Implementation method of a fault-tolerant logic H gate based on an RMQC code

Abstract

The invention provides an implementation method of a fault-tolerant logic H gate based on an RMQC code, and solves the problems of non-fault tolerance caused by the fact that a single quantum bit error is not considered and large resource consumption caused by repeated measurement of a stabilizer. The method comprises the following implementation steps: adding an H gate to a coded state to obtainan intermediate state; measuring the stabilizers to obtain symptom values; according to the symptom value, obtaining the type and position of a single quantum bit error; establishing a graph model ofthe RMQC code; Performing geometric classification on the stabilizers; grouping the stabilizers according to the geometric types of the stabilizers and determining repair operators corresponding to the stabilizers; correcting the symptom value according to the single quantum bit error, and determining a repair operator for repairing the intermediate state according to the corrected symptom value;and then adding the repair operator and the single quantum bit error to the intermediate state. The method has the advantages of fault tolerance and high resource utilization rate, and can be used forrealizing the fault-tolerant general logic gate set in the quantum computer.

Description

technical field

[0001] The invention belongs to the technical field of quantum computing and quantum error correction codes, and relates to a method for realizing a fault-tolerant logic H gate, in particular to a method for realizing a fault-tolerant logic H gate based on RMQC codes, which can be applied to fault-tolerant general logic gates in quantum computers realization of the set. Background technique

[0002] Quantum computing has attracted the attention of people from all walks of life because of its potential powerful computing power. Its essence is to use quantum coherence to complete quantum computing. However, in practical applications, maintaining this state of quantum coherence is very difficult. Therefore, in order to realize quantum computing, a key issue is to overcome the phenomenon of quantum decoherence. Coding qubits is one of the effective ways to solve this problem, so people have invested a lot of energy in quantum error-correcting codes. However, t...

Examples

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 with 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 with 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:

[00...

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]...

technical field

[0001] The invention belongs to the technical field of quantum computing and quantum error correction codes, and relates to a method for realizing a fault-tolerant logic H gate, in particular to a method for realizing a fault-tolerant logic H gate based on RMQC codes, which can be applied to fault-tolerant general logic gates in quantum computers realization of the set. Background technique

[0002] Quantum computing has attracted the attention of people from all walks of life because of its potential powerful computing power. Its essence is to use quantum coherence to complete quantum computing. However, in practical applications, maintaining this state of quantum coherence is very difficult. Therefore, in order to realize quantum computing, a key issue is to overcome the phenomenon of quantum decoherence. Coding qubits is one of the effective ways to solve this problem, so people have invested a lot of energy in quantum error-correcting codes. However, t...

Examples

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 with 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 with 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:

[00...

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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