1 Introduction	3
1.1 Quantum Resources	3
1.2 Previous Results Using QSL	4
1.3 Structure of the Present Paper	5
2 Preliminaries	5
2.1 Turing Machines	5
2.2 Oracle Turing Machines and Oracle Notions	6
2.3 Quantum Computation	8
3 Quantum Simulation Logic	11
3.1  Elementary Systems	12
3.1.1 States	12
3.1.2 Transformations	14
3.1.3 No Universal Spin-1/2 Inverter	17
3.1.4 Measurement	18
3.1.5 Preparation	18
3.1.6 Non-Commutativity of Measurements	18
3.1.7 QKD—BB84	18
3.2  Pairs of Elementary Systems	20
3.2.1 Transformations	20
3.2.2 Entanglement	21
3.2.3 Remote Steering	23
3.2.4 Anticorrelation in Spin-Measurements of the Singlet	24
3.2.5 No-Cloning	24
3.2.6 Interference	25
3.2.7 Measurements	27
3.2.8 Superdense Coding	28
3.3  Higher Number of Elementary Systems	29
3.3.1 Teleportation	30
3.3.2 Transformations	31
3.4  Properties and Relations to Other Theories	32
3.4.1 The Relation to Stabilizer Quantum Mechanics, Locality and Contextuality	32
3.4.2 QSL Extends the State Space of Spekkens’ Model	33
3.4.3 QSL Is an Example of a Generalized Probability Theory	34
4 The Bernstein-Vazirani Problem	35
4.1  Problem Formulation	35
4.2  Classical Algorithm	35
4.3  Quantum Algorithm	36
4.4  QSL Simulation	36
5 The Deutsch-Jozsa Problem	38
5.1  Problem Formulation	38
5.2  Deterministic and Probabilistic Algorithms	38
5.3  Quantum Algorithm	39
5.4  The Problem for Small Input	40
5.5  QSL Simulation Guaranteed a Constant or Balanced Function	41
5.6  QSL Simulation Accepting Arbitrary Boolean Functions	42
5.7  Query Complexity	45
6 Oracles as a Comparison	45
6.1  The Additional Structure and Constraints	45
6.2  Is the Black Box Black?	46
6.3  Assumptions in the Use of Oracles	47
6.4  Systematic Phase Errors	47
6.5  Starting with Something Else Than Access to an Oracle	50
7 Grover’s Algorithm	50
7.1  Problem Formulation	51
7.2  One-Shot Grover	51
7.3  The n-Toffoli	53
7.4  A Scaling Algorithm	55
7.5  Comparison with a 3-qubit Experiment	56
7.6  Application to Ciphers	56
8 Simon’s Algorithm	57
8.1  Problem Formulation	57
8.2  Probabilistic Solution	57
8.3  Quantum Algorithm	58
8.4  QSL Simulation	59
8.5  Adding the Function Output to the Target Modulo 2	61
8.6  A Deterministic Algorithm for SIMON’S Problem	62
8.7  Application to Symmetric Ciphers	64
9 Shor’s Algorithm Factoring 15	65
10  Conclusions	69
A   Constant and Balanced Functions for Three Bits of Input	70
B   Error Probability for Different Constructions of the Majority Function	72
References