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In existing general-purpose architectures for surface-code-basedfault-tolerant quantum computers, the cost of a quantum computation isdetermined by the circuit volume, i.e., the number of qubits multiplied by thenumber of non-Clifford gates. We introduce an architecture using non-2D-localconnections in which the cost does not scale with the number of qubits, andinstead only with the number of logical operations. Each logical operation hasan associated active volume, such that the cost of a quantum computation can bequantified as a sum of active volumes of all operations. For quantumcomputations with thousands of logical qubits, the active volume can be ordersof magnitude lower than the circuit volume. Importantly, the architecture doesnot require all-to-all connectivity between N logical qubits. Instead, eachlogical qubit is connected to O(log N) other sites. As an example, we showthat, using the same number of logical qubits, a 2048-bit factoring algorithmcan be executed 44 times faster than on a general-purpose architecture withoutnon-local connections. With photonic qubits, long-range connections areavailable and we show how photonic components can be used to construct afusion-based active-volume quantum computer.

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