Questions about Grover's algorithm for quantum searches

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Discussion Overview

The discussion revolves around Grover's algorithm for quantum searches, specifically addressing the implementation of quantum gates and their physical realizations in quantum circuits. Participants explore the nature of gates, their reuse, and the implications for constructing circuits in quantum computation.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asserts that to make k calls to the oracle in Grover's algorithm, k physical copies of the gate are needed, citing the lack of loops in quantum circuits.
  • Another participant counters that while physical qubits are the actual components, gates are more virtual and can be generated on the fly, meaning no physical copies are necessary at the quantum level.
  • A participant expresses gratitude for the clarification about gate implementation and seeks references for further understanding.
  • There is a discussion about whether a single physical device can be used to construct a circuit where the gate appears multiple times, with some suggesting that it is possible depending on the definitions used.
  • One participant mentions that gates are manipulations of qubits and can be implemented through various physical means, such as laser pulses or electric and magnetic fields.
  • Another participant reiterates the question of reusing a single physical device in a circuit and concludes that it is not impossible in principle.
  • A participant shares a reference to an article about realizing a universal quantum gate with trapped ions, suggesting it may be of interest to others.

Areas of Agreement / Disagreement

Participants express differing views on the physical versus logical representation of gates and their reuse in quantum circuits. There is no consensus on the implications of these differences for constructing circuits in quantum computation.

Contextual Notes

The discussion highlights the complexity of defining physical and logical constructs in quantum computing, as well as the assumptions underlying the participants' arguments regarding gate implementation and reuse.

Who May Find This Useful

This discussion may be useful for individuals interested in quantum computing, particularly those exploring the implementation of quantum algorithms and the physical realization of quantum gates.

LLSM
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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?
 
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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.
 
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?
 
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.
 
Last edited:
LLSM said:
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.

LLSM said:
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.

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