# Questions tagged [quantum-gate]

For questions regarding usage, performance, implementation, application or theory related to quantum gates.

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### How are gates implemented in a continuous-variable quantum computer?

I've mostly worked with superconducting quantum computers I am not really familiar with the experimental details of photonic quantum computers that use photons to create continuous-variable cluster ...
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### What is the difference between quantum control and quantum optimal control?

In the context of quantum control theory, it is common to see references to both quantum control and quantum optimal control (e.g. 0910.2350 or the guide on qutip quantrum control functions). ...
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### Given a decomposition for a unitary $U$, how do you decompose the corresponding controlled unitary gate $C(U)$?

Suppose we have a circuit decomposition of a unitary $U$ using some universal gate set (for example CNOT-gates and single qubit unitaries). Is there a direct way to write down the circuit of the ...
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### Symmetry of tensor product w.r.t. Vazirani 2-qubit video

Quantum Computing (QC) pioneer Vazirani has graciously long provided some nice videos on an intro to QC. E.g. in "2 qubit gates + tensor product" (2014) he introduces the tensor product w.r.t. QC ...
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### What is the mathematical justification for the "universality" of the universal set of quantum gates (CNOT, H, Z, X and π/8)?

In this answer I mentioned that the CNOT, H, X, Z and $\pi/8$ gates form a universal set of gates, which given in sufficient number of gates can get arbitrarily close to replicating any unitary ...
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### How are quantum gates implemented in reality?

Quantum gates seem to be like black boxes. Although we know what kind of operation they will perform, we don't know if it's actually possible to implement in reality (or, do we?). In classical ...
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### How are elementary quantum gates realised?

When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions. In some sense, these are rather mysterious objects, in that they perform "...
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### How does evolving a two-qubit state through a CNOT gate entangle them?

Reading into CNOT gate I understand that, mathematically, such a gate entangles the control qubit and the target. (the resulting state is $\frac{1}{\sqrt 2}(|00\rangle+|11\rangle)$) However, looking ...
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### New algorithm for faster QC simulation by IBM

This new algorithm for QC calculation was introduced recently (2017 4Q) by IBM/ Pednault et al. to great fanfare. The paper seems more couched in the language of physics. Are there any basic ...
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### Why is it important to eliminate the garbage qubits?

Most reversible quantum algorithms use standard gates like Toffoli gate (CCNOT) or Fredkin gate (CSWAP). Since some operations require a constant $\left|0\right>$ as input and the number ...
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### How does Fourier sampling actually work (and solve the parity problem)?

I'm writing with respect to part I and part II of the Fourier sampling video lectures by Professor Umesh Vazirani. In part I they start with: In the Hadamard Transform: |0...0\rangle \to \sum_{\{...
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### If all quantum gates must be unitary, what about measurement?

All quantum operations must be unitary to allow reversibility, but what about measurement? Measurement can be represented as a matrix, and that matrix is applied to qubits, so that seems equivalent to ...
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### If quantum gates are reversible how can they possibly perform irreversible classical AND and OR operations?

Quantum gates are said to be unitary and reversible. However, classical gates can be irreversible, like the logical AND and logical OR gates. Then, how is it possible to model irreversible classical ...
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Quantum gates are represented by matrices, which represent the transformations applied to qubits (states). Suppose we have some quantum gate which operates on $2$ qubits. How does the quantum gate ...