Implementation method of fault-tolerant logic h-gate based on rmqc code
A fault-tolerant logic and implementation method technology, applied in the field of quantum computing and quantum error-correcting codes, can solve the problems of high resource consumption, fault-tolerant logic H gate implementation process, and no consideration of single-qubit, etc., to improve scalability, avoid The effect of repeated measurements
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Embodiment 1
[0045] This embodiment is used in the coded state |Ψ> RMQC(4) Fault-tolerant logic H gates are implemented.
[0046] refer to figure 1 , the present invention comprises the following steps:
[0047] Step 1) For the encoded state |Ψ> RMQC(4) Add an H gate for each qubit of :
[0048] pair containing three stable subgroups and The encoded state of |Ψ> RMQC(4) After numbering the 15 qubits in , add the H gate to get the intermediate state where |Ψ> RMQC(4) The number of stabilizers included is 14, which are Contains 4 X stabilizers, 4 Z stabilizers included, and Contains 6 Z stabilizers;
[0049] Step 2) Get three stable subgroups and The symptom value corresponding to each stabilizer in :
[0050] Step 2a) Yes The Z stabilizer in and The X stabilizers in are measured separately to get the symptom value corresponding to each Z stabilizer Symptom value corresponding to each X stabilizer i∈{1,2,...,6}, j∈{1,2,...,4}, get symptom value for:
[0051...
Embodiment 2
[0093] This embodiment is the same as step 1) to step 4) and step 7) to step 8) in embodiment 1, only step 5) and step 6) have been modified, for the coded state |Ψ> RMQC(5) Fault-tolerant logic H gates are implemented.
[0094] refer to figure 1 ,
[0095] Step 5) to All Z stabilizers included are grouped:
[0096] In each x-model contained in the 5-model, the two vertices of the inner model and the outer model respectively belong to Z stabilizer Bilaterally stabilized subgroups x∈{4,5}, index∈{1,2,...,(x-1)×2 5-x}, all x-models correspond to two-sided stable subgroups Combined into a set of bilaterally stable subgroups in:
[0097]
[0098]
[0099] in:
[0100]
[0101]
[0102]
[0103]
[0104] Also divide each x-model contained in the 5-model other than Z stabilizer Combined into one-sided stabilized subgroups All x-models correspond to one-sided stable subgroups Combined into a set of one-sided stable subgroups in:
[0105]...
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