Abstract
There are many possible architectures of qubit connectivity that designers of future quantum computers will need to choose between. However, the process of evaluating a particular connectivity graph’s performance as a quantum architecture can be difficult. In this paper, we show that a quantity known as the isoperimetric number establishes a lower bound on the time required to create highly entangled states. This metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We use this metric to evaluate the hierarchical architecture proposed by A. Bapat et al. [Phys. Rev. A 98, 062328 (2018)] and find it to be a promising alternative to the conventional grid architecture. We also show that the lower bound that this metric places on the creation time of highly entangled states can be saturated with a constructive protocol, up to a factor logarithmic in the number of qubits.
Highlights
As the development of quantum computers progresses from the construction of qubits to the construction of intermediate-scale devices, quantum information scientists have increasingly begun to explore various architectures for scalable quantum computing [1,2,3,4]
When several physical models are represented by a graph G = (V, E ), with a set of vertices V corresponding to qubits, and a set of weighted edges E corresponding to two-qubit operations, a useful metric is given by what we dub the “rainbow time,”
We show that the rainbow time is a lower bound on the time required to create a highly entangled state on the graph (i.e., states of N qubits with O(N ) bipartite entanglement)
Summary
As the development of quantum computers progresses from the construction of qubits to the construction of intermediate-scale devices, quantum information scientists have increasingly begun to explore various architectures for scalable quantum computing [1,2,3,4]. We show that the rainbow time is a lower bound on the time required to create a highly entangled state on the graph (i.e., states of N qubits with O(N ) bipartite entanglement) It is the reciprocal of a well-studied graph quantity known as the isoperimetric number [12]. We show that this lower bound is nearly tight—a procedure that distributes Bell pairs using maximum-flow algorithms nearly saturates this bound to produce O(N ) entanglement across any bipartition, up to O(log N ) overhead This suggests that beyond providing a bound, the rainbow time would be a useful witness to the speed at which entanglement can be generated
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