Advantages and limitations of quantum routing

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 $\Omega (n)$ speedup if we also allow fast local interactions.

45 pages, 7 figures

References in corpus (14)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Mirror Inversion of Quantum States in Linear Registers
• Spin Chains as Perfect Quantum State Mirrors
• Efficient Distributed Quantum Computing
• Perfect state transfer on a spin-chain without state initialization
• Qubit Teleportation and Transfer across Antiferromagnetic Spin Chains
• Non-Perturbative Entangling Gates between Distant Qubits using Uniform Cold Atom Chains
• Quantum Circuit Placement
• Upper bounds on entangling rates of bipartite Hamiltonians
• Reversible simulation of bipartite product Hamiltonians

Cited by in corpus (6)

• Surface code compilation via edge-disjoint paths
• Quantum Routing with Teleportation
• Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity
• Scalable Structure For Chiral Quantum Routing
• Frobenius light cone and the shift unitary
• Quantum Routing and Entanglement Dynamics Through Bottlenecks