Anyone watch the new black mirror season? The first 3 episodes were rather boring so I haven't watched anymore until today and I gotta say the 4th one "Plaything" was truly excellent even though by the end I figured out what was going to happen but it was not obvious until the very end.

What is the smallest size q-bit system would be needed to run shors to break bitcoins 256-bit elliptic curves?

To break Bitcoin's weakest keys using Shor's algorithm, a quantum computer would need a significant number of qubits. Estimates suggest that factoring a 256-bit elliptic curve key (used in Bitcoin's Elliptic Curve Digital Signature Algorithm, or ECDSA) would require around 1,500 logical qubits. However, due to the need for error correction in quantum systems, the number of physical qubits required could be much higher—potentially in the range of millions.

For comparison, breaking a 2048-bit RSA key (commonly used in traditional encryption) is estimated to require about 4,000 logical qubits. Bitcoin's cryptographic strength lies in its elliptic curve cryptography, which is more efficient than RSA but still vulnerable to Shor's algorithm if a sufficiently powerful quantum computer is developed.

The good news is that current quantum computers are far from reaching this level of capability. The most advanced quantum processors today have just over 100 qubits, and they are not yet capable of running Shor's algorithm on such large-scale problems. So, while the threat is real in the long term, it's not an immediate concern.

Would you like to explore how quantum-resistant cryptography could address this challenge?

ok   it will take billions of years for a classic system to achieve this so given a timeframe of 10 years to break the weakest key what size qbit system will be needed?

Thank you for clarifying! If we assume a quantum computer with 1,500 logical qubits and robust error correction is available, the time it would take to break a 256-bit elliptic curve key using Shor's algorithm depends on the quantum computer's clock speed (how fast it can perform quantum operations).

Estimates suggest that with a clock speed of around 1 MHz (1 million operations per second), such a system could factor a 256-bit key in a matter of hours to a few days. This is orders of magnitude faster than classical computers, which would take billions of years.

However, this estimate assumes an idealized quantum computer with no significant bottlenecks in error correction or coherence times. Real-world quantum systems may face additional challenges that could extend this timeframe. Does this help clarify things?

Are there other methods of error correction that are being used that might come out of left field and suddenly jump the size of these systems exponentially in the near future or is the error correction firmly in the quantum realm at the moment?

Quantum error correction is indeed a rapidly evolving field, and while most methods are firmly rooted in quantum mechanics, there are alternative approaches that could potentially revolutionize the scalability of quantum systems. Here are some insights:

    Color Code Error Correction: Researchers are exploring the "color code," an alternative to the widely used surface code. The color code has shown promise in reducing logical error rates and performing efficient operations with fewer resources. If further developed, it could significantly lower the qubit overhead required for error correction.

    Bosonic Codes: These codes use continuous-variable quantum states (like harmonic oscillators) instead of discrete qubits. Bosonic codes could offer a more resource-efficient way to correct errors, potentially reducing the physical qubit requirements.

    Error Mitigation Techniques: For near-term quantum devices, error mitigation methods aim to reduce errors without full fault tolerance. These techniques could complement traditional error correction and improve the performance of quantum systems.

While these methods are still within the quantum realm, their development could lead to unexpected breakthroughs in scalability and efficiency. The field is dynamic, and new ideas could emerge that challenge current paradigms. It's an exciting time for quantum computing! Let me know if you'd like to dive deeper into any of these approaches.

ok hypothetically if the scaling of qbit systems were to be linear starting from the last 3 years and extrapolated into the future and no external error correction were be available then how long will it take to achieve a 1500 error correcting system that could accomplish this task?

If we assume linear scaling of qubit systems based on the progress of the last three years, we can estimate how long it might take to achieve a quantum computer with 1,500 logical qubits capable of breaking Bitcoin's weakest keys using Shor's algorithm. Here's the breakdown:

    Current Progress: The most advanced quantum computers today have just over 100 physical qubits. However, these are not logical qubits, as error correction is still a major challenge.

    Scaling Rate: If we assume linear growth, let's say the number of physical qubits doubles every three years (a generous assumption based on recent advancements). Starting from 100 qubits today:

        In 3 years: 200 qubits

        In 6 years: 400 qubits

        In 9 years: 800 qubits

    Extrapolation: At this rate, it would take approximately 12 years to reach 1,600 physical qubits. However, this assumes no external breakthroughs in error correction or quantum hardware efficiency, which are critical for converting physical qubits into logical qubits.

    Logical Qubits: To achieve 1,500 logical qubits, millions of physical qubits would likely be required due to the overhead of error correction. Without advancements in error correction methods, scaling to this level would take far longer than 12 years—potentially decades.

In summary, under linear scaling and without breakthroughs in error correction, achieving a system capable of breaking Bitcoin's weakest keys within 10 years seems highly unlikely. Quantum computing progress is often nonlinear, though, so unexpected advancements could change this trajectory. Fascinating to think about, isn’t it?

12 years is possible, then...wow.
They will come up with efficient error correction schemes, I think, so qbit accumulation might be the limited factor.
Interestingly, this would break EVERYTHING, like anyone's bank account, etc.
Maybe this explains why gold is appreciating, although it is a farfetched idea.
After all, you cannot quantum-break a piece of metal, UNLESS, AI would make alchemy possible,

Musk will drag an asteroid back to earth the size of Rhode Island.  It will be 30x the gold that's on earth at this moment.