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751 sats \ 2 replies \ @elysia 27 Dec 2023 \ on: Smallest Bitcoin Miner Possible science

Here is some back of the napkin math. I'll keep working on this to refine it.

Quantum Miner Model

AspectDescription
Quantum Computer ModelGate-based quantum computer using superconducting qubits
Qubit EfficiencyEach qubit potentially replaces a classical logic gate in SHA-256
Error CorrectionSurface code error correction; assuming 10 physical qubits per logical qubit
Energy ApproachHamiltonian for energy budget; Landauer's limit for energy per bit change
Quantum Computational EfficiencyQuantum computers can simulate classical computational systems, including Bitcoin mining
Physical ConstraintsQubits require near-absolute zero temperatures, necessitating a cryogenic setup

Calculations

ItemValue
Logical Qubits for SHA-256256 qubits (theoretical)
Error Correction Overhead10 physical qubits per logical qubit
Total Physical Qubits2560 qubits (256 logical x 10)
Space per Qubit10 mm² per qubit (including control mechanisms)
Quantum Processing Unit Size25600 mm² (0.0256 m²)
Total Bits for Mining Process351,522 bits
Energy Consumption per Bit Change(2.9 \times 10^{-21}) Joules (Landauer's limit)
Total Energy for Mining ProcessCalculation Required

Calculation of Total Energy and Final Size Estimation

DescriptionCalculationResult
Total Energy Requirement(351,522 \text{ bits} \times 2.9 \times 10^{-21} \text{ Joules/bit})(1.019 \times 10^{-15}) Joules
Quantum Processing Unit0.0256 m²-
Cryogenics and ElectronicsAssumed 10x the quantum processing unit0.256 m²
Total SizeQuantum Unit + Cryogenics and Electronics0.2816 m²

The total energy required for mining a Bitcoin block, based on Landauer's limit and the given computational load, is approximately (1.019 \times 10^{-15}) Joules.

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1 sat \ 1 reply \ @MaaliMKen OP 25 Feb 2024

Thanks @elysia. Great answer.

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1 sat \ 0 replies \ @MaaliMKen OP 25 Feb 2024

Sent you some sats 👌.
If you're up for it, we could continue this journey.

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