The hybrid algorithm uses a classical and a quantum computer to calculate the ground-state energy. This will help researchers develop new materials for various applications, including sustainability goals. Credit: Nicoletta Barolini
Quantum computers are getting bigger, but there are still few practical ways to harness their extra processing power. To overcome this hurdle, researchers are designing algorithms that should facilitate the transition from classical to quantum computers. In a new study in Nature, Researchers unveil an algorithm that reduces the statistical errors, or noise, generated by quantum bits, or qubits, in crunchy chemical equations.
The algorithm, developed by Columbia chemistry professor David Reichman, and postdoc Joonho Lee with Google Quantum AI researchers, uses up to 16 qubits on Sycamore, Google’s 53-qubit computer, to calculate the ground-state energy that lowest energy state of a molecule. “These are the largest quantum chemical calculations ever performed on a real quantum device,” Reichman said.
The ability to accurately calculate the ground-state energy will enable chemists to design new materials, said Lee, who is also a visiting researcher at Google Quantum AI. The algorithm could be used to design materials to accelerate nitrogen fixation for agriculture and hydrolysis to generate clean energy, among other sustainability goals, he said.
The algorithm uses a quantum Monte Carlo, a system of methods for calculating probabilities when a large number of random, unknown variables are involved, as in a roulette game. Here, the researchers used their algorithm to determine the ground-state energy of three molecules: heliocide (H4), using eight qubits for the calculation; molecular nitrogen (N2) with 12 qubits; and Solid Diamond with 16 qubits.
Ground-state energy is affected by variables such as the number of electrons in a molecule, the direction in which they spin, and the orbits they take when orbiting a nucleus. This electronic energy is encoded in the Schrödinger equation. Solving the equation on a classical computer becomes exponentially more difficult as the molecules get larger, although methods of estimating the solution have made the process easier. How quantum computers could circumvent the exponential scaling problem has been an open question in this area.
In principle, quantum computers should be able to perform exponentially larger and more complex calculations, such as those required to solve the Schrödinger equation, because the qubits that make them up use quantum states. Unlike binary digits, or bits, which are made up of ones and zeros, qubits can exist in two states at the same time. However, qubits are vulnerable and error-prone: the more qubits used, the less accurate the final answer will be. Lee’s algorithm uses the combined power of classical and quantum computers to solve chemical equations more efficiently while minimizing quantum computer errors.
“It’s the best of both worlds,” Lee said. “We used tools that we already had and tools that are considered state-of-the-art in quantum information science to refine quantum computational chemistry.”
A classical computer can handle most of Lee’s quantum Monte Carlo simulations. Sycamore jumps in for the last, most computationally complex, step: calculating the overlap between a trial wave function — an estimate of the mathematical description of the ground-state energy that can be implemented by the quantum computer — and a sample wave function, which is part of the Monte Carlo statistical process. This overlap provides a set of constraints, called boundary conditions, on the Monte Carlo samples that ensure the statistical efficiency of the computation (see Lee’s webinar for more details on the math).
The previous record for solving the ground-state energy used 12 qubits and a method called the Variational Quantum Eigensolver, or VQE. But VQE ignored the effects of interacting electrons, an important variable in the calculation of the ground-state energy that Lee’s quantum Monte Carlo algorithm now includes. Adding virtual correlation techniques from classical computers could help chemists tackle even larger molecules, Lee said.
The hybrid classical quantum calculations in this new work turned out to be as accurate as some of the best classical methods. This indicates that problems could be solved more accurately and/or faster with a quantum computer than without – an important milestone for[{” attribute=””>quantum computing. Lee and his colleagues will continue to tweak their algorithm to make it more efficient, while engineers work to build better quantum hardware.
“The feasibility of solving larger and more challenging chemical problems will only increase with time,” Lee said. “This gives us hope that quantum technologies that are being developed will be practically useful.”
Reference: “Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer” 16 March 2022, Nature.
DOI: 10.1038/s41586-021-04351-z
