In 1983, Richard Feynman taught a course at Caltech titled “Potentialities and Limitations of Computing Machines”. It gave an adventurous yet careful introduction to the subject of quantum computation to students such as myself. In the current intense competition for developing quantum technology, with considerable media hype, the notion of what is really practical is being overlooked. It is well-established that the size of quantum advantage is problem-dependent, and it is essential to carefully look at the basic features of quantum theory to figure out where and how it can appear.
“Quantum advantage can be obtained only when features of density matrices that are absent in classical probability distributions are exploited.“
Quantum theory originated with the introduction of a new constant of nature, the Planck constant h. It quantifies the commutator of canonically conjugate pair of coordinates, appears as the minimal area in the structure of the phase space, is the unit of angular momentum and is part of the definition of the energy quantum. The involvement of a nonzero Planck constant is indispensable for quantum effects to appear in an algorithm and lead to quantum advantage. There are many physical phenomena in classical dynamics, where the Planck constant does not appear, and it would be silly to expect quantum advantage in explaining them.
Another fact is that quantum dynamics is highly fragile against external disturbances. The infrastructure needed to shield the quantum signal from environmental noise makes quantum technology expensive. Economics then dictates that quantum technology will be attractive only in cases where the advantage offered by it is sufficiently large to offset its cost. Hence, quantum technology will be practical only as special-purpose devices, as custom subroutines in larger applications. We also need such a hybrid quantum-classical setup to interpret the quantum results, because we live at a classical level.
A quantum state is fully specified by its density matrix. ρ, which generalises the framework of a classical prob- ability distribution. The quintessential quantum features appear in its off-diagonal elements. In the ensemble language, the Boltzmann weight e–βH describes classical probability distributions, while the quantum weights require a more general description such as the Wigner distribution or the Feynman path integral weight eiS/h. The peculiarities of quantum weights is that they can go outside the real interval [0, 1], which is often called the “sign problem”. Weights with a sign problem are mandatory for observing constructive and destructive interference. Furthermore, the expectation value of an observable O measured for a quantum state is <O> = Tr(ρO). When ρ and O commute, their simultaneous diagonalisation reduces <O> to ΣipiOi, which can be realised by a classical probability distribution. Quantum features therefore appear only in situations where ρ and O do not commute, and the largest quantum effect would appear in a setup where the norm of [ρ, O] is maximal.
Given all these considerations, the foremost on- going applications of quantum devices are in the area of high precision sensing and measurements, where small quantum modules are embedded in large classical peripherals. Time, location, movement, rotation, electric field, magnetic field, gravitational field—all physical quantities—can be measured more precisely by quantum devices than by classical ones. That has wide-ranging applications from physics to engineering and medical diagnostics. The next in line are dynamical simulations of physical quantum systems, which can provide information about their quantum correlations and time evolution, and help in the design of new molecules and materials. Going beyond that stage would need technological breakthroughs in controlling fragile quantum signals.
We in India should certainly keep track of world- wide quantum technology developments and learn from them. But given the limitations of available infrastructure and skilled workforce, we need to judiciously select areas to pursue vigorously. Standout instances based on our capabilities are: (1) Develop quantum design software platforms that can estimate quantum device performance in presence of imperfections. (2) Use these simulators to fabricate elementary quantum components (e.g. various type of qubits, single photon sources and detectors, squeezed states), with high fidelity and good control. (3) Integrate reliable quantum components into quantum devices for high precision sensing, measurement and imaging. (4) Explore quantum-inspired classical algorithms that simultaneously process magnitude and phase information of signals to yield im- proved performance. (5) Develop quantum-safe classical cryptography, and other strategies to guard against quantum adversaries, along with true random number generators based on quantum phenomena. (6) Use interferometry involving multiple sensors and long time exposures to improve the signal-to-noise ratio in communications. (7) Develop efficient simulation methods for small molecules and their reactions to closely mimic natural processes.
These are all tough challenges, but they can be tackled with O(10) qubit systems. They re- quire collaborative sustained and focused effort, while providing full freedom of exploration to scientists. They are also within our reach, as we have demonstrated while indigenously developing nuclear technology and space technology.
