Algorithms for quantum computing, communication networks, and metrology: a near-term perspective

Recent years have seen rapid progress in the development of quantum technologies, ranging from quantum computing to quantum repeaters to quantum sensors. At the same time, today's qubits are imperfect, leading to losses and errors that limit the use of these technologies. In the absence of full-scale, fault-tolerant quantum error correction, which can in principle overcome the limitations arising from noise and loss and allow us to achieve the ideal performance for our tasks of interest, to what extent can we circumvent these limitations, and thereby make the best possible use of our currently noisy, imperfect quantum devices? In other words, what is the best possible performance that can be achieved using today's noisy, imperfect quantum devices? In this talk, I present some of the progress that has been made on answering this question. I present recent work on devising algorithms and protocols (along with their performance analysis) for quantum computing, communication networks, and metrology, in the regime of limited and noisy qubits. Such a near-term analysis often necessitates diving deeper into the physics, and the use of new mathematical tools. I will in particular highlight how mathematical tools such as Markov chains and classical and quantum hypothesis testing have elucidated our understanding of algorithms for quantum error mitigation, quantum repeaters, and quantum metrology. While such analyses are at the outset tailored to the near-term regime of few and noisy qubits, it is expected that such a perspective will nevertheless better guide the development of quantum devices on the path towards quantum fault-tolerance.