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Morphing Quantum Codes
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DOI：10.1103/PRXQuantum.3.030319.png)
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Abstract
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We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a [[10,1,2]] code that is the smallest-known stabilizer code with a fault-tolerant logical T gate. In addition, we construct a family of hybrid color-toric codes by morphing the color code. Our code family inherits the fault-tolerant gates of the original color code, implemented via constant-depth local unitaries. As a special case of this construction, we obtain toric codes with fault-tolerant multiqubit control-Z gates. We also provide an efficient decoding algorithm for hybrid color-toric codes in two dimensions and numerically benchmark its performance for phase-flip noise. We expect that morphing may also be a useful technique for modifying other code families such as triorthogonal codes.
Keywords:
MAGIC-STATE DISTILLATION
COMPUTATION
THRESHOLD
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11
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919
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PHYSICAL REVIEW B
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PHYSICAL REVIEW BIF3.7
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