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Current, near-term quantum devices have shown great progress in recent yearsculminating with a demonstration of quantum supremacy. In the medium-term,however, quantum machines will need to transition to greater reliabilitythrough error correction, likely through promising techniques such as surfacecodes which are well suited for near-term devices with limited qubitconnectivity. We discover quantum memory, particularly resonant cavities withtransmon qubits arranged in a 2.5D architecture, can efficiently implementsurface codes with substantial hardware savings and performance/fidelity gains.Specifically, we *virtualize logical qubits* by storing them in layersdistributed across qubit memories connected to each transmon.  Surprisingly, distributing each logical qubit across many memories has aminimal impact on fault tolerance and results in substantially more efficientoperations. Our design permits fast transversal CNOT operations between logicalqubits sharing the same physical address which are 6x faster than latticesurgery CNOTs. We develop a novel embedding which saves ~10x in transmons withanother 2x from an additional optimization for compactness.  Although Virtualized Logical Qubits (VLQ) pays a 10x penalty inserialization, advantages in the transversal CNOT and area efficiency result inperformance comparable to 2D transmon-only architectures. Our simulations showfault tolerance comparable to 2D architectures while saving substantialhardware. Furthermore, VLQ can produce magic states 1.22x faster for a fixednumber of transmon qubits. This is a critical benchmark for futurefault-tolerant quantum computers. VLQ substantially reduces the hardwarerequirements for fault tolerance and puts within reach a proof-of-conceptexperimental demonstration of around 10 logical qubits, requiring only 11transmons and 9 attached cavities in total.

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