btccyberhornet on Nostr: The 105 qubit willow released by google is physical qubit. Here is why sha256 is safe ...
The 105 qubit willow released by google is physical qubit. Here is why sha256 is safe for atleast 10 years plus there is always hard fork option
#bitcoin #sha256 #quantumfud #willow #qubit
source: chatgpt
The number of logical qubits needed to crack SHA-256 encryption using a quantum computer depends on the quantum algorithm used, the error rates of the quantum system, and the depth of the quantum circuits required. Here's an analysis based on current research:
Cracking SHA-256 with Quantum Computing
To crack SHA-256 encryption, a quantum computer would use Grover's Algorithm, which can find a preimage (input to the hash function) in approximately \( 2^{n/2} \) operations, where \( n \) is the bit length of the hash. For SHA-256:
- Classical brute force requires \( 2^{256} \) operations.
- Grover’s algorithm reduces this to \( 2^{128} \), making it significantly faster but still computationally expensive.
Logical Qubits Estimate
1. Memory Requirements
Grover’s algorithm requires:
- Superposition over \( 2^{128} \) states** for a 128-qubit register to store candidate inputs.
- Additional qubits for the oracle (which implements the SHA-256 hash function quantumly) and ancilla qubits for intermediate calculations.
A recent estimate suggests that:
- Around 3000 logical qubits would be required to run Grover’s algorithm for breaking SHA-256 efficiently, assuming high-fidelity error correction.
2. Error Correction Overhead
Logical qubits are constructed from physical qubits using error-correcting codes. The overhead depends on:
- Error rates of the physical qubits.
- Error correction method used (e.g., surface code).
Error correction overhead is typically
1 logical qubit = 1000–10,000 physical qubits with current technology. Therefore:
- Cracking SHA-256 might require 3–30 million physical qubits** using today's error correction methods.
Time to Solve
The time required depends on:
1. Quantum gate depth: Grover’s algorithm requires \( \mathcal{O}(2^{128}) \) iterations of the SHA-256 oracle.
2. Gate speed: Current quantum gates are slow compared to classical systems, which could make execution impractically long.
Estimates suggest that even with millions of physical qubits, it could take several hours or days to complete the computation due to circuit depth and qubit coherence limits.
Key Challenges
1. High Circuit Depth: The SHA-256 oracle has a complex structure, leading to very deep quantum circuits.
2. Error Rates: Current error rates and decoherence times make it hard to sustain such long computations without overwhelming error correction overhead.
3. Scalability: Building millions of physical qubits for practical quantum computers is still decades away.
Conclusion
Cracking SHA-256 encryption would require:
- Around 3000 logical qubits for Grover’s algorithm.
- Between 3–30 million physical qubits, depending on error rates and the efficiency of error correction.
Given the current pace of quantum computing advancements, SHA-256 encryption is safe for the foreseeable future, as building a sufficiently powerful quantum computer may take decades. In the meantime, cryptographers are developing
quantum-resistant algorithms to mitigate this potential threat.
#bitcoin #sha256 #quantumfud #willow #qubit
source: chatgpt
The number of logical qubits needed to crack SHA-256 encryption using a quantum computer depends on the quantum algorithm used, the error rates of the quantum system, and the depth of the quantum circuits required. Here's an analysis based on current research:
Cracking SHA-256 with Quantum Computing
To crack SHA-256 encryption, a quantum computer would use Grover's Algorithm, which can find a preimage (input to the hash function) in approximately \( 2^{n/2} \) operations, where \( n \) is the bit length of the hash. For SHA-256:
- Classical brute force requires \( 2^{256} \) operations.
- Grover’s algorithm reduces this to \( 2^{128} \), making it significantly faster but still computationally expensive.
Logical Qubits Estimate
1. Memory Requirements
Grover’s algorithm requires:
- Superposition over \( 2^{128} \) states** for a 128-qubit register to store candidate inputs.
- Additional qubits for the oracle (which implements the SHA-256 hash function quantumly) and ancilla qubits for intermediate calculations.
A recent estimate suggests that:
- Around 3000 logical qubits would be required to run Grover’s algorithm for breaking SHA-256 efficiently, assuming high-fidelity error correction.
2. Error Correction Overhead
Logical qubits are constructed from physical qubits using error-correcting codes. The overhead depends on:
- Error rates of the physical qubits.
- Error correction method used (e.g., surface code).
Error correction overhead is typically
1 logical qubit = 1000–10,000 physical qubits with current technology. Therefore:
- Cracking SHA-256 might require 3–30 million physical qubits** using today's error correction methods.
Time to Solve
The time required depends on:
1. Quantum gate depth: Grover’s algorithm requires \( \mathcal{O}(2^{128}) \) iterations of the SHA-256 oracle.
2. Gate speed: Current quantum gates are slow compared to classical systems, which could make execution impractically long.
Estimates suggest that even with millions of physical qubits, it could take several hours or days to complete the computation due to circuit depth and qubit coherence limits.
Key Challenges
1. High Circuit Depth: The SHA-256 oracle has a complex structure, leading to very deep quantum circuits.
2. Error Rates: Current error rates and decoherence times make it hard to sustain such long computations without overwhelming error correction overhead.
3. Scalability: Building millions of physical qubits for practical quantum computers is still decades away.
Conclusion
Cracking SHA-256 encryption would require:
- Around 3000 logical qubits for Grover’s algorithm.
- Between 3–30 million physical qubits, depending on error rates and the efficiency of error correction.
Given the current pace of quantum computing advancements, SHA-256 encryption is safe for the foreseeable future, as building a sufficiently powerful quantum computer may take decades. In the meantime, cryptographers are developing
quantum-resistant algorithms to mitigate this potential threat.