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CSS型量子卷积码的编译码方法
Introduction
CSS(Calderbank-Shor-Steane)quantumerror-correctingcodesareessentialforprotectingquantuminformationfromerrorsthatariseduetonoisyenvironments.OneofthemostimportanttypesofCSScodesisCSS-likestabilizercodes,whichareformedbyconcatenatingtwostabilizercodestoobtainalargerstabilizercode.Quantumconvolutionalcodesareobtainedbyreplacingclassicalconvolutionalcodeswithquantumcodes,whichcanbeusedinanoisyquantumchannel.Inthisarticle,wediscussthecodinganddecodingmethodsofCSS-typequantumconvolutionalcodes.
CSS-typeQuantumConvolutionalCodes
Quantumconvolutionalcodesaretheanalogofclassicalconvolutionalcodesandprovideapowerfulmeansofencodinginformationinaquantumsystem.Aquantumconvolutionalcodehastwocomponents:theencoderandthedecoder.Theencodermapsaninformationsequencetoaquantumstatethatcanbetransmittedoverthenoisyquantumchannel,whilethedecodermapsthereceivednoisyquantumstatetoanestimateoftheoriginalinformationsequence.
CSS-typequantumconvolutionalcodesareaspecialclassofquantumconvolutionalcodesthatarebasedonCSScodes.SuchcodesareconstructedbyconcatenatingtwoCSScodesthatareallowedtovarywithtime.TheCSS-likestabilizercodesareformedbyconcatenatingtwostabilizercodestoobtainalargerstabilizercode.TheadvantageofsuchcodesovertraditionalCSScodesisthattheycancorrectalargernumberoferrorsinashorteramountoftime,andtheyaremoreefficientintermsofqubitusage.
CodingofCSS-typeQuantumConvolutionalCodes
ThecodingofaCSS-typequantumconvolutionalcodeinvolvesthefollowingsteps:
Step1.ConstructionoftheEncoder
TheencoderisconstructedbyconcatenatingtwoCSScodesthatareallowedtovarywithtime.Thetime-varyingCSScodecanbeobtainedbyaddingadditionalqubitstoanexistingCSScode.Thetimeevolutionofthequbitsisgivenbyaunitaryoperator,whichisappliedatregularintervalsoveracontinuoustimeinterval.
Step2.MappingoftheInformationSequence
Theinformationsequenceismappedtoaquantumstatebyapplyingaunitaryoperationtothequbits.TheunitaryoperationischoseninsuchawaythatitsatisfiestheCSScondition.Thisensuresthatthequantum