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Energy and degeneracy of the ground state and excitations of the toric code

One of the major points of the Toric code Hamiltonian is that all the terms commute, each of which as $\pm 1$ eigenvalues. So, to find the ground state, you need something that is the $+1$ eigenstate ...
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What is the actual probability of not losing information (in a depolarizing channel)

I'm not sure what you mean by the probability of not losing information. The entropy of the qubit's mixed state after the depolarizing channel is higher than it was before the depolarizing channel. ...
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Why does code switching not allow for universal fault-tolerant quantum computation?

One reference is here. The authors switch between the 7-qubit Steane code and 15-qubit Reed-Muller code. Clifford group operators can be performed in the Steane code, and the T-gate in the 15-qubit ...
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Scaling of magic state distillation with single & two-qubit gate error

The physical gate error rates determine the initial magic state fidelity you are starting from, and how big of a code distance you need for the factories as you boost the fidelity. The initial ...
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Lattice surgery: how is merged code stabilized by 'merging stabilizers' if their measurement outcome can be -1?

As far as computation goes, it doesn't matter whether the state stabilized by a stabilizer or its negation. What matters is that you know the sign of the stabilizer with confidence, via the ...
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Prove that the Bures metric satisfies a contractive property and has unitary invariance

Contractivity refers to the fact that, under the action of any CPTP map $\mathcal{E}$, a given metric satisfies $M(\rho,\sigma) \geq M(\mathcal{E}(\rho), \mathcal{E}(\sigma))$. Unitary invariance ...
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2 ways to do the three qubits bit-flip code

The question is "why do we need two more ancillary qubits in the second algorithm ?" The answer is in the no-cloning theorem: "by the qbits nature, they cannot be copied you can only ...
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The statevector of three-qubit bit-flip encoding circuit for entangled state

The method Statevector.evolve()[1] returns the evolution result. It does not change the instance it called in. So all what you need is to change your code to become:...
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The statevector of three-qubit bit-flip encoding circuit for entangled state

I suggest you make 2 repetition logical qubits first and entangle them with logical CNOT operator. you can check every single steps separately. Make $|+_L\rangle_{Alice} = {1\over\sqrt{2}} (|000 \...
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Is fault-tolerant computation easier than we thought?

The problem is that the code defined by $G$ is not error-detecting at all. As is explained bellow, the logical operators of that code are just $X_5$ and $Z_5$, so it has distance $1$ and cannot detect ...
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How can a finite set of gates be universal?

$\{H,CCZ\}$ is just the generating set. The set of gates it generates, i.e. $\langle H, CCZ \rangle$, has an infinite number of gates so it could be universal. The argument in Eastin-Knill says the ...
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