## How many qubits does it take to break a 10 characters password?

4

1

Let's assume we developed a hashcat-like programs for quantum computer. How many qubits we need to find the correct hash (WPA, MD5,...) from a 10 characters password make from upper, lower & numeric characters (about 604,661,760,000,000,000 combinations)

4

$$\log_2 604,661,760,000,000,000 \approx 59.07$$

So use $$60$$ qubits for the data lines where you will put a uniform superposition. This gives a total of $$61$$ qubits to run Grover's.

$$2^{59} = 5.764607523034e+17$$ so if you can throw away about $$2.8e+16$$ possibilities first, you would be able to do it $$60$$.

Edit: As cautioned this is for logical qubits.

2Should note these are logical error-corrected qbits, not physical qbits (lest we give the impression existing quantum computers can do this). – ahelwer – 2018-10-02T16:25:12.400

1Also it will take millions of years to run, because you need to do a billion MD5 applications under superposition and a single AND gate takes on the order of a millisecond to apply under superposition. You're better off using a bunch of GPUs. – Craig Gidney – 2018-10-02T21:18:56.287

Thanks. I read that grover's algorithm can reduce search space to 2^(n/2) (2^30 in this case). Apply it to the program, can we make it to do the task with 30 qubits? – Dan Minh Toan – 2018-10-03T02:21:11.467

That's the asymptotic for length of the circuit not number of qubits. – AHusain – 2018-10-03T19:26:31.273

@CraigGidney in the future, is there any possible solution for quantum computer to run this in one go, i mean fast? – Dan Minh Toan – 2018-10-08T04:12:52.903

1@QuanLee What do you mean by "in one go"? Grover's algorithm requires O(sqrt(N)) applications of the function, not just one. And overcoming the huge constant factor penalty of quantum computation vs classical computation means you need an unstructured problem with implausibly gigantic N before you see any advantage in absolute dollars. – Craig Gidney – 2018-10-08T06:26:56.033

@CraigGidney that's what i mean, run trillions of operation as long as you have enough qubits as fast as you can. I don't have much knowledge about quantum computer, i just know that the more qubits you have the more operation you can do. So somehow can we make quantum computer hash millions of possibility & compare the output as fast as GPU in the future? – Dan Minh Toan – 2018-10-08T06:33:57.853

@QuanLee If the energy cost of the quantum computation is 1000x the energy cost of the classical computation, going twice as fast by having twice as many qubits won't change that fact. And if you're going to scale up the quantum computer, you have to correspondingly scale up its classical competition in order to do a fair comparison, dollar for dollar. – Craig Gidney – 2018-10-08T17:20:24.657