- Hartmut Neven at Google - Law describes - How quickly quantum computers are gaining on classical ones. - quantum computers are gaining computational power relative to classical ones at a **“doubly exponential” rate** - Doubly exponential growth is far more dramatic. Instead of increasing by powers of 2, quantities grow by powers of powers of 2: 2^(2^n) - the extreme rate at which certain computational problems increase in complexity -Doubly exponential growth is so singular that it’s hard to find examples of it in the real world. The rate of progress in quantum computing may be the first Why? - **Intrinsic Exponential Advantage** - If a quantum circuit has four quantum bits, for example, it takes a classical circuit with 16 ordinary bits to achieve equivalent computational power. This would be true even if quantum technology never improved. - **Rapid Improvement of Quantum Processors** - Reduction in error rate permitting us to build larger quantum processors If classical computers require exponentially more computational power to simulate quantum processors, and those quantum processors are growing exponentially more powerful with time, you end up with this doubly exponential relationship between quantum and classical machines. --------- #quantum #firstprinciple