Locality-aware Pauli-based computation for local magic state preparation

TL;DR

The paper addresses the bottleneck of magic state distillation and transfer in fault-tolerant quantum computing with surface codes. It proposes locality-aware Pauli-based computation (LAPBC), which distills magic states locally within the computation area and preserves gate locality to enable parallel $T$ gates, using a factory-less layout. Through a custom scheduler and runtime simulator, the authors demonstrate substantial reductions in execution time for random circuit sampling and 2D Ising Hamiltonian simulation, with minimal additional spatial overhead and favorable scaling as qubit count grows. The work also provides design insights on the interplay between distillation cost, acceptance probability, and overall runtime, suggesting LAPBC as a practical standard for highly parallel FTQC workloads when high-performance distillation is available.

Abstract

Magic state distillation, a process for preparing magic states needed to implement non-Clifford gates fault-tolerantly, plays a crucial role in fault-tolerant quantum computation. Historically, it has been a major bottleneck, leading to the pursuit of computation schemes optimized for slow magic state preparation. Recent advances in magic state distillation have significantly reduced the overhead, enabling the simultaneous preparation of many magic states. However, the magic state transfer cost prevents the conventional layout from efficiently utilizing them, highlighting the need for an alternative scheme optimized for highly parallel quantum algorithms. In this study, we propose locality-aware Pauli-based computation, a novel compilation scheme that distills magic states in the computation area, aiming to reduce execution time by minimizing magic state transfer costs and improving locality. Numerical experiments on random circuit sampling and 2D Ising Hamiltonian simulation demonstrate that our scheme significantly reduces execution time, while incurring little or no additional spatial overhead, compared to sequential Pauli-based computation, a conventional computation scheme, and scales favorably with increasing qubit count.

Figures (27)

• Figure 1: Performing a T gate in the conventional layout. (i) Magic state distillation. (ii) Magic state transfer from the distillation area (blue) to the computation area (green). (iii) Gate teleportation.
• Figure 2: A Pauli gate $P$ followed by a Clifford gate $C$ is equivalent to $C$ followed by another Pauli gate.
• Figure 3: A surface code patch. Solid and dashed lines represent logical $Z$ and $X$ operators, respectively. These lines may be omitted when not relevant to computation.
• Figure 4: An example of routing. Lattice surgery can be performed directly on $q_1$ and $q_2$ because they are adjacent and their logical $Z$ operators are aligned. The green region represents a path required to perform $M_{Z_3Z_4}$. The purple region depicts a path required to perform $M_{Z_5Z_6}$ without conflicting with the green path.
• Figure 5: An example of scheduling. Because $CZ_{14}$ and $CZ_{23}$ cannot be executed in parallel, the compiler determines their execution order.