Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [toffoli-gate]

10 questions
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How to prove that this family of gates is in the Clifford Hierarchy?

Apologies. In the previous version of this question I drew the wrong circuit family. That circuit was order 6 and, therefore, by my own result (arxiv.org/2410.04711) the family was not in the Clifford Hierarchy. The description of the problem was…
Jonas Anderson
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Understanding Knill-Gottesman theorem: what role does the Toffoli gate play?

I’m trying to understand the relationship between the Toffoli gate, Clifford gates, and the classical simulation of quantum circuits. -I know that the Toffoli gate is universal for classical computation, since it can simulate gates like NAND. -I’m…
Tom_tomato
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When building a Toffoli gate, why add an S-gate instead of a simpler form

Refer to Quantum Computation and Quantum Information 10th Anniversary Edition exercises 4.21, 4.22, and 4.24. We all know that the Toffoli gate can be represented differently in the following form. It follows from the following conclusion. That is,…
user35586
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Is it possible to approximately compile Toffoli using H and CSWAP?

Question: Given all controlled-SWAP (CSWAP) and Hadamard (H) gates on 3 qubits, is it possible to approximately compile the Toffoli (CCX) gate? Discussion From basic simulations, it appears that all $\text{CSWAP}$s and $H$s on 3 qubits generate an…
Jonas Anderson
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Can you decompose a 4-qubit Toffoli gate (CCCX) into basic gates without an ancillary state?

I have a problem relevant to the circuit depth of a $\text{CCCX}$ gate, but I can't find any literature on decomposing this gate into basic gates without an ancillary qubit. Is this possible, and are there any sources where I can read about this?
Braedin Tabler
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Circumventing the Eastin-Knill theorem by means of Shor's fault tolerant Toffoli gate

I have been reading about the Eastin-Knill theorem, which states that no quantum error correction code can can transversely implement a universal gate set. In this context, for example, the surface code admits Clifford gates in a transversally,…
Josu Etxezarreta Martinez
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Is there a quantum error correcting code that has a transversal toffoli gate?

Given that Shor's algorithm is mostly Toffolis, it would be nice to run these gates transversally while leaving the less used gates up to distillation/cultivation. There are codes with transversal CCZs but this would call for the need to teleport…
Victory Omole
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Showing the Toffoli gate can be constructed from one-qubit gates using computer matrix multiplication

I need help coming up with the code that I can use in a computer algebra system like Sage, Python, or Mathematica that can evaluate the circuit. I am not a programmer and used ChatGPT to try to help me create the code. However, I believe these are…
user2521987
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Intro book on classical and quantum computing by Thomas G Wong

Looking at his book, and am obviously new to studying this. Could someone help explain to me how the truth table is valid here? To my understanding, when $C=0$, the circuit behaves like a reversible AND gate, and when $C=1$, it acts as reversible…
anthony
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How to implement multi controlled X gates in Qasm

I wanted to know the easiest way to implement a large multi controlled x gate using Qasm and not Qiskit, if it's possible
beginnerCoder7
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