantum Computers

Quantum computing has the potential to significantly speed up complex computational tasks, and arguably the most promising application area for near-term quantum computers is the simulation of quantum mechanics. To make the most of our limited quantum computing resources, we need new and more compact algorithms and mappings. Whereas previous work, including recent demonstrations, has focused primarily on general mappings for fermionic systems, we propose instead to construct customized mappings tailored to the considered quantum mechanical systems. Specifically, we take advantage of existing symmetry, which we build into the mappings a priori to obtain optimal compactness. To demonstrate this approach, we have performed quantum computing calculations of the fluorine molecule, in which we have mapped 16 active spin-orbitals to 4 qubits. This is a four-fold reduction in the qubit requirement, as compared to the standard general mappings. Moreover, our compact system-to-qubits mappings are robust against noise that breaks symmetry, thereby reducing non-statistical errors in the computations. Furthermore, many systems, including F2, are described by real Hamiltonians, allowing us to also reduce the number of single-qubit operations in the hardware-efficient ansatz for the quantum variational eigensolver by roughly a factor of three.

quant-ph↗

arXiv2018

Correlated Dynamics in Aqueous Proton Diffusion

The aqueous proton displays an anomalously large diffusion coefficient that is up to 7 times that of similarly sized cations. There is general consensus that the proton achieves its high diffusion through the Grotthuss mechanism, whereby protons hop from one molecule to the next. A main assumption concerning the extraction of the timescale of the Grotthuss mechanism from experimental results has been that, on average, there is an equal probability for the proton to hop to any of its neighboring water molecules. Herein, we present ab initio simulations that show this assumption is not generally valid. Specifically, we observe that there is an increased probability for the proton to revert back to its previous location. These correlations indicate that the interpretation of the experimental results need to be re-examined and suggest that the timescale of the Grotthuss mechanism is significantly shorter than was previously thought.

physics.chem-ph↗