Yes @sophchoe, that sounds right!
In this picture,
is Gaussian Boson sampling performed much faster on X8 than on classical computers, or the fact it is done on X8 of importance?
Hi @sophchoe,
Since classical computers are extremely advanced in their development compared to quantum hardware they are generally capable of solving the same sampling problems at comparable speeds however the aim is indeed to find problems well suited to GBS and use devices like X8 to demonstrate and advantage. Section IV of this paper details several problems that GBS is well suited to solving.
Thank you so much @Ant_Hayes. The paper was very helpful.
One more concept I want clarification on: observables
Would it be correct or incorrect to say
- Qubit based observables are amplitude and phase of an electron
- Qumode based observables are position and momentum of a photon?
Hi @sophchoe,
This is a very fundamental question! Arguably, all we can ever measure of any physical system is position and momentum.
Amplitude and phase of a qubit observable will determine the probability the qubit’s observable of interest being in a given state. Often these measurement are realised through counting particles. This is also true of qumode (photons).
Thinking back to Young’s double slit experiment is a great example of quantum measurements. Again, this is simply counting particles that appear at certain positions!
Just to clarify my understanding when I see the term “Observable” on Pennylane documentation. What would be the best way to interpret that? The photon count?
@Tom_Bromley Can we access the state vector before measurement of a circuit only on simulators or on X8 as well? I can understand the final quantum state of the circuit before measurement being represented mathematically on a simulator. Do we have the same kind of access on a QPU without measurement?
Hi @sophchoe,
Observables in PennyLane can be thought of a matrices which act on quantum state vectors to give eigenvalues which tell us the state of the system. These matrices have a special property of being Hermitian which guarantees the eigenvalues they return are real numbers.
Hi @sophchoe,
In general it is not possible to access information on a quantum state without performing a projective measurement which inherently changes the state of the system. This is know as wave function collapse.
There are active areas of research on accessing states without collapsing the wave function for example see weak measurements but this is not yet a practical option for quantum computation.
Hi @Ant_Hayes,
In Strawberry Fields, you have an option of extracting state vectors. Is it an accurate understanding that it is possible only on a simulator, not on an X8 chip?
Hi @sophchoe,
Yes that’s accurate since the X8 chip is a quantum device. We can only build up information on the quantum state through many repeated measurements.
Great! Thank you!
For each qumode, the pre-measurement state is an infinite sum of Fock basis, approximated by the number of basis defined by the cutoff dimension.
In multi-qumodes, it is a tensor product space of those Fock spaces?
Hi @sophchoe,
Yes, the state of the full system can be described by the tensor product of the individual modes in a given basis such as the Fock basis.
Hi @Ant_Hayes,
The Kerr gate is represented by 
Do you have a matrix representation of this? How do we derive a hat?
Hey @sophchoe,
remember that the number operator in Fock basis is a diagonal matrix diag(0, 1, 2, 3, ...), which means that n^2 = diag(0, 1, 4, 9, ...). Since exponentiating a diagonal matrix is the same as a matrix with exponentials of the diagonal elements, we get
exp(i k n^2) = diag(1, e^ik, e^4ik, ...)
Hope this helps!
PS: For cases that are not as simple you may try to consult the StrawberryFields source code.
Great! Thank you so much.