the exact size and specifications of a quantum computer required to break Bitcoin encryption or efficiently simulate complex molecules are still uncertain. However, I can provide you with some general information on the subject.
Breaking Bitcoin Encryption: Bitcoin currently relies on the Elliptic Curve Digital Signature Algorithm (ECDSA) for its encryption. To break this encryption using Shor's algorithm, which is a widely discussed quantum algorithm for factoring large numbers and solving the discrete logarithm problem, a quantum computer would need a sufficient number of qubits and a low error rate.
It is estimated that a quantum computer with around 2,048 to 4,096 logical qubits, known as a "fault-tolerant" quantum computer, could potentially break the ECDSA encryption used in Bitcoin. However, it's important to note that the exact number of qubits required and the level of fault tolerance needed depend on the specific implementation of quantum algorithms and the advances in quantum computing technology.
Simulating Molecules: Simulating the behavior of molecules is a complex task that can be greatly enhanced by quantum computers. Quantum computers could enable the simulation of quantum systems, such as chemical reactions and properties of materials, with a level of accuracy that classical computers cannot achieve efficiently.
The number of qubits required to simulate a molecule depends on the complexity and size of the molecule. It is generally understood that to accurately simulate small, simple molecules, a few dozen to a few hundred qubits may be sufficient. However, for larger and more complex molecules, thousands to millions of qubits could be necessary.
It's important to note that both breaking Bitcoin encryption and simulating molecules are considered "hard" problems for classical computers and "quantum advantage" in solving these problems is still an area of ongoing research and development in the field of quantum computing. The size and specifications of the quantum computers required for these tasks may evolve as technology progresses, and further advancements in algorithms and error correction are made.