Bengaluru Mar 12, 2020, (Research Matters):

Nature is an enigma; an ensemble of complex structures and functions come together to form a variety of mesmerising artefacts, including life. Richard Feynman, the well-known American Nobel Laureate and physicist, famously said—"Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy". In 1982, he proposed that the workings of nature can be simulated with computers. Only that, we would need to do away with the classical binary computers and make way for quantum computers. Who knew it would take about four decades until we got closer to a real quantum computer?

In these four decades, scientists around the world have made immense advances in the field of quantum theory and computing, which have now yielded the progress we see with quantum computing. Unlike classical computers, which store information through zeroes and ones, quantum computers use qubits for storing data. These qubits use physical quantities, like the spin of an electron or that of a photon, to represent information as a quantum superposition of possible states of the particle. Akin to how logic gates, built from silicon, make up the hardware of classical computers, quantum gates are used in a quantum computer.

In a new study, researchers from the Indian Institute of Science, Bengaluru, and the Indian Institute of Technology, Gandhinagar, have theoretically demonstrated the design of an efficient quantum circuit using a minimal number of quantum gates. The study, published in the journal *Physical Review Letters*, brings together principles from quantum mechanics and string theory to realise this design. The study was funded by the Department of Science and Technology (DST).

“The quantum mechanics of nature, used as a starting point, scales linearly with time and spatial volume, governed by the symmetry of spacetime in nature,” says Prof Aninda Sinha from IISc, who led the study. “The best quantum circuit can be expected to follow this linear scaling. In technical terms, this is called circuit complexity. The best quantum circuit should use as few a number of quantum gates as possible since each gate always operates within some error tolerance.”

However, these errors soon add up and a generic circuit has a non-linear scaling with time and space. The error factor limits the utopian view of 'simulating physics with computers'. A better design of quantum circuits, which can handle these errors, is seen as a solution to this problem.

In the current study, the researchers have proposed an algorithm to design such quantum circuits with the minimum number of logic gates. The researchers have modified an earlier approach, which used the principles of geometry and mathematical techniques, to find an optimum quantum circuit by using the shortest path between two points.

"The algorithm that Pratik, Arpan and I developed, bringing together several existing results in the quantum literature, retains the inherent physical symmetry but does so by using fewer resources in terms of a linear scaling with spatial volume”, explains Prof Sinha.

This scaling is important from the perspective of black hole physics as well, as has been pointed out by Leonard Susskind, an American physicist from Stanford University, and his collaborators in recent times.

Although the study is theoretical, the design of better quantum circuits has many evolving practical applications in the realm of physics. "An exact simulation of nature can answer many questions we see in physics today. Using our approach, one can build a custom algorithm to calculate, say, the behaviour of the specific heat of water, which is the amount of heat required to raise the temperature of a litre of water by a degree Celsius, at the so-called critical point", says Prof. Sinha. Such optimum algorithms can then be used to build better calculational schemes in quantum physics, which can represent other, complex phenomenon.

As a next step, Prof Sinha and his group are trying to explore if we could use principles from string theory and quantum gravity to use classical computers to solve such complex problems.

“Prof John Preskill from Caltech, in a very inspirational lecture, said that Ken Wilson, who was awarded the Nobel prize in Physics in 1982, invented the renormalization group by thinking about how to do quantum field theory on the classical computer. Maybe, we will learn something about quantum gravity by trying to understand quantum field theory on a quantum computer. Our study is in sync with such an expectation,” he signs off.

*This arricle has been run past the researchers, whose work is covered, to ensure accuracy.*