Abstract
To control a quantum system, recently the coherent feedback method has attracted wide attention thanks to its several advantages over the conventional measurement-based feedback method. However, for nonlinear quantum systems, no systematic guiding principle for designing a coherent feedback controller has been known, while for the measurement case one can employ the so-called quantum non-demolition (QND) feedback method as a systematic strategy. In this paper, we develop a coherent feedback counterpart of this QND-based control strategy. The effectiveness of this proposal is evaluated in some control problems; qubit stabilization and single photon production.
| Original language | English |
|---|---|
| Pages (from-to) | 11760-11763 |
| Number of pages | 4 |
| Journal | 20th IFAC World Congress |
| Volume | 50 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2017 Jul |
Keywords
- Quantum control
- coherent feedback
- single photon
ASJC Scopus subject areas
- Control and Systems Engineering
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In: 20th IFAC World Congress, Vol. 50, No. 1, 07.2017, p. 11760-11763.
Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Dispersive-dissipative control strategy for quantum coherent feedback
AU - Kashiwamura, Yoshiki
AU - Yamamoto, Naoki
N1 - Funding Information: Abstract: To control a quantum system, recently the coherent feedback method has attracted Abstract: To control a quantum system, recently the coherent feedback method has attracted Abstract: To control a quantum system, recently the coherent feedback method has attracted fweieddebaactktemnteitohnodt.hHanokwsevteor,iftosr sneovnelrianleaardqvuanantatguems soyvsetremths,encoosnyvsetnetmioantaicl gmuiedaisnugrepmrienncti-pbleasfeodr wide attention thanks to its several advantages over the conventional measurement-based feedback method. However, for nonlinear quantum systems, no systematic guiding principle for feedback method. However, for nonlinear quantum systems, no systematic guiding principle for designing a coherent feedback controller has been known, while for the measurement case one can designing a coherent feedback controller has been known, while for the measurement case one can employ the so-called quantum non-demolition ΛQND) feedback method as a systematic strategy. employ the so-called quantum non-demolition ΛQND) feedback method as a systematic strategy. TInhteheifsfepcatpiveern,ewsse odfetvheilsoppraopcohsaelreisntevfaeeludabtaecdkincosuonmterpcoanrttroofl tphriosbQleNmDs;-bqausbeidt sctoanbtirloizlasttioranteagnyd. In this paper, we develop a coherent feedback counterpart of this QND-based control strategy. The effectiveness of this proposal is evaluated in some control problems; qubit stabilization and sTinhgeleffpehcotitvoennepsrsoodfutchtiiosnp.roposal is evaluated in some control problems; qubit stabilization and The effectiveness of this proposal is evaluated in some control problems; qubit stabilization and single photon production. © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Quantum control, coherent feedback, single photon Keywords: Quantum control, coherent feedback, single photon Keywords: Quantum control, coherent feedback, single photon 1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION To control a quantum system via feedback, we have two To control a quantum system via feedback, we have two To control a quantum system via feedback, we have two options in designing a controller; that is, the measurementfi boanseedwhfeicehdbiascckal(leMdFt)heschoehmereenatnfdeedtbhaeckno(nC-Fm)e.aTsuhreembaesnict one which is called the coherent feedback (CF). The basic one which is called the coherent feedback (CF). The basic strategy of MF is that, we first measure the target system strategy of MF is that, we first measure the target system and fed the measurement result back to control it. While tahned tMheilobruyrnofΛ2M00F9);haJsacboebesnΛ2w0e1l4l )]esatnadblissohmede i[mWpisoermtaannt the theory of MF has been well established [Wiseman aexnpderMimilbenutrsnhΛa2v0e0b9)e;enJadceombsonΛs2t0r1a4te)d] a[Snadyrsionmeet aiml.pΛo2r0t1a1n)t; experiments have been demonstrated [Sayrin et al. Λ2011); experiments have been demonstrated [Sayrin et al. Λ2011); Vijay et al. Λ2012)], we need to recall its critical draw- bTahcakt, isw,hbicehcauaseathreesfueeltdbliamckitsloothpeincvoonltvreosl spomerefocrlmasasniccael. back, which as a result limits the control performance. Tcohmapt oisn,ebnetscaΛudseetetchteorfes,edsibgancakl lporoopceinssvoorlsv,esansdomaectculaatsosircsa)l, components Λdetectors, signal processors, and actuators), components Λdetectors, signal processors, and actuators), the controller always suffers from significant signal loss the controller always suffers from significant signal loss Fig. 1. The schematic of the proposed CF control, for the Fig. 1. The schematic of the proposed CF control, for the and time delays. This is the main reason why recently the Fig. p1.roTbhleemscohfemgeanteircaotifntghea psqroupeeozseedd sCtFatec.ontrol, for the CmFethcoondtrfoolr hfeaesdabtatcrakccteodntmroul;chthaattteins,tiboencaus saeninaltperrinnactipivle problem of generating a squeezed state. method for feedback control; that is, because in principle problem of generating a squeezed state. method for feedback control; that is, because in principle In this paper, we propose a CF version of the above any CF loop does not involve any classical component, it aisnybaCsiFcallolyopfrdeoeefsronmot tihnevoalvbeovaen-ymcelnatsisoincaedl cdormawpobnaecnkt.,Iint In this paper, we propose a CF version of the above is basically free from the above-mentioned drawback. In In this paper, we propose a CF version of the above is basically free from the above-mentioned drawback. In mmnveennestttiionoignaedetdeQQitNDNs eDff-b-ebcasedatsievdenapaepsspprrwooiaatcchhhsffooromreccooennxttarrmololpllerelresdd.esieTsihgngencanaonndd- fact recently some important progress both in theory and mentioned QND-based approach for controller design and factrecentlysomeimportantprogressbothintheoryand itnnrovvleesspttiirgatgoacteeeduiittrsseeffecefoffecttthiivviseennmessesesthwiwoidtthhisomessomasefexeoxllampaomwps.lles.eFs.igThTuhreeconc1onis-- experiment have been reported in the research field of CF investigate its effectiveness with some examples. The con-experiment have been reported in the research field of CF thoel pphraosce-dspuareceorfetphriessemnteatthioond iilsluasstrafotilnlogwtsh. eFiidgeuarees1peis-[James et al. Λ2008); Gough and James Λ2009); Hamerly trol procedure of this method is as follows. Figure 1 is [James et al. Λ2008); Gough and James Λ2009); Hamerly chiaellpyhfaosre-tshpeacaesreepofressqeuneteazteiodnstilalutestgraentienrgattihone.idΛae)a Fesirpset-, and Mabuchi Λ2012); Iida et al. Λ2012); Yamamoto Λ2014); the phase-space representation illustrating the idea espe-aLniud eMt aabl.uΛc2h0i1Λ62)0]1. 2); Iida et al. Λ2012); Yamamoto Λ2014); cially for the case of squeezed state generation. Λa) First, andMabuchiΛ2012);Iidaetal.Λ2012);YamamotoΛ2014); ainalliynitfoiarltshteatceasiesopfrespqaureeedz.edInsttahtegfiegnuerrea,tiitoni.sΛgai)veFnirsbty, LiLiuu etet alal.. ΛΛ2016)2016)]].. anvainciutuiaml ssttaattee.isΛbp)reTpahreedsy.sItnemtheintfiegruarcet,s iwtiitshgaivepnrobye However, a systematic designing method of a CF controller anvainitiacuuml sstatatete.isΛb)preTpahered.sysItenmtheintfigeraurects, itwithis gaivepron bbye However, a systematic designing method of a CF controller afievldacthrouumugshtaated. iΛsbpe)rTsihvee csoyustpelminginHtaermaiclttsonwiaitnh, wahpicrhobies However, a systematic designing method of a CF controller field through a dispersive coupling Hamiltonian, which is isstilllacking,incontrasttothecaseofMFwherepar-itissicssuttillliallrlllayaccfkkoiirnnggt,,heiinnliccnooennattrrraacssattsettoothttheheeqccuaaassneetuoomff MMFvFerswwiohhenerreoefppatahrr-e- field through a dispersive coupling Ham1iltonian, which is ticularly for the linear case the quantum version of the represented by a Hermitian operator φ1. Then the joint lin∞ulaearrlyquafodrar thetic Galineusasriacnas[Ne theurdinquaetntaul.mΛ2v0e0rs9)]ionandof thethe represented by a Hermitian operator φ1. Then the joint syyrstotbem-pemf-iperldob,bethstetatstyestbeecomesmcomstaesteenptranonbglalbedidli;stificwalelymeasucehaasnugresthtoe H∞ control [James et al. Λ2008)] have been established. probe field, the system state probabilistically cchhaangngeess toto EsHpecciaonlltyr,olin[JtheamesMFetcalas.eΛ,2008)the qua] hanvteumbeenonn-estdeabmloilitioshedn. probe field, the system sta1 te probabilistically changes to Especially, in the MF case, the quantum non-demolition measurement.Inthefiguonmneeaofsufrtehmeeieingente.nIstntattthesseofffigφu1reφisgivenbyamomentumr,ewφhichiscgoirrevreenspboyndsdastomoothmheenQNtNumD ΛQND) based control for deterministic state stabilization opmeasueratrorempe,nint. Inwhitchhecfaigsuertehφe1coisndgiitvioennablysyastmemomsteantteumis ΛQND)basedcontrolfordeterministicstatestabilization measurement. In the figure φ1 is given by a momentum works very effectively, for a wide class of nonlinear quan-operator p, in which case the conditional system state is worksveryeffectively,forawideclassofnonlinearquan- operator p, in which case the conditional system state is tum systems [Mirrahimi and van Handel Λ2007); Inoue aa squeezed state. Λc) In the MF case, this probabilistic tum systems [Mirrahimi and van Handel Λ2007); Inoue chasqnugeeeszecdanstbaetec.omΛcp) eInnsattheed MbyFdcisapsela,ctinhgis tphreobstaabtielisutsic-★ This work was supported in part by JSPS Grant-in-Aid No. changes can be compensated by displacing the state us-★ This work was supported in part by JSPS Grant-in-Aid No. changes can be compensated by displacing the state us-1★5Kh06is15w1o.rk was supported in part by JSPS Grant-in-Aid No. intogchthaestimcecaosmupremnseanttiornespurlot.ceOssubryidaeacoihserteontredpilsascipeatthivies This work was supported in part by JSPS Grant-in-Aid No. ing the measurement result. Our idea is to replace this 15K06151. stochastic compensation process by a coherent dissipative 15K06151. stochastic compensation process by a coherent dissipative Publisher Copyright: © 2017
PY - 2017/7
Y1 - 2017/7
N2 - To control a quantum system, recently the coherent feedback method has attracted wide attention thanks to its several advantages over the conventional measurement-based feedback method. However, for nonlinear quantum systems, no systematic guiding principle for designing a coherent feedback controller has been known, while for the measurement case one can employ the so-called quantum non-demolition (QND) feedback method as a systematic strategy. In this paper, we develop a coherent feedback counterpart of this QND-based control strategy. The effectiveness of this proposal is evaluated in some control problems; qubit stabilization and single photon production.
AB - To control a quantum system, recently the coherent feedback method has attracted wide attention thanks to its several advantages over the conventional measurement-based feedback method. However, for nonlinear quantum systems, no systematic guiding principle for designing a coherent feedback controller has been known, while for the measurement case one can employ the so-called quantum non-demolition (QND) feedback method as a systematic strategy. In this paper, we develop a coherent feedback counterpart of this QND-based control strategy. The effectiveness of this proposal is evaluated in some control problems; qubit stabilization and single photon production.
KW - Quantum control
KW - coherent feedback
KW - single photon
UR - http://www.scopus.com/inward/record.url?scp=85044866922&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044866922&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2017.08.1984
DO - 10.1016/j.ifacol.2017.08.1984
M3 - Article
AN - SCOPUS:85044866922
SN - 2405-8963
VL - 50
SP - 11760
EP - 11763
JO - 20th IFAC World Congress
JF - 20th IFAC World Congress
IS - 1
ER -