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p-Bits and q-Bits = probabilistic an...
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Datta, Supriyo, (1954-)

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  • p-Bits and q-Bits = probabilistic and quantum computing /
  • Record Type: Electronic resources : Monograph/item
    Title/Author: p-Bits and q-Bits/ Supriyo Datta.
    Reminder of title: probabilistic and quantum computing /
    Author: Datta, Supriyo,
    Published: Singapore :World Scientific, : c2025.,
    Description: 1 online resource (287 p.) :ill.
    [NT 15003449]: Intro -- Contents -- Acknowledgements -- A Note to Readers -- 1. Prologue -- 1.1 Fig. 1.1: n versus 2n -- 1.2 Figs. 1.2-1.3: Spintronics -- 1.2.0.1 Fig. 1.2 -- 1.2.0.2 Fig. 1.3 -- 1.3 Fig. 1.4: It's the correlations! -- 1.4 Figs. 1.5-1.6: q-bits versus p-bits -- 1.4.0.1 Fig. 1.5: q-bits -- 1.4.0.2 Fig. 1.6: p-bits -- 1.5 Figs. 1.7-1.8: The key difference -- 1.5.0.1 Fig. 1.7 -- 1.5.0.2 Fig. 1.8 -- 1.6 Fig. 1.9: Hardware acceleration -- 1.7 Statistical mechanics -- 2. Statistical Mechanics -- 2.1 State Space -- 2.1.1 Fig. 2.1: Fermi function -- 2.1.2 Fig. 2.2: Boltzmann law -- 2.1.3 Figs. 2.3-2.4: Fermi function from Boltzmann law -- 2.1.3.1 Fig. 2.3 -- 2.1.3.2 Fig. 2.4: Boltzmann Law is NOT the Boltzmann approximation -- 2.1.4 Figs. 2.5-2.7: Two non-interacting energy levels -- 2.1.4.1 Fig. 2.5 -- 2.1.4.2 Fig. 2.6: E - μN -- 2.1.4.3 Fig. 2.7: Probabilities -- 2.1.5 Fig. 2.8: Two levels with interaction -- 2.1.6 Quiz -- 2.1.6.1 Question 1 -- 2.1.6.2 Question 2 -- 2.1.6.3 Question 3 -- 2.2 Boltzmann Law -- 2.2.1 Fig. 2.9: System and reservoir -- 2.2.2 Figs. 2.10-2.13: Justifying the law -- 2.2.2.1 Fig. 2.11 -- 2.2.2.2 Fig. 2.12 -- 2.2.2.3 Fig. 2.13 -- 2.2.3 Fig. 2.14: Canonical ensemble -- 2.2.4 Fig. 2.15: Grand canonical ensemble -- 2.2.5 Quiz -- 2.2.5.1 Question 1 -- 2.2.5.2 Question 2 -- 2.2.5.3 Question 3 -- 2.3 Entropy -- 2.3.1 Figs. 2.16-2.18: Entropy from reservoir model -- 2.3.1.1 Fig. 2.16: Model for reservoir -- 2.3.1.2 Fig. 2.17 -- 2.3.1.3 Fig. 2.18 -- 2.3.2 Figs. 2.19-2.20: Thermodynamic versus information entropy -- 2.3.2.1 Fig. 2.19 -- 2.3.2.2 Fig. 2.20: Expression for entropy -- 2.3.3 Figs. 2.21-2.22: Reservoir model with d-level units -- 2.3.3.1 Fig. 2.21 -- 2.3.3.2 Fig. 2.22 -- 2.3.4 Fig. 2.23: μ, T from entropy S -- 2.3.5 Quiz -- 2.3.5.1 Question 1 -- 2.3.5.2 Question 2 -- 2.3.5.3 Question 3 -- 2.4 Free Energy.
    [NT 15003449]: 2.4.1 Fig. 2.24: Free energy, F -- 2.4.2 Fig. 2.25: Gibbs' inequality -- 2.4.3 Fig. 2.26: Equilibrium free energy -- 2.4.4 Figs. 2.27-2.28: Entropy drives flow -- 2.4.4.1 Fig. 2.27 -- 2.4.4.2 Fig. 2.28: Flow driven by temperature -- 2.4.5 Quiz -- 2.4.5.1 Question 1 -- 2.4.5.2 Question 2 -- 2.4.5.3 Question 3 -- 2.5 Self-Consistent Field -- 2.5.1 Figs. 2.29-2.32: The exponential problem -- 2.5.1.1 Figs. 2.29 -- 2.5.1.2 Fig. 2.30: Toy example -- 2.5.1.3 Fig. 2.31 -- 2.5.1.4 Fig. 2.32 -- 2.5.2 Figs. 2.33-2.36: SCF method -- 2.5.2.1 Fig. 2.34 -- 2.5.2.2 Fig. 2.35 -- 2.5.2.3 Fig. 2.36 -- 2.5.3 Fig. 2.37: SCF and neural networks -- 2.5.4 Quiz -- 2.5.4.1 Question 1 -- 2.5.4.2 Question 2 -- 2.5.4.3 Question 3 -- 2.6 Fig. 2.38: 5-minute Summary -- 3. Boltzmann Machines -- 3.1 Sampling -- 3.1.1 Figs. 3.1-3.4: From f to n -- 3.1.1.1 Fig. 3.1: Recap -- 3.1.1.2 Fig. 3.2: Replace f with n -- 3.1.1.3 Fig. 3.3 -- 3.1.1.4 Fig. 3.4: Generating samples -- 3.1.2 Figs. 3.5-3.8: Synapse from interaction energy -- 3.1.2.1 Fig. 3.5 -- 3.1.2.2 Fig. 3.6 -- 3.1.2.3 Fig. 3.7 -- 3.1.2.4 Fig. 3.8: A simple code -- 3.1.3 Figs. 3.9-3.15: Toy example -- 3.1.3.1 Fig. 3.9: Solution, the Boltzmann way -- 3.1.3.2 Fig. 3.10 -- 3.1.3.3 Fig. 3.11: How NOT to sample -- 3.1.3.4 Fig. 3.12: Solution by sampling -- 3.1.3.5 Fig. 3.13 -- 3.1.3.6 Fig. 3.14 -- 3.1.3.7 Fig. 3.15: Sampling method, key points -- 3.1.4 Quiz -- 3.1.4.1 Question 1 -- 3.1.4.2 Question 2 -- 3.1.4.3 Question 3 -- 3.2 Orchestrating Interactions -- 3.2.1 Figs. 3.16-3.20: Generalizing the toy model -- 3.2.1.1 Fig. 3.16 -- 3.2.1.2 Fig. 3.17 -- 3.2.1.3 Fig. 3.18: Four level example -- 3.2.1.4 Fig. 3.19 -- 3.2.1.5 Fig. 3.20 -- 3.2.2 Figs. 3.21-3.23: From natural to orchestrated interactions -- 3.2.2.1 Fig. 3.21 -- 3.2.2.2 Fig. 3.22: Software implementation -- 3.2.2.3 Fig. 3.23 -- 3.2.3 Figs. 3.24-3.25: p-bits and q-bits.
    [NT 15003449]: 3.2.3.1 Fig. 3.24 -- 3.2.3.2 Fig. 3.25 -- 3.2.4 Quiz -- 3.2.4.1 Question 1 -- 3.2.4.2 Question 2 -- 3.3 Optimization -- 3.3.1 Figs. 3.26-3.27: Graph partitioning -- 3.3.1.1 Fig. 3.26 -- 3.3.1.2 Fig. 3.27 -- 3.3.2 Figs. 3.28-3.31: Defining energy -- 3.3.2.1 Fig. 3.28 -- 3.3.2.2 Fig. 3.29 -- 3.3.2.3 Figs. 3.30-3.31: Finding x,w -- 3.3.3 Figs. 3.32-3.38: Imposing constraints -- 3.3.3.1 Fig. 3.32: State space response -- 3.3.3.2 Figs. 3.33-3.35: Constraints through energy -- 3.3.3.3 Fig. 3.36 -- 3.3.3.4 Figs. 3.37-3.38: From min-cut to max-cut -- 3.3.3.5 Fig. 3.37 -- 3.3.3.6 Fig. 3.38 -- 3.3.4 Figs. 3.39-3.40: Summary -- 3.3.4.1 Fig. 3.39 -- 3.3.4.2 Fig. 3.40 -- 3.3.5 Quiz -- 3.3.5.1 Question 1 -- 3.3.5.2 Question 2 -- 3.4 Inference -- 3.4.1 Figs. 3.41-3.45: Logic gates -- 3.4.1.1 Fig. 3.41 -- 3.4.1.2 Fig. 3.42 -- 3.4.1.3 Figs. 3.43 and 3.44 -- 3.4.1.4 Fig. 3.45 -- 3.4.2 Fig. 3.46: Image classification -- 3.4.3 Figs. 3.47-3.48: A simple learning rule -- 3.4.3.1 Fig. 3.47 -- 3.4.3.2 Fig. 3.48 -- 3.4.4 Figs. 3.49-3.50: Binary-bipolar interconversion -- 3.4.5 Quiz -- 3.4.5.1 Question 1 -- 3.4.5.2 Question 2 -- 3.5 Learning -- 3.5.1 Fig. 3.51: Learning rule #1 -- 3.5.2 Figs. 3.52-3.55: Average value and correlation matrix -- 3.5.2.1 Fig. 3.53 -- 3.5.2.2 Fig. 3.54 -- 3.5.2.3 Fig. 3.55 -- 3.5.3 Figs. 3.56-3.58: Learning rule #2 -- 3.5.3.1 Fig. 3.57 -- 3.5.3.2 Fig. 3.58 -- 3.5.4 Fig. 3.59: Learning a full adder -- 3.5.5 Figs. 3.60-3.62: Learning with hidden units -- 3.5.5.1 Fig. 3.60 -- 3.5.5.2 Fig. 3.61 -- 3.5.5.3 Fig. 3.62 -- 3.5.6 Quiz -- 3.5.6.1 Question 1 -- 3.5.6.2 Question 2 -- 3.5.6.3 Question 3 -- 3.6 Fig. 3.63: 5-minute Summary -- 4. Transition Matrix -- 4.1 Markov Chain Monte Carlo -- 4.1.1 Figs. 4.1-4.4: Transition matrix -- 4.1.1.1 Fig. 4.1: Definition -- 4.1.1.2 Fig. 4.2: Properties -- 4.1.1.3 Fig. 4.3 -- 4.1.1.4 Fig. 4.4.
    [NT 15003449]: 4.1.2 Figs. 4.5-4.9: Stationary distribution -- 4.1.2.1 Fig. 4.5 -- 4.1.2.2 Fig. 4.6 -- 4.1.2.3 Fig. 4.7 -- 4.1.2.4 Fig. 4.8 -- 4.1.2.5 Fig. 4.9 -- 4.1.3 Fig. 4.10: Metropolis algorithm -- 4.1.4 Quiz -- 4.1.4.1 Question 1 -- 4.1.4.2 Question 2 -- 4.2 Gibbs' Sampling -- 4.2.1 Figs. 4.11-4.12: How it works -- 4.2.1.1 Fig. 4.11 -- 4.2.1.2 Fig. 4.12 -- 4.2.2 Figs. 4.13-4.20: Toy example with n = 2 -- 4.2.2.1 Fig. 4.13 -- 4.2.2.2 Fig. 4.14: Transition matrix for updating p-bit 1 -- 4.2.2.3 Figs. 4.15-4.16 -- 4.2.2.4 Figs. 4.17-4.18 -- 4.2.2.5 Fig. 4.19: Transition matrix for updating p-bit 2 -- 4.2.2.6 Fig. 4.20 -- 4.2.3 Quiz -- 4.2.3.1 Question 1 -- 4.2.3.2 Question 2 -- 4.3 Sequential Versus Simultaneous Updates -- 4.3.1 Figs. 4.21-4.23: Sequential update -- 4.3.1.1 Fig. 4.21: Toy example -- 4.3.1.2 Fig. 4.22: Transition matrix -- 4.3.1.3 Fig. 4.23 -- 4.3.2 Fig. 4.24: Simultaneous update -- 4.3.3 Figs. 4.25-4.26: Sequential versus simultaneous -- 4.3.3.1 Fig. 4.25 -- 4.3.3.2 Fig. 4.26 -- 4.3.4 Fig. 4.27: Restricted Boltzmann machine -- 4.3.5 Quiz -- 4.3.5.1 Question 1 -- 4.3.5.2 Question 2 -- 4.4 Bayesian Networks -- 4.4.1 Figs. 4.28-4.35: Bayesian versus reciprocal networks -- 4.4.1.1 Figs. 4.29-4.30: Bayesian networks -- 4.4.1.2 Fig. 4.31 -- 4.4.1.3 Fig. 4.32: Why no energy function -- 4.4.1.4 Fig. 4.33 -- 4.4.1.5 Fig. 4.34 -- 4.4.1.6 Fig. 4.35 -- 4.4.2 Figs. 4.36-4.37: Bayes theorem -- 4.4.3 Quiz -- 4.4.3.1 Question 1 -- 4.4.3.2 Question 2 -- 4.5 Feynman Paths -- 4.5.1 Figs. 4.38-4.42: Multiplying W-matrices -- 4.5.1.1 Fig. 4.38: Why W-matrix? -- 4.5.1.2 Fig. 4.39 -- 4.5.1.3 Fig. 4.40 -- 4.5.1.4 Figs. 4.41-4.42 -- 4.5.1.5 Fig. 4.42 -- 4.5.2 Figs. 4.43-4.45: Matrix multiplication as sum over paths -- 4.5.2.1 Fig. 4.44 -- 4.5.2.2 Fig. 4.45 -- 4.5.3 Quiz -- 4.5.3.1 Question 1 -- 4.5.3.2 Question 2 -- 4.5.3.3 Question 3 -- 4.6 Fig. 4.46: 5-minute Summary.
    [NT 15003449]: 5. Quantum Boltzmann Law -- 5.1 Quantum Spins -- 5.1.1 Figs. 5.1-5.3: Classical spin -- 5.1.1.1 Fig. 5.1 -- 5.1.1.2 Fig. 5.2 -- 5.1.1.3 Fig. 5.3 -- 5.1.2 Figs. 5.4-5.5: Quantum spins -- 5.1.2.1 Fig. 5.4 -- 5.1.2.2 Fig. 5.5 -- 5.1.3 Fig. 5.6: Density matrix -- 5.1.4 Figs. 5.7-5.10: Predicting measurements -- 5.1.4.1 Figs. 5.7 -- 5.1.4.2 Fig. 5.8 -- 5.1.4.3 Fig. 5.9 -- 5.1.4.4 Fig. 5.10 -- 5.1.5 Quiz -- 5.1.5.1 Question 1 -- 5.1.5.2 Question 2 -- 5.1.5.3 Question 3 -- 5.2 One q-bit System -- 5.2.1 Fig. 5.11: Hamiltonian -- 5.2.2 Figs. 5.12-5.14: Density matrix -- 5.2.2.1 Fig. 5.12 -- 5.2.2.2 Fig. 5.13 -- 5.2.2.3 Fig. 5.14 -- 5.2.3 Figs. 5.15-5.17: Predicting mz -- 5.2.3.1 Fig. 5.15 -- 5.2.3.2 Fig. 5.16 -- 5.2.3.3 Fig. 5.17 -- 5.2.4 Quiz -- 5.2.4.1 Question 1 -- 5.2.4.2 Question 2 -- 5.2.4.3 Question 3 -- 5.3 Spin-Spin Interactions -- 5.3.1 Figs. 5.18-5.19: Interaction Hamiltonian -- 5.3.1.1 Fig. 5.18 -- 5.3.1.2 Fig. 5.19 -- 5.3.2 Figs. 5.20-5.21: 2-spin matrices -- 5.3.2.1 Fig. 5.20 -- 5.3.2.2 Fig. 5.21 -- 5.3.3 Figs. 5.22-5.26: Product matrices -- 5.3.3.1 Fig. 5.22 -- 5.3.3.2 Fig. 5.23 -- 5.3.3.3 Fig. 5.24 -- 5.3.3.4 Fig. 5.25 -- 5.3.3.5 Fig. 5.26 -- 5.3.4 Fig. 5.27: n-spin matrices -- 5.3.5 Figs. 5.28-5.29: Why quantum computers? -- 5.3.5.1 Fig. 5.28 -- 5.3.5.2 Fig. 5.29 -- 5.3.6 Quiz -- 5.3.6.1 Question 1 -- 5.3.6.2 Question 2 -- 5.3.6.3 Question 3 -- 5.4 Two q-bit System -- 5.4.1 Figs. 5.30-5.31: Hamiltonian -- 5.4.1.1 Figs. 5.30 -- 5.4.1.2 Fig. 5.31 -- 5.4.2 Figs. 5.32-5.33: Ising spins -- 5.4.2.1 Fig. 5.32 -- 5.4.2.2 Fig. 5.33 -- 5.4.3 Figs. 5.34-5.35: Quantum spins -- 5.4.3.1 Fig. 5.34 -- 5.4.3.2 Fig. 5.35 -- 5.4.4 Quiz -- 5.4.4.1 Question 1 -- 5.4.4.2 Question 2 -- 5.4.4.3 Question 3 -- 5.5 Quantum Annealing -- 5.5.1 Figs. 5.36-5.38: Why anneal? -- 5.5.1.1 Fig. 5.36 -- 5.5.1.2 Fig. 5.37 -- 5.5.1.3 Fig. 5.38.
    [NT 15003449]: 5.5.2 Figs. 5.39-5.40: Translating to quantum spins.
    Subject: Statistical mechanics. -
    Online resource: https://www.worldscientific.com/worldscibooks/10.1142/13877#t=toc
    ISBN: 9789811294501
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