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Is there an expectation of how hard it'll be to scale up the number of qubits? As in, do we think it'll be 10 times as hard each time we add another qubit, or t

by IanCal 10y ago

Is there an expectation of how hard it'll be to scale up the number of qubits? As in, do we think it'll be 10 times as hard each time we add another qubit, or that once we've got the stability sorted going from 5 to 10 to 50 to 100 is more a case of just building a bigger version? Other random questions, is there a feeling for when they'd be useful? A 5 qubit processor isn't really useful for much, but is a 10? Do they suddenly go from not-useful to "wow" very quickly as we scale up? Is there something everyone is waiting to hit, like a "once we reach about X qubits we'll be able to do Y which was totally infeasible before", or is it a bit early for that?

krastanov 10y ago
Depends on what exactly you are asking: How difficult it is to scale the simulation of N qubits? Naively you need a list of 2^N complex numbers to represent the state of N qubits. So, naively, adding one qubit to the simulation makes it a factor of 2 more difficult. This is not exact but it is a good enough intuition. (However, it is only a conjecture that quantum computers are more powerful than classical ones, even if it conjecture as strongly believed as NP!=P). How difficult it is to make a quantum computer of N+1 qubits when you have already built a computer of N qubits? Today my biased opinion would be to say that it takes a few years to create something reliable with one more qubit than the current state of the art (which is about 5). People are actively working on methods that would scale better (until then it is just scientists playing with cool hardware, but nothing practical). As to how many qubits we need to do something practical. To factor a thousand bit number in its prime factors you will need a few thousand qubits. But you will need to implement error correcting codes (qubits are unreliable so you encode one "logical" qubit redundantly in multiple "physical" qubits). If you count the physical qubits, you will need a few million. Currently we do not have machines that reliably work on more than 10ish. But another active field of research is "shallow depth circuits". Those are simple non-universal quantum circuits that require just a few qubits but do things that can not be done on classical computers efficiently. An example might be the Quantum Approximate Optimization Algorithm which for a few months was the most efficient way to find approximate solutions to NP-complete problems of certain type (until we found a better classical approach). But I would like to stress that those are not universal quantum computers.

by IanCal 10y ago

krastanov 10y ago

Depends on what exactly you are asking: How difficult it is to scale the simulation of N qubits? Naively you need a list of 2^N complex numbers to represent the state of N qubits. So, naively, adding one qubit to the simulation makes it a factor of 2 more difficult. This is not exact but it is a good enough intuition. (However, it is only a conjecture that quantum computers are more powerful than classical ones, even if it conjecture as strongly believed as NP!=P). How difficult it is to make a quantum computer of N+1 qubits when you have already built a computer of N qubits? Today my biased opinion would be to say that it takes a few years to create something reliable with one more qubit than the current state of the art (which is about 5). People are actively working on methods that would scale better (until then it is just scientists playing with cool hardware, but nothing practical). As to how many qubits we need to do something practical. To factor a thousand bit number in its prime factors you will need a few thousand qubits. But you will need to implement error correcting codes (qubits are unreliable so you encode one "logical" qubit redundantly in multiple "physical" qubits). If you count the physical qubits, you will need a few million. Currently we do not have machines that reliably work on more than 10ish. But another active field of research is "shallow depth circuits". Those are simple non-universal quantum circuits that require just a few qubits but do things that can not be done on classical computers efficiently. An example might be the Quantum Approximate Optimization Algorithm which for a few months was the most efficient way to find approximate solutions to NP-complete problems of certain type (until we found a better classical approach). But I would like to stress that those are not universal quantum computers.