5 votes
Accepted

Injecting arbitrary rotations into the surface code

Generally speaking, you would never do a $\pi/2^{10}$ rotation by physical injection and distillation. It would be horrendously expensive. It's far cheaper to use a series of T and H gates to ...
Craig Gidney's user avatar
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4 votes
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15-to-1 distillation protocol: why is the probability of error of the distilled state $35p^3$ and not $\binom{15}{3} p^3=455p^3$?

It's because not every triplet is a failure. Most are detected. A basic error is for one of the T gates to instead be Z*T. There are 15 T gates. Each of the 15 possible basic errors has a unique ...
Craig Gidney's user avatar
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3 votes

Magic state distillation of physical vs logical qubit

You would distill at the physical level whenever the fidelity of the output state is lower than the fidelity of your physical operations and storage. For magic states, my guess is you would never do ...
Craig Gidney's user avatar
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3 votes
Accepted

How to prove that the distillable entanglement satisfies $E_D(|\psi_d\rangle\!\langle\psi_d|)\ge \log d$?

The distillable entanglement of this state is equal $\log d$ by definition. Thus, both $E_D(\lvert \psi_d\rangle\langle\psi_d\rvert)\ge \log d$ and $E_D(\lvert \psi_d\rangle\langle\psi_d\rvert)\le \...
Norbert Schuch's user avatar
2 votes
Accepted

Understanding entanglement distillation via stabilizer codes?

In stabilizer circuits, there's an equivalence between a qubit's worldline just sitting around and a Bell pair preparation or measurement linking two qubits. This is the basis of quantum teleportation,...
Craig Gidney's user avatar
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2 votes

15-to-1 distillation protocol implemented with lattice surgery: don't we loose transversality by commuting Clifford toward measurements?

We don't actually care about the fact that the T gates are "transversal". That's just a way of explaining why the circuit works. The underlying thing we care about is the fact that replacing ...
Craig Gidney's user avatar
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1 vote
Accepted

15-to-1 distillation protocol in lattice surgery: doesn't the potential rejection of the level-1 magic states makes it last longer than $15$ timestep?

Yes, it takes slightly longer on average due to discards. If the injection error rate is 0.1%, then your first stage factory will discard 1-0.999^15 ~= 1.5% of the time. Accounting for this increases ...
Craig Gidney's user avatar
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