5 votes
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Does a $[\![3,1,2]\!]$ code exist?

No, there is no $[\![3,1,2]\!]$ code. Background As in classical error correction, existence of quantum codes can often be ruled out using a range of inequalities that codes must satisfy. Indeed, the ...
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4 votes
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Stabilizer codes and 1,-1 coefficients

Yes, any stabilizer codespace is a linear span of stabilizer states. Any stabilizer state has a power of 2 non-zero amplitudes, which are $\pm 1, \pm i$ up to a common factor. See Eq. (2) in https://...
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4 votes

What is the difference between Error Mitigation (EM) and Quantum Error Correction (QEC)?

Error correction: make each shot good Error mitigation: extract good signal from bad shots Error mitigation focuses on techniques for noticing that a shot is bad, or for quantifying how a shot is bad. ...
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4 votes
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What is the difference between Error Mitigation (EM) and Quantum Error Correction (QEC)?

The basic difference is that QEC involves the detection and correction of errors that occur during computation, while EM schemes allow errors to occur and try to compensate for the negative effects of ...
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3 votes

What is the difference between Error Mitigation (EM) and Quantum Error Correction (QEC)?

Here is a partial answer for the questions you've made. Quantum Error Mitigation is a way of mitigating errors in NISQ devices. When full Quantum Error Correction will be possible there will be no ...
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2 votes
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Different codes with the same parameters

Example 1 The $3\times 3$ rotated surface code and the $9$-qubit Shor's code are both $[\![9,1,3]\!]$ codes. They are inequivalent under local unitaries since the logical states have different ...
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2 votes

stim: how to control sign of syndrome measurements

Basically what you are trying to solve is: what Paulis do I insert to flip the sign of one stabilizer, but not the others or the logical qubit. The easiest way to solve this problem is to not consider ...
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2 votes
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Example non-stabilizer code?

You're looking for non-additive quantum codes. There are many examples but I'll refer you to the seminal paper by Rains, Hardin, Shor & Sloane: https://arxiv.org/abs/quant-ph/9703002. There's also ...
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2 votes
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Does every code have transversal Pauli group?

Remember that the definition of the code space (which determines the distance of the code) and the logical operators within the code space are effectively separate, and the choice of logical operators ...
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1 vote
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How to train neural network decoder with stim?

Stim has various options for outputting the observables in addition to the detection events. For your use case I recommend using ...
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