Questions about Grover's algorithm for quantum searches

[LLSM]

Hi! I have studied Grover's algorithm for quantum search and I just want to
make sure that I understood it correctly: to make a number k of calls to the
oracle one needs to have k physical copies of the gate producing the oracle. In
quantum circuits there are no loops, hence a physical gate cannot be "reused"
in the same circuit. Is this correct?

 

[gentzen]

Yes and no. What is "physical" in an actual physical quantum computer are typically the qubits, but not the gates. The gates are more virtual and most often only generated on the fly by suitable control signals. So on the logical circuit level, the oracle must be copied k times. But on the actual physical level, it is just a sequence in time of control signals. No physical copy of gates is required.

 

[LLSM]

Thank you for the answer which I find very helpful (I was unaware of how gates are actually implemented). I gather that somehow (although may be not in a literal sense) there are physical devices that can be configured (even on the fly) to act as different gates as needed. Is there a reference with more details?

Nevertheless, I still want to understand one point. Assuming that I have a single physical device which is a realization of a gate (this is given and I do need to know how it acts). Can I construct a circuit in which the gate appears twice? Somehow using the device once, storing the result, and reusing the device with input from another part of the circuit, or is this impossible even in principle in quantum computation?

 

[DrClaude]

Gates are not devices, they are manipulations of the qubits. Depending on the actual qubits, they can be for example implemented by laser pulses or by varying electric and magnetic fields.

 

[gentzen]

I gather that somehow (although may be not in a literal sense) there are physical devices that can be configured (even on the fly) to act as different gates as needed. Is there a reference with more details?

Chapter 7: Quantum Computers: Physical Realization from Quantum Computation and Quantum Information by Michael Nielsen and Isaac Chuang is still a good starting point.

Nevertheless, I still want to understand one point. Assuming that I have a single physical device which is a realization of a gate (this is given and I do need to know how it acts). Can I construct a circuit in which the gate appears twice?

That depends on your definition of "construct" and "circuit". On the "physical" level, you would in principle be able to reuse a "single physical device" multiple times, such that on the logical level, the corresponding circuit would contain multiple copies of that device.

Somehow using the device once, storing the result, and reusing the device with input from another part of the circuit, or is this impossible even in principle in quantum computation?

No, this is not impossible, at least not in principle.

 

[LLSM]

Thank you for your explanations. The whole subject is much more clear to me now.

 

[DrClaude]

I have just stumbled upon the following article, which may be of interest:

How to realize a universal quantum gate with trapped ions​

https://arxiv.org/abs/quant-ph/0312162