FoQaCiA Foundations of quantum computational advantage

Project description

New techniques underlying the design of efficient quantum algorithms

The success of quantum computing critically depends on advances at the most fundamental level. Efficient quantum algorithms can have a significant impact on important, broad-reaching problems, solving mathematical problems faster than their classical counterparts. While several powerful quantum algorithms are known, the basic techniques they employ are few. The EU-funded FoQaCiA project aims to extend the theoretical basis for the design of quantum algorithms. To this end, researchers will study four areas of quantum phenomenology: quantum contextuality, non-classicality and quantum advantage; the complexity of classical simulations of quantum computations; arithmetic of quantum circuits; and efficiency of fault-tolerant quantum computation.

Objective

In FoQaCiA, we will expand the theoretical basis for the design of quantum algorithms. Our view is that the future success of quantum computing critically depends on advances at the most fundamental level, and that large-scale investments in quantum implementations will only pay off if they can draw on additional foundational insights and ideas. While several powerful quantum algorithms are known, the basic techniques they employ are few and far between. Largely, it still remains to be discovered how to systematically harness the quantum for computation.

We study four areas of quantum phenomenology: (i) Quantum contextuality, non-classicality, and quantum advantage, (ii) Complexity of classical simulation of quantum computation, (iii) Arithmetic of quantum circuits, and (iv) Efficiency of fault-tolerant quantum computation.

These fields are chosen for two reasons. First, their progress is of great importance for the physical realisation and the broad applicability of quantum computation. Regarding (i), one of the simplest proofs of quantum contextuality, Mermin’s star, has recently been employed to prove (Bravyi, Gosset, König) that bounded-depth quantum circuits are more powerful than their classical analogues. We seek to expand this result beyond bounded depth. In (ii), we study the quantum speedup by shaving off the redundant part – the efficiently classically simulable. In (iii), we aim to provide more efficient techniques for gate and circuit synthesis, utilising the number-theoretic underpinnings of the problem. Regarding (iv), given the celebrated threshold theorem, and the fact that the error threshold is now known to be within reach of experiment, we will tackle the remaining challenge of reducing the cost of fault tolerance.

The second reason for selecting the above work areas is to mine them for foundational quantum mechanical structures and find related quantum algorithmic uses.