Advantages and limitations of quantum routing
ORAL
Abstract
The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (1) allowing arbitrary two-qubit unitaries, or (2) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constraints, and give a generalized upper bound for all simple connected n-vertex graphs. In particular, we give conditions for a superpolynomial classical-quantum routing separation, which exclude graphs with a small spectral gap and graphs of bounded degree. Finally, we provide examples of a quadratic separation between gate-based and Hamiltonian routing models with a constant number of local ancillas per qubit and of an Ω(n) speedup if we also allow fast local interactions.
*A.B. and A.V.G. acknowledge funding by the NSF PFCQC program, ARO MURI, DoE QSA, DoE ASCR Quantum Testbed Pathfinder program, NSF QLCI, DoE ASCR ARQC, DARPA SAVaNT ADVENT, AFOSR, AFOSR MURI. E.S. and A.M.C. acknowledge support by the U.S. DoE, Office of Science, Office of Advanced Scientific Computing Research, Quantum Testbed Pathfinder program and the U.S. Army Research Office. E.S. acknowledges an IBM PhD Fellowship.
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Publication: Quantum Routing with Teleportation
Presenters
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Eddie Schoute
- Los Alamos National Laboratory
- LANL