In this post, we do simple math to calculate how many qubits are required for QCs to break encryptions of crypto blockchains. We will use publicly available information, which is embedded even in results of AI requests.
First of all, we need to distinguish physical qubits from logical qubits. Physical qubits are real hardware qubits, which have errors. Logical qubits are artificial qubits, constructed from physical qubits, which have a so low errors rate that it allows long time calculations on QCs. It is required from 5 to 7 physical qubits to get a single logical working qubit. The more physical qubits are used to form a logical qubit the more stable the logical qubit is. See [1].
Secondly, we need to understand that there are different algorithms to break encryptions on QCs.
The first group of algorithms is based on Shor’s algorithm and its optimized modifications. Such algorithms can be run on general purposes QCs. To break N-bit encryptions such algorithms require from 0.5*N (Regev's algorithm) to 2*N (Zalka or Craig Gidney) logical qubits. See [2]. Therefore, for 256-bit encryptions and 0.5*N requirement we have that QCs need 128 logical qubits to break encryptions of crypto blockchains. If we convert this number to physical qubits with ratios of 5-7 we get that it is required from 640 to 896 physical qubits to break encryptions of crypto blockchains.
Thirdly, arises a question: Do we have such QCs today or will have them in the near future?
According to publicly available information the answer is -yes. See, [3].
IBM has the 1,121-qubit "Condor" superconducting processor.
Atom Computing has the second-generation machine, used in partnership with Microsoft, which supports 1,180 physical qubits.
Caltech developed a 6,100-qubit device.
QuantWare announced the VIO 40k architecture, enabling 10,000-qubit processors using 3D scaling.
The next major planned D-Wave system, Advantage3, is expected to feature a significant leap in qubit count, often discussed in the context of reaching 100,000 qubits in its future roadmap. The currently available, sixth-generation Advantage2 system features 4,400+ qubits.
The second group of algorithms is based on reduction of a factorization problem to an optimization problem and finding the solution. Researchers in early 2023 suggested that such algorithm could use about 372-qubit machine, but in 2024 Chinese experts reported factorizing a set of 2048-bit RSA integers, using about 6-10 qubits on a D-Wave quantum annealer. See [4].
The third group of algorithms is based on specially constructed QCs. Recent theoretical research proposes that a 1-qubit system combined with quantum oscillators could theoretically factor RSA-2048 encryption, representing a drastic reduction in the qubit count compared to standard gate-based models. See [5].
Attention! The results of queries below may change each time, because AI is constantly modifying results to suit owners requirements and agendas.
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