*By Andre, Saraiva, UNSW*

Before full quantum error correction is achieved, the range of problems that can be solved with the current small, noisy quantum computers is very limited. Among the most exciting applications is the computer simulations of molecules, with potential applications for drug design and discovery of special materials. These algorithms can use near-term quantum processors to their advantage, and the complexity of the calculation is limited by how long a calculation can be run before quantum error dominates. In quantum computers with no error correction, this is limited by the coherence time of the qubits.

Scientists from Los Alamos National Laboratories, in collaboration with scientists from Oxford University and Imperial College of London, have found a way to perform simulation beyond the coherence time limit. Their approach, called variational fast forwarding (VFF), is based on a hybrid quantum-classical code that finds the total quantum evolution by patching together many small clips that are obtained by separate runs of the quantum computer. This means that, if each small clip is simple enough to be simulated with the given number of qubits, the algorithm can simulate quantum processes that last longer than the coherence time of the qubits themselves.

The mathematical trick which allow chopping the total time evolution in small clips, called “trotterization” after the mathematician Hale Trotter, has been explored before in the context of simulations run in quantum computers. The advantage of the method developed by Cristina Cîrstoiu and others is that it does not rely on the quantum computer to render the full long-time simulations. Instead, each clip is obtained using a variational approach – starting from a guessed solution, they vary parameters in the trial solution until a cost function defined by the authors is minimised. The updating of the trial solution and estimation of the cost function is performed in the quantum computer but only for the duration of each short clip. After a few cycles the trial solution converges to the real answer.

This way, the method cheats the so-called “no fast forwarding” theorem. This theorem roughly states that the quantum resources required to simulate a quantum system grow in proportion with the total time that one is trying to simulate. For this reason, the authors call the algorithm “Variational Fast Forwarding”.

The authors even ran their algorithm in Rigetti’s Aspen-4 quantum computer, comparing it to regular trotterization schemes. The systems simulated are all quite small, such that an exact solution using classical computers is available for benchmarking the quality of the simulations.

* So, what’s next?* The authors performed some initial calculations relating the noise levels in the quantum computer to the maximum achievable fidelity of the calculations, but a clear answer regarding how many qubits would be needed and how good they must be before we start answering questions that are out of reach for modern classical computers. The authors mention this in their manuscript, which could indicate that answering this question is one of their next goals.

*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).*

October 18, 2020

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