“Imaginary time is a genuine scientific concept. One can picture it in the following way. One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there’s another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time.”
– Professor Stephen Hawking
Imaginary time is a powerful concept, widely used in physics. Moving forwards in imaginary time is similar to lowering the temperature. This lets us find the lowest energy states of quantum systems, such as molecules and superconductors. This is an important problem in chemistry and physics. Solving it may lead to the discovery of new medicines and materials. Unfortunately, classical computers cannot study large quantum systems. This is because the memory and time requirements scale exponentially with the system size.
In contrast, it is natural and efficient to simulate quantum systems on quantum computers. So, can we simply use quantum computers to simulate imaginary time evolution? At first glance, the answer is, ‘no’. In quantum mechanics, real time evolution can be decomposed into a sequence of operations or ‘gates’. These gates can then be implemented on a quantum computer. The same is not true for imaginary time evolution.
In our new paper, we introduce an algorithm which can simulate imaginary time evolution on a quantum computer. Our ‘hybrid’ algorithm combines quantum and classical resources, and can make use of short quantum circuits. This makes it suitable for emerging quantum hardware. We use our algorithm to numerically find the lowest energy of small molecules. Our method successfully finds the lowest energy states, and outperforms the established method in quantum computational chemistry; the Variational Quantum Eigensolver.
Our algorithm can also be applied to general optimisation problems, and quantum machine learning. As a result, it may enable many exciting applications for emerging quantum technology.
The full paper can be found here.
