On Distributed Quantum Computing with Distributed Fan-Out Operations

TL;DR

The paper addresses how to perform distributed quantum computations efficiently by leveraging distributed fan-out gates constructed from GHZ states, comparing them to Bell-pair–based approaches. It formalizes distributed fan-out, analyzes fundamental primitives like dCNOT, and studies concrete cases such as distributed QFT and distributed QAOA to illustrate potential depth and resource benefits. A general circuit-decomposition framework is proposed, combining layers of local gates with distributed fan-out to realize arbitrary $n$-qubit unitaries, with depth scaling that can be favorable when GHZ-state preparation is efficient. The findings suggest GHZ-based distributed fan-out could serve as a scalable primitive for distributed quantum computation, motivating development of efficient GHZ-state generation and caching for practical large-scale deployments.

Abstract

We compare different circuits implementing distributed versions of quantum computations, using entangled pairs only, and using distributed fan-out operations (using GHZ states). We highlight the advantages of using distributed fan-out operations in terms of reductions in circuit depth and (possibly) entanglement resources. We note that distributed fan-out operations (or notably, distributed GHZ states) could be a ``primitive'' building block for distributed quantum operations in the same way as entangled pairs are, if distributed GHZ states could be realized efficiently.

Figures (8)

• Figure 1: Distributed control-$U$ (i.e., dCNOT is when U=$X$ ($\oplus$) as shown) between nodes $QC$ and $QC'$ (the computation qubits are $c$, the control qubit, and $t$, the target qubit), and the wavy line illustrates a Bell pair involving the communication qubits from the two nodes both initially $\ket{0}$. The right hand side shows the notation we will use for a distributed controlled-$U$ operation.
• Figure 2: Distributed fan-out operation with single control qubit (on $A'$) for multiple target qubits (one on $A$, one on $B$ and one on $C$) - all target qubits on different nodes from the control qubit. The right hand side shows the notation we will use for distributed fan-out throughout the paper.
• Figure 3: Quantum Fourier Transform with 4 qubits using controlled rotations.
• Figure 4: Quantum Fourier Transform with 4 qubits using controlled phase operations.
• Figure 5: Distributed QFT over 4 qubits on 4 nodes (one qubit per node), ignoring bit reversal operations.