Converse for Quantum Fault-tolerance

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As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this talk, we discuss a lower bound on the redundancy required for 𝜖-accurate implementation of a large class of operations that includes unitary operators. For the practically relevant case of sub-exponential depth and sub-linear gate size, our bound on redundancy is tighter than the known lower bounds. We obtain this bound by connecting fault-tolerant computation with a set of finite blocklength quantum communication problems whose accuracy requirements satisfy a joint constraint. The lower bound on redundancy obtained here leads to a strictly smaller upper bound on the noise threshold for non-degradable noise. Our bound directly extends to the case where noise at the outputs of a gate are non-i.i.d but noise across gates are i.i.d.

Avhishek Chatterjee, IIT Madras

Avhishek Chatterjee is an assistant professor in the Department of Electrical Engineering at the Indian Institute of Technology Madras. He received BE from the Jadavpur University, ME from the Indian Institute of Science Bangalore and PhD from The University of Texas at Austin, and was a postdoctoral research associate at the University of Illinois at Urbana-Champaign. His research interest lies in stochastic and information networks with applications in (classical and quantum) communication and computation networks and human-centric networks.