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5 | 5 | State-of-the-art quantum devices, such as IBM's Condor and Atom Computing's optical lattices, contain more than |
6 | 6 | a thousand qubits. Does this qubit count suffice for valuable quantum algorithms with clear speedups? |
7 | 7 | The reality is that there is more to the story than the sheer number of qubits. As we currently stand, quantum |
8 | | -devices are still prone to errors that increase with device size. For this reason, **quantum error correction**--one of the most important domains in the universe of quantum computing--has |
| 8 | +devices are still prone to errors that increase with device size. For this reason, **quantum error correction**-one of the most important domains in the universe of quantum computing-has |
9 | 9 | been gaining traction. |
10 | 10 |
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11 | 11 | Quantum error correction is implemented through **error correction codes,** which come in many varieties that address different error types. |
@@ -506,7 +506,7 @@ def classify_pauli(operator, logical_ops, generators, n_wires): |
506 | 506 | # ----------------------------------- |
507 | 507 | # |
508 | 508 | # The 5-qubit code, also called as Laflamme's code [#Laflamme1996]_, holds a special place as the smallest |
509 | | -# error correcting code capable of correcting arbitrary Pauli Errors--unwanted applications of :math:`X,` :math:`Y,` or :math:`Z` |
| 509 | +# error correcting code capable of correcting arbitrary Pauli Errors---unwanted applications of :math:`X,` :math:`Y,` or :math:`Z` |
510 | 510 | # gates on a single qubit. In this section, we will build and implement the complete error correction procedure |
511 | 511 | # starting from its stabilizer generators: |
512 | 512 | # |
@@ -558,7 +558,7 @@ def classify_pauli(operator, logical_ops, generators, n_wires): |
558 | 558 | # |
559 | 559 | # \vert \bar{1}\rangle = X_1 X_2 X_3 X_4 X_5 \vert \bar{0} \rangle. |
560 | 560 | # |
561 | | -# The logical operators bit-flip and phase-flip are for this code are :math:`\bar{X}= X^{\otimes 5}` and :math:`\bar{Z}=Z^{\otimes 5}.`` |
| 561 | +# The logical operators bit-flip and phase-flip are for this code are :math:`\bar{X}= X^{\otimes 5}` and :math:`\bar{Z}=Z^{\otimes 5}.` |
562 | 562 | # |
563 | 563 | # Let us implement this encoding circuit in PennyLane. |
564 | 564 |
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