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Comment by mentos | Hacker News Reader

Is it possible that a massive array of GPUs might be more economical than a few real quantum chips that need to be cooled to absolute zero?

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In the short term, yes, while the number of qubits is small and even smaller when you consider logical qubits require multiple real qubits to account for error.

In simplified terms though, for every logical qubit you add to the system, you effectively double the power of the machine. To double the power of your GPU stack, you'd need 2x more GPUSs each time. There is also the additional caveat of the type of problem - not every problem currently suited for a gpu is going to be better run on a qpu.

That depends on the number of qbits you want to simulate. Doing the calculations on classical computers has an exponential slowdown as you need 2^n classical bits to store n qbits. It's pretty unlikely that you will ever be able to simulate a quantum computer with more than a few dozen qbits.

Indeed. I'd expect this to top of at about 64 qbits with smart maths. (Mostly due to pointer limitations.) You could try to extend addressing but it'll be even slower...

Just as a data point: Current state-of-the-art methods for Lanczos-type methods on state vectors are around 40 spins/qubits incorporating many symmetries and additional shortcuts one does not have in a generic "quantum computer simulator". Without those symmetries/shortcuts, the limit is likely closer to 30 qubits (i.e. approx. 16-64 GB per state vector), as it’s not only necessary to store these beasts but also do operations on them.

If you don’t insist on a single dense state vector but a sparser tensor network-based formulation, you can go to much larger systems (hundreds or thousands of spins) but will be limited by the amount of entanglement you can represent in your system.

That absolutely is the case right now, it may not be in a few decades.

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