Dynamic qubit allocation and routing for constrained topologies by CNOT circuit re-synthesis

Abstract

Many quantum computers have constraints regarding which two-qubit operations are locally allowed. To run a quantum circuit under those constraints, qubits need to be allocated to different quantum registers, and multi-qubit gates need to be routed accordingly. Recent developments have shown that Steiner-tree based compiling strategies provide a competitive tool to route CNOT gates. However, these algorithms require the qubit allocation to be decided before routing. Moreover, the allocation is fixed throughout the computation, i.e. the logical qubit will not move to a different qubit register. This is inefficient with respect to the CNOT count of the resulting circuit.In this paper, we propose the algorithm PermRowCol for routing CNOTs in a quantum circuit. It dynamically reallocates logical qubits during the computation, and thus results in fewer output CNOTs than the algorithms Steiner-Gauss [11] and RowCol [23].Here we focus on circuits over CNOT only, but this method could be generalized to a routing and allocation strategy on Clifford+T circuits by slicing the quantum circuit into subcircuits composed of CNOTs and single-qubit gates. Additionally, PermRowCol can be used in place of Steiner-Gauss in the synthesis of phase polynomials as well as the extraction of quantum circuits from ZX-diagrams.

Global Synthesis of CNOT Circuits with Holes

“…Finally, through a series of computational experiments, we demonstrated that for large circuits our quantum comb generalisation of RowCol outperforms the slicing procedure on a range of architectures and CNOT/non-CNOT proportions. Work has recently been done on improving the performance of RowCol by allowing the qubits to be permuted by the synthesis algorithm [10], investigating whether the performance of CombSynth could be improved in a similar way would be an interesting research direction. Currently, comb synthesis is designed to work with a subroutine that only works with one qubit (and hence one row/column) at a time, but it would be worth adapting it to work with synthesis algorithms which operate one more than one row or column at once, like the Patel-Markov-Hayes algorithm.…”

“…Synthesis algorithms provide a means of reducing the size of CNOT circuits [15], or allow the resynthesis of circuits under topological constraints [11,14,10]. The ability to perform both of these tasks efficiently is vital for NISQ computing, as it provides a way to best utilise the machines we have available whilst minimising the consequences of their limitations.…”

“…While this is an important aspect of RowCol and related algorithms, we can treat this process essentially as a "black box" for the purposes of our algorithm. We refer readers to the paper that introduced RowCol [18] or other Steiner-tree based algorithms [11,14,10] for details.…”

“…By restricting which row operations are possible when reducing a parity matrix to the identity, circuits that obey specific connectivity constraints can be synthesised from ones that don't. A variety of techniques for introducing these constraints based on Steiner trees [14,11,18,10] and integer programming [3] have been introduced in recent years. These synthesis methods provide a way to optimise circuits that mitigates some of the current limitations of NISQ devices.…”