Algorithms for quantum state compression – QPEG

This project aims at developing a classical numerical tool to qualify the potential of a given quantum technology. Numerous algorithms and software packages allow to simulate a quantum computer with a classical computer. All these algorithms run into the exponential difficulty of simulating quantum computers. This difficulty is a crucial element, since its absence would mean that quantum computers could be replaced by simple classical software and would thus be completely useless. Simulations of quantum computers are thus currently limited to a range of about forty qubits. In this project, we are to develop a new type of algorithm that is able to simulate hundreds of quantum bits. To this aim, we will use methods to “compress quantum states” that exponentially decrease the computational overhead of the simulation at the cost of a precision loss of the simulations (finite compression rate). The algorithm will therefore behave very similarly to real quantum computers, which are nowadays limited by decoherence phenomena and more generally by precision loss: each quantum gate will be characterized by a finite fidelity (or, equivalently, by an error or compression rate). The computational complexity will thus be an exponential function of the error rate, but linear in the number of quantum bits or in the circuit depth.
This algorithm will be suitable to qualify quantum technologies in a variety of ways. First of all, it will give a target threshold for claiming that a quantum processor is useful. For instance, if the algorithm can simulate qubits with a 99.5% fidelity, then any real machine with a fidelity below 99.5% will lose its disruptive potential. This would show that the limitation of today’s quantum computers does not lie in the integration of ever more qubits but in their fidelity, which is currently rather poor. Then, the algorithm will allow us to study how the performance of different quantum algorithms, in particular algorithms with applications for national defense (internet network security, nuclear stability problems), decreases with a decreasing fidelity. This will lead to a clear-cut identification of the bottlenecks preventing these algorithms from being used in practice. Finally, we will be able to assess and compare the potential of various existing quantum technologies (ultracold atoms, superconducting systems, semiconducting systems, quantum optics) as a function of their difficulty to be classically simulated. We will thus obtain an objective ranking of state-of-the-art experimental platforms.
Our project is going to deliver a tool that we think is crucial for enlightened decision-making on the potential of the various quantum technologies. It will be fully integrated into the Atos quantum simulation platform. It is based on preliminary results that prove it feasibility [Zhou2020] by showing fidelities in excess of 99% at a very low numerical cost.