Realization Calculus

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1 @book{Serre1977,
2   author    = {Jean Pierre Serre},
3   title     = {Linear Representations of Finite Groups},
4   series    = {Graduate Texts in Mathematics},
5   volume    = {42},
6   publisher = {Springer},
7   address   = {New York},
8   year      = {1977}
9 }
10 
11 @book{FultonHarris1991,
12   author    = {William Fulton and Joe Harris},
13   title     = {Representation Theory: A First Course},
14   series    = {Graduate Texts in Mathematics},
15   volume    = {129},
16   publisher = {Springer},
17   address   = {New York},
18   year      = {1991}
19 }
20 
21 @book{NielsenChuang2010,
22   author    = {Michael A. Nielsen and Isaac L. Chuang},
23   title     = {Quantum Computation and Quantum Information},
24   edition   = {Tenth Anniversary},
25   publisher = {Cambridge University Press},
26   address   = {Cambridge},
27   year      = {2010}
28 }
29 
30 @book{Watrous2018,
31   author    = {John Watrous},
32   title     = {The Theory of Quantum Information},
33   publisher = {Cambridge University Press},
34   address   = {Cambridge},
35   year      = {2018}
36 }
37 
38 @book{Bhatia1997,
39   author    = {Rajendra Bhatia},
40   title     = {Matrix Analysis},
41   series    = {Graduate Texts in Mathematics},
42   volume    = {169},
43   publisher = {Springer},
44   address   = {New York},
45   year      = {1997}
46 }
47 
48 @article{Kato1950,
49   author  = {Tosio Kato},
50   title   = {On the adiabatic theorem of quantum mechanics},
51   journal = {Journal of the Physical Society of Japan},
52   volume  = {5},
53   pages   = {435{\textendash}439},
54   year    = {1950}
55 }
56 
57 @book{Kato1995,
58   author    = {Tosio Kato},
59   title     = {Perturbation Theory for Linear Operators},
60   publisher = {Springer},
61   address   = {Berlin},
62   year      = {1995}
63 }
64 
65 @article{Berry1984,
66   author  = {Michael V. Berry},
67   title   = {Quantal phase factors accompanying adiabatic changes},
68   journal = {Proceedings of the Royal Society of London. Series A},
69   volume  = {392},
70   number  = {1802},
71   pages   = {45{\textendash}57},
72   year    = {1984}
73 }
74 
75 @article{WilczekZee1984,
76   author  = {Frank Wilczek and A. Zee},
77   title   = {Appearance of gauge structure in simple dynamical systems},
78   journal = {Physical Review Letters},
79   volume  = {52},
80   number  = {24},
81   pages   = {2111{\textendash}2114},
82   year    = {1984}
83 }
84 
85 @book{Kraus1983,
86   author    = {Karl Kraus},
87   title     = {States, Effects, and Operations},
88   series    = {Lecture Notes in Physics},
89   volume    = {190},
90   publisher = {Springer},
91   address   = {Berlin},
92   year      = {1983}
93 }
94 
95 @article{Stinespring1955,
96   author  = {W. Forrest Stinespring},
97   title   = {Positive functions on {C} star algebras},
98   journal = {Proceedings of the American Mathematical Society},
99   volume  = {6},
100   number  = {2},
101   pages   = {211{\textendash}216},
102   year    = {1955}
103 }
104 
105 @article{Choi1975,
106   author  = {Man Duen Choi},
107   title   = {Completely positive linear maps on complex matrices},
108   journal = {Linear Algebra and its Applications},
109   volume  = {10},
110   number  = {3},
111   pages   = {285{\textendash}290},
112   year    = {1975}
113 }
114 
115 @article{Lindblad1976,
116   author  = {Goran Lindblad},
117   title   = {On the generators of quantum dynamical semigroups},
118   journal = {Communications in Mathematical Physics},
119   volume  = {48},
120   number  = {2},
121   pages   = {119{\textendash}130},
122   year    = {1976}
123 }
124 
125 @article{KnillLaflamme1997,
126   author  = {Emanuel Knill and Raymond Laflamme},
127   title   = {Theory of quantum error correcting codes},
128   journal = {Physical Review A},
129   volume  = {55},
130   number  = {2},
131   pages   = {900{\textendash}911},
132   year    = {1997}
133 }
134 
135 @article{SchumacherNielsen1996,
136   author  = {Benjamin Schumacher and Michael A. Nielsen},
137   title   = {Quantum data processing and error correction},
138   journal = {Physical Review A},
139   volume  = {54},
140   number  = {4},
141   pages   = {2629{\textendash}2635},
142   year    = {1996}
143 }
144 
145 @article{BenyKempfKribs2007,
146   author  = {C{\'{e}}dric B{\'{e}}ny and Achim Kempf and David W. Kribs},
147   title   = {Generalization of quantum error correction via the {Heisenberg} picture},
148   journal = {Physical Review Letters},
149   volume  = {98},
150   number  = {10},
151   pages   = {100502},
152   year    = {2007}
153 }
154 
155 @article{Feshbach1958,
156   author  = {Herman Feshbach},
157   title   = {Unified theory of nuclear reactions},
158   journal = {Annals of Physics},
159   volume  = {5},
160   number  = {4},
161   pages   = {357{\textendash}390},
162   year    = {1958}
163 }
164 
165 @article{BravyiDiVincenzoLoss2011,
166   author  = {Sergey Bravyi and David P. DiVincenzo and Daniel Loss},
167   title   = {{Schrieffer} {Wolff} transformation for quantum many body systems},
168   journal = {Annals of Physics},
169   volume  = {326},
170   number  = {10},
171   pages   = {2793{\textendash}2826},
172   year    = {2011}
173 }
174 
175 @article{Nakajima1958,
176   author  = {Sadao Nakajima},
177   title   = {On quantum theory of transport phenomena: steady diffusion},
178   journal = {Progress of Theoretical Physics},
179   volume  = {20},
180   number  = {6},
181   pages   = {948{\textendash}959},
182   year    = {1958}
183 }
184 
185 @article{Zwanzig1960,
186   author  = {Robert Zwanzig},
187   title   = {Ensemble method in the theory of irreversibility},
188   journal = {The Journal of Chemical Physics},
189   volume  = {33},
190   number  = {5},
191   pages   = {1338{\textendash}1341},
192   year    = {1960}
193 }
194 
195 @article{OsterwalderSchrader1973,
196   author  = {Konrad Osterwalder and Robert Schrader},
197   title   = {Axioms for {Euclidean} {Green} functions},
198   journal = {Communications in Mathematical Physics},
199   volume  = {31},
200   number  = {2},
201   pages   = {83{\textendash}112},
202   year    = {1973}
203 }
204 
205 @article{OsterwalderSchrader1975,
206   author  = {Konrad Osterwalder and Robert Schrader},
207   title   = {Axioms for {Euclidean} {Green} functions. {II}},
208   journal = {Communications in Mathematical Physics},
209   volume  = {42},
210   number  = {3},
211   pages   = {281{\textendash}305},
212   year    = {1975}
213 }
214 
215 @book{GlimmJaffe1987,
216   author    = {James Glimm and Arthur Jaffe},
217   title     = {Quantum Physics: A Functional Integral Point of View},
218   edition   = {Second},
219   publisher = {Springer},
220   address   = {New York},
221   year      = {1987}
222 }
223 
224 @book{Connes1994,
225   author    = {Alain Connes},
226   title     = {Noncommutative Geometry},
227   publisher = {Academic Press},
228   address   = {San Diego},
229   year      = {1994}
230 }
231 
232 @article{Vassilevich2003,
233   author  = {Dmitri V. Vassilevich},
234   title   = {Heat kernel expansion: user's manual},
235   journal = {Physics Reports},
236   volume  = {388},
237   number  = {5},
238   pages   = {279{\textendash}360},
239   year    = {2003}
240 }
241 
242 @book{Strikwerda2004,
243   author    = {John C. Strikwerda},
244   title     = {Finite Difference Schemes and Partial Differential Equations},
245   edition   = {Second},
246   publisher = {Society for Industrial and Applied Mathematics},
247   address   = {Philadelphia},
248   year      = {2004}
249 }
250 
251 @book{ReedSimon1972,
252   author    = {Michael Reed and Barry Simon},
253   title     = {Methods of Modern Mathematical Physics. {I}: Functional Analysis},
254   publisher = {Academic Press},
255   address   = {New York},
256   year      = {1972}
257 }
258 
259 @book{Dirac1964,
260   author    = {Paul A. M. Dirac},
261   title     = {Lectures on Quantum Mechanics},
262   publisher = {Yeshiva University},
263   address   = {New York},
264   year      = {1964}
265 }
266 
267 @book{HenneauxTeitelboim1992,
268   author    = {Marc Henneaux and Claudio Teitelboim},
269   title     = {Quantization of Gauge Systems},
270   publisher = {Princeton University Press},
271   address   = {Princeton, New Jersey},
272   year      = {1992}
273 }

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