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You're probably confusing physical qubits (inside the actual physical device) and logical qubits (on which the platonic ideal calculation takes place). If we h

You're probably confusing physical qubits (inside the actual physical device) and logical qubits (on which the platonic ideal calculation takes place). If we had 1000 logical qubits, we could indeed do useful things, but real-world implementations require huge amounts of error correction, which is much tricker on quantum computers than classical ones. Asymptotically the ratio of physical to logical qubits can approach 1 (just polylog overhead), but for early calculations the ratio will literally be more than a factor of a thousand. (This is true for all concrete proposals to date; people have speculated that there might be something useful to do with 1000 physical qubits for certain problems if the error could be small enough to be ignored and not corrected, but no one has actually shown explicitly how to do this, or produced the components with the quality that would be necessary.)

wbhart 9y ago
Yes, I was certainly confused. When IBM announced they are building a 7x7 = 49 qubit machine, I naturally assumed they meant logical qubits, not physical ones. Using surface codes, they can probably get one logical bit. But what confuses me are past records where they used Shor's algorithm to factor small integers on a quantum computer. How is this possible if we haven't even built a single logical qubit yet? It's surely necessary to have ~2N logical qubits to factor an integer of N bits. I have an idea that might help though: if logical qubits are so difficult to build and require thousands of times more physical qubits, and physical qubits are also difficult to build, perhaps we can simulate physical qubits with thousands of times more "ultra-physical" qubits.
- jessriedel 9y ago
  Two excellent questions. Regarding claims of factoring small numbers: First note that error correction becomes exponentially more important for longer computations. Second, see this https://arxiv.org/abs/1301.7007 https://arxiv.org/abs/1301.7007 Regarding building a tower of ever less noisy qubits: it turns out there is something called a threshold theorem which requires a certain minimal level of noise before concatenating error correction schemes makes things better rather than worse. https://en.m.wikipedia.org/wiki/Quantum_threshold_theorem https://en.m.wikipedia.org/wiki/Quantum_threshold_theorem Reaching this threshold for physical qubits in the laboratory is perhaps the primary goal of experimental quantum computing.
  - wbhart 9y ago
    That first article you cite certainly puts the whole thing in perspective. I was tempted to put an article on Arxiv announcing a new architecture for billions of "super-physical" qubits, but you've convinced me that not only would the real experts see right through this, but that it might bring me down to the level of some of the qubit measuring contests currently on display from the likes of IBM, Google and Microsoft. Thanks for the genuinely interesting answers, especially to the not completely serious question!

wbhart 9y ago

Yes, I was certainly confused. When IBM announced they are building a 7x7 = 49 qubit machine, I naturally assumed they meant logical qubits, not physical ones. Using surface codes, they can probably get one logical bit. But what confuses me are past records where they used Shor's algorithm to factor small integers on a quantum computer. How is this possible if we haven't even built a single logical qubit yet? It's surely necessary to have ~2N logical qubits to factor an integer of N bits. I have an idea that might help though: if logical qubits are so difficult to build and require thousands of times more physical qubits, and physical qubits are also difficult to build, perhaps we can simulate physical qubits with thousands of times more "ultra-physical" qubits.

jessriedel 9y ago
Two excellent questions. Regarding claims of factoring small numbers: First note that error correction becomes exponentially more important for longer computations. Second, see this https://arxiv.org/abs/1301.7007 https://arxiv.org/abs/1301.7007 Regarding building a tower of ever less noisy qubits: it turns out there is something called a threshold theorem which requires a certain minimal level of noise before concatenating error correction schemes makes things better rather than worse. https://en.m.wikipedia.org/wiki/Quantum_threshold_theorem https://en.m.wikipedia.org/wiki/Quantum_threshold_theorem Reaching this threshold for physical qubits in the laboratory is perhaps the primary goal of experimental quantum computing.
- wbhart 9y ago
  That first article you cite certainly puts the whole thing in perspective. I was tempted to put an article on Arxiv announcing a new architecture for billions of "super-physical" qubits, but you've convinced me that not only would the real experts see right through this, but that it might bring me down to the level of some of the qubit measuring contests currently on display from the likes of IBM, Google and Microsoft. Thanks for the genuinely interesting answers, especially to the not completely serious question!