Cover of Science Advances Successful measurement of quantum resources required for chemical simulations!

In a recent report published on the cover of Science Advances, Chan Hans Hon Sang and a team of researchers in materials, chemistry and quantum photonics at the University of Oxford generated exact simulations of quantum computers with up to 36 quantum bits to explore resource-saving algorithms and to model two- and three-dimensional atoms with single, paired particles.

Chemical modeling is a natural property of quantum computers, although existing methods are impractical for developing near-perfect quantum bits. In this work, quantum chemists explore a range of tasks from ground state preparation and energy estimation to scattering and ionization dynamics of electrons to evaluate various approaches in split-operation simulations to model the quantum chemistry of several molecules of interest.

Quantum chemists envision quantum computers to be transformative tools for chemical prediction and exploration. While conventional computers are useful for exploring quantum molecular dynamics to predict reaction outcomes and experimental observations, the hardware cost and time length grow exponentially with the number of particles simulated. In this work, Hansheng Chen's group at the University of Oxford accelerated the fundamental features of chemical kinetics simulations on an early version of a quantum computer based on the real-space grid approach.

Hansheng Chen

These early versions of quantum computers had a limited number of error-correcting quantum bits. The team encoded features such as particle symmetry during the study, providing optimal resource scaling for complex and interesting molecules.

However, most quantum computers are noise-burdened and costly. Therefore, the researchers took a different approach by deploying classical computing resources to simulate small but noise-free quantum computers, thereby simulating quantum molecular dynamics in them and directly examining cost and performance metrics. While they did not reintroduce pre-existing classical lattice techniques for lattice-based simulations, they performed simulations of real, noise-free quantum machines in lieu of chemically relevant quantum dynamics.

The PITE technique was used to prepare the ground state of 2D hydrogen. The method was simulated on a quantum computer with 1+2×10 quantum bits.

Ultimately, the researchers found that the lattice-based approach performed exceptionally well and will be applied in the era of fault-tolerant quantum computing.

This time, the quantum computer simulations were limited to a modest size of 36 quantum bits due to cost constraints.

Specifically, the research team used the experimental setup to explore several information schemes for two- and three-dimensional simulations of single- and two-electron systems. They chose two key areas of interest in chemistry and estimated the necessary quantum resources to simulate the dynamics of strong external fields, simulating particle scattering dynamics.

In the first experiment, the team suddenly applied an external field, which resulted in dipole oscillations and the ionization of a single bound electron. They envision that efforts in this direction will include topics such as photochemistry and laser excitation. Physicists and quantum chemists consider coherent quantum regulation of small molecules to be one of the "holy grails" of chemical science: for example, this process could allow scientists to study ammonia in the context of hydrogen atom removal to explore its potential in modern agriculture.

In the second case, the team studied electron-molecule scattering in relation to spectroscopy, astrochemistry and manufacturing processes, because the processes of collision and scattering are highly dynamic and difficult to model classically.

Performance of the ASO (augmented split-operator) technique. The simulated quantum computer has 13=1+6×6 quantum bits.

Scientists use split-operator quantum Fourier transform (SO-QFT) Hamiltonian simulation methods for wave packet manipulation and present a series of results that are applicable to lattice-based methods for 2-3D systems using single and paired particles.

The numerical results are implemented through open source tools (e.g. QuEST, QuEST-link and pyQuEST) to simulate quantum processors. They explored the number of quantum bits, estimated the execution time to achieve a given accuracy of the simulation, and investigated the scheme of a sampling-based approach to estimate the energy of the system, which proved to be very sensitive to imperfections. They estimated the accompanying cost of quantum resources and indicated a suitable hardware layout for a quantum computer.

Simulation of helium atoms in real space.

The team performed an alternative approach to preparing real-space ground states based on probabilistic imaginary time evolution (PITE) on a quantum computer and simulated the ground state of two-dimensional hydrogen, while detailing the drawbacks of the method. They performed quantum dynamics simulations for two cases that rely on two scenarios: 1) ionization by strong external fields and 2) dependence on electron-electron scattering.

The team next introduced the enhanced splitting operator (ASO) to optimize the fidelity of the simulations by proposing additional elements to the basic splitting operator quantum Fourier transform loop. Using this device, the team simulated the three-dimensional dynamics of a helium atom and used Schrödinger's equation to approximate the true electronic eigenstate of the helium atom.

The quantum chemists studied the resource requirements for performing quantum modeling that is beyond the reach of classical algorithms and adapted a quantum architecture suitable for such expressions. They estimated the number of quantum bits needed to build quantum schemes of interest for hexafluoroethane (C2F6) and ammonia (NH3) molecules: lattice-based simulations of C2F6 require about 2250 computational quantum bits, while ammonia molecules require less than 450 quantum bits.

Three techniques for fault-tolerant quantum circuits for early real-space chemistry explored in this work.

The time cost of the simulations is also dependent on the hardware implementation. Thus, the most easily understood code requires hundreds of physical quantum bits per logical quantum bit relative to the deep algorithm and error rate, a performance comparable to the best quantum computing prototypes available today.

Ultimately, in this way, Hansheng Chen's team explored split-arithmetic quantum Fourier transform (SO-QFT) methods to simulate exact quantum bits and tested the techniques behind real-space quantum chemical simulations. They explored several known quantum techniques and introduced several others to express key aspects of quantum simulations. Ultimately, the scientists characterized the resources underlying the implementation of digital experiments on an early fault-tolerant quantum computer.

This result can accelerate the learning/prediction cycle of chemical discovery by augmenting physical experiments with machine learning. These results can be applied to diverse areas of quantum technology, including building special relativity for high-energy particle models and playing a role in financial engineering.

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