Questions tagged [logical-gates]

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How to figure out the action of a circuit form its effect on logical operators?

I am looking at the following circuit from "The Heisenberg Representation of Quantum Computers" by Daniel Gottesman. I understand how the circuit acts on the logical operators. I understand ...
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What is the explicit action of the following circuit?

Would somebody please be able to explain the action of this circuit to me? (Taken from Arthur Pesah's blog post "Computing with Quantum Codes using Transversal Gates") I understand overall ...
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Why is the first logical unitary gate in this example fault tolerant?

From Arthur Pesah's blog on "Computing with Quantum Codes using Transversal Gates", found here: https://arthurpesah.me/blog/2023-12-25-transversal-gates/ He gives the following examples of ...
am567's user avatar
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2 votes
2 answers
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Implementing error correction (from physical qubit point of view)

I have worked with physical qubits, and I am fairly familiar with gates and sequences from initialisation to readout. I don't know much about error correction, and I love to learn how error correction ...
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Can quantum algorithms include conditional jumps/change an instruction pointer?

From what I've seen (in talks for a general physics audience, but I'm not in the field of quantum computing), all or most quantum algorithms are fixed sequences of instructions applied to registers ...
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3 votes
1 answer
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Smallest stabilizer codes with transversal CCZ or CS gates?

It has been shown that $[[15,1,3]]$ quantum Reed-Muller code is the smallest stabilizer code with a transversal T gate. What are the smallest codes with transversal CCZ or CS gates (which are the ...
tomek's user avatar
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2 votes
1 answer
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Understanding the operation of commutation of stabilizer operators

I want to show that the stabilizer operators ($M_{0}, M_{1}, M_{2}, M_{3}$) for the 5-qubit quantum error correcting code: If $M_{1} = [XXZIZ]$ and $M_{2} = [XZIZX]$ They commute iff $[M_{1},M_{2}]=0$....
am567's user avatar
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Verifying CNOT on different qubits of a 3 - qubit system yields this measurement state

Below is a circuit involving two CNOT unitary gates that yields a post - measurement state $|a, b, a \oplus b \rangle$. I am struggling to convince myself this is true. Let $|a\rangle, |b\rangle$ be ...
Physkid's user avatar
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How to perform the $2\pi$ pulse in the two-ion Cirac-Zoller CNOT gate?

When implementing the Cirac-Zoller CNOT gate between two ions $A$ and $B$, the second step of the procedure changes the sign of the second ion when the ion is in its ground state $|0_B\rangle$ and the ...
grav.field's user avatar
1 vote
1 answer
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Using Pymatching to decode lattice surgery process

I want to simulate the error correction procedure for a CNOT gate on surface code and RHG cube, made by the lattice surgery process of "merge and split". In this case, the code has an H-...
Yaron Jarach's user avatar