*By Andre Saraiva, UNSW*

Designing and analysing molecules and materials was the first application envisioned for quantum computers back in 1982 by legendary Nobel laureate Richard Feynman. The argument is relatively simple: the interaction between electrons is hard to describe in a classical computer because its bits are constrained by classical physics; meanwhile, qubits have the same exponentially growing complexity as any other quantum particle. Converting this abstract argument into practice, however, is nothing short of a Herculean task. Google just gave that a try in a recent preprint.

“The details of the proof are left as an exercise for the reader” is the phrase that is often used jokingly when difficult scientific demonstrations are dodged by the author. The first large attempt to connect the dots left by Feynman was the Variational Quantum Eigensolver (VQE, learn more here and here). Same as all other NISQ applications, this is a hybrid quantum-classical approach, meaning one needs a classical and a quantum processor to work simultaneously, solving separate parts of the problem.

The new approach developed by the team led by Dr. Joonho Lee from Columbia University and Google is also a hybrid algorithm, but the division of labour between classical and quantum is done differently. And this is important because it provides another potential pathway for quantum advantage. No one knows which path is going to be the shortest.

In VQE, the part that is left for the quantum processor is to represent the quantum states of molecules in the quantum computer, which in a sense is the most intuitive use for qubits. It is like a game of “hot and cold”, where the classical computer proposes new trials to compare with the true molecule quantum state, and the quantum processor is responsible for letting the classical computer know if they are getting close to the answer.

The problem is that a classical computer can only propose answers that it can “wrap its mind around”. For example, a quantum computer can efficiently model electrons if it describes the movement of only one of the electrons while assuming that the others are frozen in time. This approach (mean field theory in chemist jargon) led to huge successes, such as Hartree-Fock and Density Functional Theory, but only specific materials can be described in these simplified terms. A lot of the more interesting applications need to take interactions more completely, such as superconductivity, protein folding, and magnetism.

To free their algorithm from preconceptions about the electron interactions, the Google team used a method that leverages the power of randomness. This approach, called Quantum Monte Carlo after the extravagant destination for gamblers, tries to create a physically inspired initial trial and improves its guess iteratively. Instead of tweaking parameters of that trial solution like VQE, it simulates how the electrons starting at the tentative state would settle down to the ground state (which describes the molecule as it would occur in the lab). This method is considered the gold standard for describing electrons that have their behaviour dominated by interactions with each other (instead of with the atomic nuclei). Google’s added twist is to get assistance from a quantum processor when judging what a “physically inspired trial function” is by calculating the distance between the two quantum states.

This calculation is where the potential for a speed up is proposed by the team. They test their algorithm using in up to 16 qubits in Google’s Sycamore quantum processor (same one used for the Quantum Supremacy experiment). Their results break the record for chemistry simulations in a quantum processor by more than doubling the complexity of the molecules studied before but are still within the realm that can be performed by a classical computer.

**So, what’s next?**

The next step would be to clearly define how many qubits are needed to get true quantum advantage. This will guide quantum computer users on which of the available quantum processors may be able to give them the competitive advantage in their chemistry applications. The authors try to discuss this issue in their manuscript, but a clear requirement in qubit quantity and quality is not drawn.

*Dr. Saraiva has worked for over a decade providing theoretical solutions to problems in silicon spin quantum computation, as well as other quantum technologies. He works on MOS Silicon Quantum Dot research and commercially-oriented projects at the University of New South Wales (UNSW)*.

July 12, 2021

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