Computational power for quantum computers goes as 2^n, where n is the number of qubits, so unlike classical computing this machine should be orders of magnitude superior to Google's 53-quibit Sycamore.
If you wanna learn more about the subject, a couple of years back I wrote a introduction to quantum computing for programmers which you may find useful:
Roughly, computational power = number of operations per cycle.
Classical computers can only perform a number of operations per cycle linearly proportional to the amount of hardware architecture available (ex: one core, two cores, quad-core). Quantum computers can take advantage of superposition and entanglement to, given some restrictions, perform multiple operations per cycle, proportional to "two" to the power of the number of qubits.
That's not quite it. The power of a QC comes from modeling an exponentially large probabilistic state space using entanglement and superposition. The operations performed by a QC are also different, they can be analog (arbitrary rotations), but circuit depths (i.e. the number of operations) are still expected to be polynomial.
The difference is that the probabilistic state space uses probability amplitudes, which are complex valued and can be positive or negative, allowing for constructive and destructive interference over the probabilities tied to each state. Orchestrate the right kind of interference, and for some problems, you have an algorithm that outputs a solution to that problem with (relatively high probability) in time that, depending on the problem, may be exponentially faster. Examples of those problems include prime factorization/discrete logarithms (Shor's algorithm) and ones in quantum simulation (hence the interest in QC by chemists, physicists, etc.)
Thanks for detailing. I was explaining in laymen terms, using less technical details, with some reservations ("roughly" and "given some restrictions").
> Orchestrate the right kind of interference, and for some problems, you have an algorithm that outputs a solution to that problem with (relatively high probability) in time that, depending on the problem, may be exponentially faster.
Exactly. Given some restrictions, it's possible to implement algorithms that are equivalent to performing an exponentially large amount of classical operations per "cycle".
> Examples of those problems include prime factorization/discrete logarithms (Shor's algorithm)
Indeed. I provide an implementation of the Deutsch–Jozsa algorithm [1][2] based in my own quantum computing simulator that I linked in my blog post (in the original comment) to address this.
If you wanna learn more about the subject, a couple of years back I wrote a introduction to quantum computing for programmers which you may find useful:
- https://thomasvilhena.com/2019/11/quantum-computing-for-prog...