Scheduling Lattice Surgery with Magic State Cultivation

TL;DR

Fault-tolerant quantum computing with surface codes hinges on efficient non-Clifford gate implementation via magic states, but static bus routing and distillation-heavy pipelines impose large resource overheads. Pure Magic scheduling dynamically repurposes magic-state cultivation qubits for routing, using Steiner-forest packing to build Pauli-product executions and interrupting cultivation as needed; this eliminates dedicated bus infrastructure while maintaining or increasing parallelism. Across 17 Benchpress benchmarks and random circuits, Pure Magic achieves 19%–223% improvements in scheduling volume and reduces average cultivation time by $2.4\times$–$6.7\times$, with larger gains for highly parallel circuits. The approach represents a paradigm shift from static resource allocation to demand-driven scheduling, offering substantial reductions in qubit overhead and latency and potential generalization to other QECCs reliant on magic-state injection, thereby accelerating practical fault-tolerant quantum computation.

Abstract

Fault-tolerant quantum computation using surface codes relies on efficient scheduling of non-Clifford operations, realized via the injection of magic states produced through a probabilistic process that dominates spacetime costs. Existing scheduling approaches use dedicated bus qubits for routing and separate peripheral ancilla qubit factories for magic state preparation, leading to inefficient resource utilization. With the advent of magic state cultivation, preparation qubits can be placed anywhere within the surface code architecture. We introduce Pure Magic scheduling, which dynamically re-purposes magic state cultivation qubits for routing operations, eliminating dedicated bus infrastructure. By interrupting cultivation when qubits are needed for routing, Pure Magic naturally favors shorter cultivation times while ensuring no ancilla qubit remains idle. Our evaluation across 17 benchmark circuits improves scheduling efficiency by 19% to 223% compared to traditional bus routing and decreases average magic state preparation time by 2.6x to 9.7x. Benefits scale with circuit parallelism, making Pure Magic particularly valuable for highly parallel quantum algorithms. The Pure Magic architecture represents a paradigm shift from static to dynamic, demand-driven scheduling in fault-tolerant quantum architectures.

Figures (13)

• Figure 1: Representations of surface code logical qubits. (a) A distance 5 surface code storing one logical qubit. Black circles are physical data qubits, white circles are physical ancilla qubits. Blue (orange) squares represent $Z$ ($X$) stabilizers. (b) Single logical qubit patch with rough ($X$, dashed) and smooth ($Z$, solid) edges. This patch represents the same qubit as (a). (c) Double-qubit patch encoding two logical qubits with accessible $X$/$Z$ operators on both sides. Top (bottom) edges expose joint $ZZ$ ($XX$) operators.
• Figure 2: Smooth ($Z$ type) merge operations. (a) Adjacent patches merge by adding joint stabilizers, then split by measuring bridge qubits. (b) Diagrammatic representation combining $Z$ edges.
• Figure 3: T state injection via lattice surgery. Magic T states (orange) enable $\pi/8$ rotations of type $X$, $Y$, or $Z$ through different merge operations. These primitives are used to implement Pauli products.
• Figure 4: A sequence of Pauli products taken from a benchmark circuit. Each product is represented by a different color rectangle, and the operators that are assigned to qubits are indicated by the $X$, $Y$ and $Z$ letters. Products shown in the same layer (vertical column) are eligible for co-scheduling.
• Figure 5: A bus routing architecture with eight data qubits (blue), 27 bus qubits (white, red, green, and purple) and 24 magic qubits (orange). Also shown are three products scheduled on the layout: the double $XX$ in the green product can be connected to the bottom of the $0/1$ double qubit. Other single $X$ and $Z$ values must connect to the sides of their target data qubits. The $Y$ operator in the red product must connect to both a $X$ and $Z$ on the side of the $4/5$ data qubit.