# Questions tagged [quantum-gate]

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

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### Can you programatically check whether a given set of gates is universal?

I am wondering if there is an automated way to determine whether a given set of quantum operations is universal. More precisely given a set of 1 and 2 qubit gates can we write a program to determine ...
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### Sequential circuit using quantum gates

Without feedback/loop how can we build a sequential circuit? The basic feature of sequential circuit is that is depends not only on the current inputs but also on the previous inputs/outputs. I've ...
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### Universal gate set for the $[[15,1,3]]$ code

The $[[15,1,3]]$ triorthogonal code implements transversal $T$. Since it is a CSS code, two blocks will also have a transversal $CNOT$ gate. To get a universal gate set all that is required is ...
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### Resources on the energy consumption of IBM quantum computers?

I am seeking information regarding the energy consumption of IBM Quantum Computers, specifically inquiring about the energy requirements associated with individual gate operations. Could you also ...
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### Solovay-Kitaev Balanced Group Commutators in SU(2) Implementation

I am currently looking into quantum compilation and came across Dawson and Nielsen's paper on the Solovay-Kitaev Algorithm, which seems like a good starting point as it is referenced in a many of the ...
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### Postselection and hardness of estimating amplitudes

Let $A$ be a class of quantum circuits such that $$\text{Post}A = \text{Post}BQP,$$ where $\text{Post}$ indicates post-selection. Is only this amount of information ...
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### Is the universality of a qubit based quantum computer different from the universality of a continuous-variable quantum computer?

I understand that a quantum computer is universal if it can compute anything that a quantum Turing machine can. Another way to think about universality is that any unitary transformation on, e.g., a ...
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### Equivalence checking of quantum circuits up to error

Suppose you are given two circuit descriptions $A$ and $B$ where by a circuit description I mean a sequence of gates (in the order they are applied) and the qubits they are applied on. (For the sake ...
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### How many qubits and how many gates, are required for finding the eigenvalues of a matrix?

Say I have an $N \times N$ matrix and I want to know the eigenvalues to a precision of $\pm \epsilon$. How many qubits and how many gates do I need?
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### How exactly is the stated composite state of the two registers being produced using the $R_{zz}$ controlled rotations?

This is a sequel to How are two different registers being used as "control"? I found the following quantum circuit given in Fig 5 (page 6) of the same paper i.e. Quantum Circuit Design for ...
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### Where does this upper bound relating the $T$ count and $H$ count come from?

I am reading this paper on optimisation of the Hadamard gate count (Optimal Hadamard Gate count for Clifford + $T$ synthesis of Pauli rotations sequences). The idea of the paper is to optimise the ...
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### A measure of entanglement created by a unitary operation

Let $U$ be a unitary matrix acting on a 3-qubit system. If there is no correlation among any pairs of the three qubits, the unitary operation can be represented as $U = U_1 \otimes U_2 \otimes U_3$, ...
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### What other discrete non-trivial non-Clifford groups of gates are there?

I do not know many groups (as in group theory) of quantum gates. Aside from trivial ones, I know there is Pauli group and the Clifford group. Recently I discovered another interesting group generated ...
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### Gate times for different qubit technologies

Different qubit technologies exist and for each, operations are implemented differently. My question is what the typical times are for the standard gates (single qubit rotations, Hadamard, CNOT, T, ...
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### Understanding shared Bell states from quantum entanglement

I'm trying to understand an entanglement swapping derivation provided in this PDF (pages 2 - 3) I have several things about this process that I don't understand, and I was hoping someone could ...
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### Identity Gate Timing Discrepancy

I have been examining problems where gate timing is important. When implementing an identity gate, the issue of timing has resulted in a few verification experiments to compare the gate time to that ...
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