Virtualized Logical Qubits: A 2.5D Architecture for Error-Corrected Quantum Computing

Current, near-term quantum devices have shown great progress in recent years culminating with a demonstration of quantum supremacy. In the medium-term, however, quantum machines will need to transition to greater reliability through error correction, likely through promising techniques such as surface codes which are well suited for near-term devices with limited qubit connectivity. We discover quantum memory, particularly resonant cavities with transmon qubits arranged in a 2.5D architecture, can efficiently implement surface codes with substantial hardware savings and performance/fidelity gains. Specifically, we *virtualize logical qubits* by storing them in layers distributed across qubit memories connected to each transmon. Surprisingly, distributing each logical qubit across many memories has a minimal impact on fault tolerance and results in substantially more efficient operations. Our design permits fast transversal CNOT operations between logical qubits sharing the same physical address which are 6x faster than lattice surgery CNOTs. We develop a novel embedding which saves 10x in transmons with another 2x from an additional optimization for compactness. Although Virtualized Logical Qubits (VLQ) pays a 10x penalty in serialization, advantages in the transversal CNOT and area efficiency result in performance comparable to 2D transmon-only architectures. Our simulations show fault tolerance comparable to 2D architectures while saving substantial hardware. Furthermore, VLQ can produce magic states 1.22x faster for a fixed number of transmon qubits. This is a critical benchmark for future fault-tolerant quantum computers. VLQ substantially reduces the hardware requirements for fault tolerance and puts within reach a proof-of-concept experimental demonstration of around 10 logical qubits, requiring only 11 transmons and 9 attached cavities in total.