## Factorization using Qlasskit and DWave Quantum Annealer

In the last release of Qlasskit, I introduced a new feature able to export a qlassf function to a binary quadratic model (as bqm, qubo or ising model). This...

Traditionally, creating quantum circuits requires specialized knowledge in quantum programming. This requirement holds true when encoding a classical algorithm inside a quantum circuit, for instance, for an oracle or a black-box component of a quantum algorithm. This often becomes a time wasting job, since we almost always already have a classical implementation in a traditional high level language.

*Qlasskit*, an open-source Python library developed with the support of a Unitary Fund microgrant, addresses this challenge head-on by allowing direct translation of standard Python code into invertible quantum circuits without any modification to the original code. Furthermore, *qlasskit* implements some well-known quantum algorithms and offers a comprehensive interface for implementing new ones.

To illustrate *qlasskit*’s capabilities, we will demonstrate its use in performing a pre-image attack on a cryptographic hash function using Grover’s search algorithm, obtaining a quadratic speedup compared to classical approaches. The beauty of *qlasskit* lies in its simplicity – you can write the entire software without needing to understand any concept of quantum computing.

A pre-image attack, in cryptography, targets a hash function `h(m)`

with the aim to discover an original message `m`

that corresponds to a specific hash value. On a traditional computer, to perform this attack without any hints, we must run `h(m)`

with every possible input (`N=2**n`

).

Thanks to the Grover search algorithm, we are able to find a pre-image with only `pi/2 * sqrt(N)`

iterations, obtaining the quadratic speedup I mentioned before.

We write a toy hash function `hash_simp`

which operates on messages composed of two 4 bit values and uses bitwise xor to create an 8 bit hash value.

```
from qlasskit import qlassf, Qint4, Qint8, Qlist
@qlassf
def hash_simp(m: Qlist[Qint4, 2]) -> Qint8:
hv = 0
for i in m:
hv = ((hv << 4) ^ (hv >> 1) ^ i) & 0xff
return hv
```

The first things you can notice in this code are:

- the
`qlassf`

decorators, indicating that the function will be translated to a quantum circuit. - special bit-sized types Qlist, Qint4, and Qint8. These are required as qubits are a precious resource, and we want to use as few as possible.
- and, it is normal Python code.

To see the resulting quantum circuit we can export and draw in qiskit:

```
hash_simp.export('qiskit').draw('mpl')
```

And this is the resulting circuit, produced by the *qlasskit* internal compiler:

Thanks to the fact that *qlasskit* function are standard Python functions, we can call the `original_f`

to perform some kind of analysis and test on the hash function. Since the input space is tiny (it is a toy hash function), we can check if the hash function is uniform (if it maps equally to the output space).

```
from collections import Counter
d = Counter(hex(hash_simp.original_f((x, y))) for x in range(2**4) for y in range(2**4))
print('Hash function output space:', len(d))
```

We got that `hash_simp`

is following an uniform distribution.

Now we use our quantum function as an oracle for a Grover search, in order to find which input maps to the value `0xca`

.

```
from qlasskit.algorithms import Grover
q_algo = Grover(hash_simp, Qint8(0xca))
```

Then we use our preferred framework and simulator for sampling the result; this is an example using `qiskit`

with `aer_simulator`

.

```
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.visualization import plot_histogram
qc = q_algo.export('qiskit')
qc.measure_all()
simulator = Aer.get_backend("aer_simulator")
circ = transpile(qc, simulator)
result = simulator.run(circ).result()
counts = result.get_counts(circ)
counts_readable = q_algo.decode_counts(counts, discard_lower=5)
plot_histogram(counts_readable)
```

And this is the result of the simulation, where we can see that the pre-image that leads to `h(x) = 0xca`

is the list `[12,12]`

.

Using `QlassF.original_f`

we can double check the result without invoking a quantum simulator; calling it with the list `[12,12]`

must result in the hash value `0xca`

.

```
print(hex(hash_simp.original_f((12,12))))
```

Although *qlasskit* can handle hundreds of qubits, in this post we use a toy hash function because currently, we lack a simulator or quantum computer capable of handling hundreds of qubits. Using these same tools, in the near future we may be able to perform a Grover search on real hash functions like `md5`

or `sha2`

.

A special thanks to the Unitary Fund that funded this idea. If you have any questions or comments, feel free to reach out to me on twitter dagide, linkedin Davide Gessa and medium @dakk.

Original post on Unitary.fund: https://unitary.fund/posts/2023_qlasskit/

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