Design of a Universal Logic Block for Fault-Tolerant Realization of any Logic Operation in Trapped-Ion Quantum Circuits

TL;DR

This paper introduces a physical mapping tool for quantum circuits that optimally designs a Universal Logic Block (ULB) to perform any fault-tolerant quantum operation with minimal latency, considering complex scheduling, placement, and routing dependencies.

Contribution

It proposes a comprehensive quantum physical mapper that integrates scheduling, placement, and routing, and introduces a method to determine the optimal ULB size based on circuit analysis.

Findings

The mapper reduces quantum circuit latency through integrated scheduling and placement.

Optimal ULB size depends on operation frequency and circuit critical paths.

The approach improves fault-tolerant quantum operation efficiency.

Abstract

This paper presents a physical mapping tool for quantum circuits, which generates the optimal Universal Logic Block (ULB) that can perform any logical fault-tolerant (FT) quantum operations with the minimum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations, which in turn determines routing latencies. The proposed flow for the quantum physical mapper captures these dependencies by applying (i) a loose scheduling step, which transforms an initial quantum data flow graph into one that explicitly captures the no-cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force-directed scheduling approach to minimize the resource contention and quantum circuit latency, (ii) a placement step, which uses timing-driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force-directed scheduler to correct scheduling levels of quantum operations as needed, and (iii) a routing step that finds dynamic values of routing latencies for the qubits. In addition to the quantum physical mapper, an approach is presented to determine the single best ULB size for a target quantum circuit by examining the latency of different FT quantum operations mapped onto different ULB sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies.