The Energy Budget of Quantum Error Correction: Power and Energy per Logical Qubit for a Surface-Code Architecture

Model calculation (SIMULATED, NOT MEASURED) of the energy budget of quantum error correction for a rotated surface-code architecture. At a physical error rate of 0.001 per operation, reaching a logical error probability of 1e-12 per syndrome cycle requires code distance 27 and 1457 physical qubits per logical qubit. Combining the cryogenic load, evaluated with the refrigerator coefficient-of-performance penalty at 4 K and at 15 mK, with room-temperature control and decoding power gives 3.94 W per physical qubit, 5741 W per logical qubit, and 0.155 J per logical operation at a 1 microsecond syndrome cycle time. This is an overhead of about 7.7e9 relative to a practical classical operation at 20 pJ. Room-temperature control and decoding dominate the budget. All numbers are produced by the deposited computation script.