Questions tagged [quantum-gate]

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

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What is the input when simulating a quantum state?

Currently I am simulating a quantum gate using verilog. I learned that: $$|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$$ I want to ask: when simulating, should I let alpha and beta be complex ...
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1 vote
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Generating Equal Amplitude Superposition States from Another Equal Amplitude Superposition State

Can we prepare a state regarding a transformation in quantum computing that seems to generate another equal amplitude superposition state when applying a Hadamard gate? Specifically, I observed that ...
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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 ...
• 1,065
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Can we somehow relate quantum volume with the total number of gates present in a circuit which the machine can succesfully run without large errors

Let's say I have a circuit which contains x number of gates and a machine with quantum volume y, Can I relate x and y somehow to determine if the circuit can be succesfully run on the machine without ...
938 views

Does the Quantum Fourier Transform require universality?

Background: In most setups of fault-tolerant quantum computation, universality is achieved using Clifford gates such as $(S, H, \text{CNOT})$ and the $T$-gate. The Eastin-Knill theorem can be ...
38 views

Proof that if W is the image of a Unitary operator with an $n^O(1)$ size quantum circuit, then $R_W$ has an $n^O(1)$ circuit as well

I have been working on the following problem Suppose $H$ is the Hilbert space of n qubits. Let $W_0$ be the subspace of $H ⊗ H$ with basis $|x_0⟩$, x = 0,...,N −1 where $N = 2^n$. Suppose $U$ is a ...
1 vote
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Proability of measuing a qubit in a two qubit system without having a perpendicular basis

I am trying to understand how to apply Born's rule on two qubit systems. From class, the teacher told us that we can write the state like so: only if $\theta_0$ and $\theta_1$ are ortogonal. But now ...
146 views

how to construct a ((7,2,3)) code and verify its properties

These two recent papers describe a process to construct (non-stabilizer) codes with "exotic" transversal gates : paper1 paper2 Most of the codes have distance $d=2$ which makes them less ...
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Connection between a Pauli measurement and the corresponding Pauli gate?

Suppose I have a qubit and the ability to act a Pauli $Z$ gate on it. This is a black box that does the phase flip and I don't know how it works on the inside. Can I use this black box to implement a ...
1 vote
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How to calculate quantum cost?

In the following two papers: Automatic Synthesis of Reversible Logic Circuit Based on Genetic Algorithm Particle Swarm Optimization based Circuit Synthesis of Reversible Logic a comparison ...
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1 vote
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Is this quantum circuit design more prone to noise?

I am designing a quantum circuit which uses one qubit as the control of many $\text{CSWAP}$ operations. And then, this qubit will be measured. Will the result be more prone to noise since all the ...
294 views

Clifford group without the phase gate

The Clifford group is generated by the Hadamard gate $H$, the phase gate $S=\sqrt{Z}$, and the $\text{CNOT}$ gate. I was wondering what happens if we dropped $S$, so that all matrices are real. I ...
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How to Use Stim for Noisy Simulation with Adaptive Circuit and Noise Tracking?

I am trying to learn stim to simulate noisy quantum circuits. My goal is to construct an adaptive circuit in which I can add quantum gates one by one and observe the changes in the circuit's check ...
27 views

What is the role of color in color code? ( theoritically and exprimentally)

We know that the color code has an extra element relative toric code . It is color . I want to know what is the role of color ?
1 vote
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Two-level unitary gates are decomposed into single-qubit gates and CNOT gates

I am currently studying the following from the book 'QUANTUM COMPUTING: From Linear Algebra to - Mikio Nakahara' and trying to apply it to Qiskit. But there is one point that I don't quite understand....
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How is involution defined for qudit gates?

A gate is involutory if $G^{2}=I$. This is true for all Pauli gates. Does the definition change if it is a gate for qutrits and beyond? Is there a good article for this?
1 vote
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Transversal CNOT implementation on stim

Re: a recent paper on the arXiv, Correlated decoding of logical algorithms with transversal gates (https://arxiv.org/abs/2403.03272). As MWPM (pymatching and stim) cannot handle errors that flip more ...
207 views

Why do we have an infinite number of possible quantum gates?

This question came to me during an online lecture by Prof. Nike Dattani, he mentioned that we have "an unlimited number of quantum gates". Simply my question is: why do we have an unlimited ...
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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 ...
123 views

What are the quantum gates necessary for universal quantum computation?

I recently have gained an interest in quantum computers and quantum computation, and I was wondering, what is the minimum number set of quantum gates that allow for arbitrary quantum computation?
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