Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections

TL;DR

The paper addresses the high cost of fault-tolerant quantum Computation under surface codes by introducing an active-volume architecture that separates useful (active) operations from idle qubits and leverages non-local photonic connections. It formalizes active volume as the sum of block costs for logical operations and shows the overall spacetime cost scales as $2 \cdot \text{ActiveVolume}$, enabling orders-of-magnitude improvements for large, multi-qubit computations. By developing a ZX-calculus–based description of logical blocks, it provides general compilation strategies for Pauli product rotations, adders, QROM reads, and magic-state distillation, with explicit active-volume costs (e.g., Toffoli $= 12$ blocks, $Z$-type weight-$w$ measurements $= \lceil \tfrac{3}{2} w \rceil$). The architecture is demonstrated in photonic fusion-based interleaving modules, where non-local connections are natural, and includes detailed resource estimates for a 2048-bit factoring task, showing dramatic runtime gains over baseline architectures. These results offer a pathway to practical, scalable, fault-tolerant quantum computing with non-local connectivity.

Abstract

In existing general-purpose architectures for surface-code-based fault-tolerant quantum computers, the cost of a quantum computation is determined by the circuit volume, i.e., the number of qubits multiplied by the number of non-Clifford gates. We introduce an architecture using non-2D-local connections in which the cost does not scale with the number of qubits, and instead only with the number of logical operations. Each logical operation has an associated active volume, such that the cost of a quantum computation can be quantified as a sum of active volumes of all operations. For quantum computations with thousands of logical qubits, the active volume can be orders of magnitude lower than the circuit volume. Importantly, the architecture does not require all-to-all connectivity between N logical qubits. Instead, each logical qubit is connected to O(log N) other sites. As an example, we show that, using the same number of logical qubits, a 2048-bit factoring algorithm can be executed 44 times faster than on a general-purpose architecture without non-local connections. With photonic qubits, long-range connections are available and we show how photonic components can be used to construct a fusion-based active-volume quantum computer.

Figures (27)

• Figure 1: Resource estimates for the 2048-bit factoring algorithm described in Ref. Gidney2021 in a baseline architectures Litinski2019Fowler2018Chamberland2022Chamberland2022aBombin2021 and in the active-volume architecture described in this paper. More details are found in Appendix \ref{['sec:resourceestimate']}.
• Figure 2: Active volume fact sheet. The numbers in (d) assume active-volume costs of CCZ states and $T$ states of around 35 and 25, respectively. In (e), the considered algorithms are layers of disjoint 20-qubit adders, and $n$-qubit QROMs loading $n$-bit numbers. In (g), a per-block error rate of $p(d) = 10^{-d/2}$ and a reaction time of $\tau_r = 5~\mu\mathrm{s} + \lambda \cdot \mathrm{ns}$ is assumed.
• Figure 3: Description of the active-volume architecture in terms of (a) surface-code patches and (b) logical blocks.
• Figure 4: Example demonstrating the structure of a quantum computation executed on an active-volume quantum computer with 12 qubit modules. (a) The quantum computation corresponds to a sequence of 5 operations on 6 qubits, where each operation has a representation as a network of logical blocks. (b) In the first logical cycle, operations 1 and 2 are executed. (c) In the second logical cycle, only operation 3 is executed. (d) In the third logical cycle, operations 4 and 5 are executed.
• Figure 5: (a) Quantum circuit of a sequence of $Z$-type measurements. In a baseline architecture, the first measurement may be executed via a lattice-surgery operation connecting qubits 1, 5 and 8. This operation can be described by (b) a spacetime diagram or (c) the corresponding ZX diagram. (d) The diagrams contain redundant volume corresponding to idle operations that do not contribute to the execution of the logical operation. (e) An active-volume quantum computer can execute the $Z$-type measurement generating only the volume relevant to the logical operation, i.e., the active volume of 6 logical blocks.