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.
Lattice surgery on the surface code is a leading route to fault-tolerant quantum computation. Compiling logical circuits into lattice surgery operations is a pivotal step that determines the resource cost of a computation. Prior compilers build on idealized assumptions, and one that works in practical settings remains to be developed. Existing works are either unscalable or route one gate at a time within a layer, so the embedding depends on the order of gates and opportunities to route many gates at once are lost. In addition, they assume magic states are always available and cost-free, even though preparing one costs more than a Clifford operation.
We present FlowRouter, the first topological lattice surgery compiler that places Clifford routing and stochastic magic state cultivation inside a single 3D embedding. At compile time, FlowRouter formulates the routing of an entire circuit layer as a maximum-flow problem, embedding many gates simultaneously. At runtime, it allows magic states to be cultivated at every idling patch, works with the realistic cultivation process with multiplexing and multi-stage post-selections, and absorbs the stochasticity by introducing delay mechanisms that add as little spacetime volume as possible. With magic states assumed free, FlowRouter reduces spacetime volume by 2.3x and compiles 10.8x faster than the state-of-the-art static topological lattice surgery compiler. With the cultivation-aware setting that includes both Clifford and magic state cost, FlowRouter reduces spacetime volume by 2.3x on a distance-13 surface code when compared with the state-of-the-art runtime compiler.
Fault-tolerant quantum processors based on topological codes execute programs through lattice surgery, where operations must be mapped, routed, and supplied with magic states across a 2D grid of physical patches. Non-Clifford operations require these magic states, produced either by distillation factories or by cultivation, each trading footprint against preparation latency, and delivering a magic state to the data patches that consume it requires routing through the same shared layout as every other operation. Yet placement, routing, scheduling, and magic-state supply cannot be optimized in isolation: two operations with no circuit-level dependency can still contend for the same ports, routes, or magic-state terminals once placed, so a compiler that decouples instruction scheduling from magic-state generation, or hard-codes a single generation protocol, is forced to trade execution time against layout footprint instead of co-optimizing both across protocols.
We present Harvest, a resource-aware compilation approach for lattice-surgery that co-optimizes magic-state consumption with circuit-aware placement and congestion-aware routing under a protocol-agnostic resource model, then reclaims unused layout footprint after scheduling. Across standard benchmark suites (QAOA, QFT, QASMBench), Harvest achieves an average speedup of
4.83× (up to
17.8×) over sequential execution, improves schedule length by up to
1.35× through circuit-aware placement, and reclaims up to
72.0% of unused magic-state patches and
33.9% of unused routing patches.
Magic
∣T⟩-state preparation dominates the cost of fault-tolerant quantum computation on surface codes, yet cultivation and distillation are typically provisioned statically, leaving much of the program's error budget unused. We present Gap-Priced
∣T⟩ States (GP
∣T⟩-S), a lattice surgery scheduler and factory allocator that co-optimizes both methods under a total
T-error budget. GP
∣T⟩-S uses the complementary gap of each cultivated state as a fidelity estimate and dynamically adjusts the cultivation gap cutoff, converting budget slack into speed by giving the scheduler control over the cultivation post-selection. GP
∣T⟩-S also characterizes distillation factories by size,
∣T⟩-state production rate, and budget slack, and introduces cultivating factories that embed cultivation within routing channels, achieving fidelities otherwise requiring two-level distillation at a single-level footprint. GP
∣T⟩-S organizes these characterizations into a factory catalog, and performs distillation factory allocation over this catalog in tandem with the gap cutoff using dynamic-programming to achieve one of i) minimum spacetime volume, ii) minimum execution time, or iii) minimum space overhead, all within a user-provided
T-error budget. Across sixteen benchmarks under high and low
T-error budgets of
10−3 and
10−5 respectively, GP
∣T⟩-S consistently outperforms cultivation-only and single-factory baselines without exceeding the budget, achieving a 5.5
× geometric mean speedup in logical cycle count and a 3.4
× geometric mean reduction in space-time volume.
Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple code blocks and lattice surgery rounds, resulting in substantial qubit overhead, especially at low target error rates.
In this work, we present practical magic state distillation factories on Bivariate Bicycle (BB) codes that execute Pauli-measurement-based Clifford circuits inside a single BB code block. We formulate distillation circuit design as a joint optimization of logical qubit mapping, gate scheduling, measurement nativization, and protocol compression via qubit recycling. Based on detailed resource analysis and simulations, our BB factories have space-time volume comparable to that of leading distillation factories while delivering lower target error at a smaller qubit footprint, and are particularly compelling as second-round distillers following magic state cultivations.
Practical quantum computation requires high-fidelity instruction executions on qubits. Among them, Clifford instructions are relatively easy to perform, while non-Clifford instructions require the use of magic states. This makes magic state distillation a central procedure in fault-tolerant quantum computing. A magic state distillation factory consumes many low-fidelity input magic states and produces fewer, higher-fidelity states. To reach high fidelities, multiple distillation factories are typically chained together into a multi-level pipeline, consuming significant quantum computational resources. Our work optimizes the resource usage of distillation pipelines by introducing a novel dynamic pipeline architecture. Observing that distillation pipelines consume magic states in a burst-then-steady pattern, we develop dynamic factory scheduling and resource allocation techniques that go beyond existing static pipeline organizations. Dynamic pipelines reduce the qubit cost by 16%-70% for large-scale quantum applications and achieve average reductions of 26%-37% in qubit-time volume on generated distillation benchmarks compared to state-of-the-art static architectures. By significantly reducing the resource overhead of this building block, our work accelerates progress towards the practical realization of fault-tolerant quantum computers.
A promising approach to achieving scalable fault-tolerant quantum computation is the use of quantum error correction (QEC) codes augmented with magic states i.e. resource states produced via distillation, cultivation, or
Rz synthesis and teleported into the circuit as needed. Because magic-state production dominates the space-time volume of fault-tolerant programs, system architects must decide how many production units to allocate. Current approaches rely on deterministic analysis that either provisions for worst-case peak demand (wasting valuable qubit resources on factories that are never simultaneously utilized) or assumes average demand, which increases execution time. In this work, we build a simulation framework that couples circuit scheduling with different stochastic magic state production models, and use it to quantify the impact of non-determinism on circuit execution. We show that non-determinism has a dual effect that deterministic models cannot capture: it inflates total execution time (the price), while deflating peak per-cycle resource demand (the payoff). For distillation-based architectures, this demand smoothing shifts the space-time-optimal provisioning point: fewer factories are needed to minimize space-time volume than deterministic analysis predicts. Across benchmarks, stochastic-aware provisioning reduces space-time volume by up to 27% compared to the deterministic optimum for distillation, while requiring up to 30% fewer factories. We characterize these effects across each preparation mechanism, map the resulting design-space tradeoffs, and demonstrate that static resource estimation systematically mis-characterizes the cost of fault-tolerant execution. Our results establish that stochastic-aware analysis is necessary for right-sizing the factory allocations and should replace deterministic heuristics as the standard methodology for FTQC resource planning.