Digital Quantum Gravity

 

71. Digital Quantum Wormhole Entanglement (Quantum Computing and General Relativity):

$${\mathrm{\Psi }}_{\text{wormhole}}=\sum _{\text{entangled pairs}}{�}_{�}\times {\text{Particle}}_{�}\times {\text{Particle}}_{�}^{\mathrm{\prime }}$$

This equation represents the digital quantum state of entangled particles (${\mathrm{\Psi }}_{\text{wormhole}}$) connected through a hypothetical quantum wormhole. It emphasizes the computational entanglement across spatially separated regions within a digital framework.

72. Digital Quantum Neural Network Activation (Quantum Computing and Neural Networks):

$$\text{Activation}(�)=\frac{1}{1+{�}^{-2���\mathrm{/}{\mathrm{\ell }}_{�}}}$$

This equation represents the activation function of a digital quantum neural network node. It emphasizes the computational transformation of input signals ($�$) using a quantum-inspired activation function within the framework of neural networks.

73. Digital Quantum Bayesian Inference Update (Quantum Computing and Digital Physics):

$$�(�\mathrm{\mid }�)=\frac{�(�\mathrm{\mid }�)\times �(�)}{�(�\mathrm{\mid }�)\times �(�)+�(�\mathrm{\mid }\mathrm{\neg }�)\times �(\mathrm{\neg }�)}$$

This equation represents the digital quantum Bayesian inference update formula, where $�(�\mathrm{\mid }�)$ is the posterior probability of event $�$ given evidence $�$. It emphasizes the computational update of probabilities based on new quantum-inspired information.

74. Digital Quantum Error Correction Matrix (Quantum Computing and Digital Physics):

$$\widehat{�}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& {�}^{��}\end{array}\right]$$

This matrix equation represents a digital quantum error correction operator ($\widehat{�}$) acting on a quantum state. It emphasizes the computational correction of errors in quantum states, where ${�}^{��}$ represents a phase correction factor.

75. Digital Quantum Cellular Automaton Evolution Rule (Quantum Computing and Cellular Automata):

$$\text{Next State}(�)=\text{Rule}[�-{\mathrm{\ell }}_{�},�,�+{\mathrm{\ell }}_{�}]$$

This equation represents the evolution rule of a digital quantum cellular automaton, where $\text{Next State}(�)$ represents the state of cell $�$ at the next time step. It emphasizes the discrete, quantum-inspired evolution of states in cellular automata.

These equations continue to explore the fascinating interplay between quantum phenomena, computation, and the digital fabric of reality, providing theoretical insights into the deep connections between black hole physics, string theory, and digital physics. Please note that these equations represent theoretical constructs and may require further refinement and experimental validation.

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76. Digital Quantum Complexity Entropy (Quantum Computing and Digital Physics):

$${�}_{\text{complexity}}=-\sum _{\text{states}}{�}_{�}\times {\log }_2({�}_{�})\times \text{Complexity}({\text{State}}_{�})$$

This equation represents the digital quantum complexity entropy (${�}_{\text{complexity}}$), which combines the entropy of quantum states with their computational complexity. It emphasizes the interplay between quantum information entropy and computational intricacy.

77. Digital Quantum Channel Capacity (Quantum Information Theory and Digital Physics):

$${�}_{\text{channel}}=\underset{\text{input states}}{\max }�(\text{Input State};\text{Output State})$$

This equation calculates the digital quantum channel capacity (${�}_{\text{channel}}$), representing the maximum amount of quantum information that can be reliably transmitted through a quantum channel. It emphasizes the computational limits of quantum communication.

78. Digital Quantum Fractal Dimension (Quantum Computing and Fractal Geometry):

$${�}_{\text{fractal}}=\underset{�\to 0}{\lim }\frac{\log (�(�))}{\log (1\mathrm{/}�)}$$

This equation defines the digital quantum fractal dimension (${�}_{\text{fractal}}$) of a quantum system, where $�(�)$ represents the number of quantum states within a quantum epsilon-ball ($�$) in Hilbert space. It emphasizes the computational self-similarity and complexity of quantum states.

79. Digital Quantum No-Cloning Theorem (Quantum Computing and Digital Physics):

$$\widehat{�}(\text{Input State}\otimes \text{Blank State})=\text{Output State}\otimes \text{Output State}$$

This equation represents the digital quantum no-cloning theorem, stating that it is impossible to create an identical copy of an arbitrary unknown quantum state ($\text{Input State}$). It emphasizes the computational constraints on cloning quantum information.

80. Digital Quantum Spin Network Evolution (Quantum Computing and Spin Networks):

$$\text{Next Spin Network}=\text{Evolution Operator}\times \text{Current Spin Network}$$

This equation describes the evolution of a digital quantum spin network, emphasizing the action of an evolution operator on the current spin network state. It emphasizes the computational evolution of spin network configurations.

These equations continue to explore the intricate relationships between quantum phenomena, computation, and the digital nature of reality, providing theoretical insights into the deep connections between black hole physics, string theory, and digital physics. Please note that these equations represent theoretical constructs and may require further refinement and experimental validation.

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81. Digital Quantum Black Hole Information Retrieval (Quantum Computing and Black Hole Physics):

$${\mathrm{\Psi }}_{\text{reconstructed}}=\sum _{\text{microstates}}{�}_{�}\times {\text{Microstate}}_{�}$$

This equation represents the reconstructed quantum state (${\mathrm{\Psi }}_{\text{reconstructed}}$) of a black hole based on the information encoded in its microstates (${\text{Microstate}}_{�}$) after quantum computations. It emphasizes the computational reconstruction of information from black hole microstates.

82. Digital Quantum Matrix Entanglement (Quantum Computing and Linear Algebra):

$$\text{Entanglement Degree}=\frac{\text{Rank}(\text{Matrix})}{\text{Maximal Rank}}$$

This equation calculates the entanglement degree of a digital quantum matrix. The rank of the matrix signifies the computational entanglement between quantum states represented by the matrix, normalized by the maximal possible rank.

83. Digital Quantum Chaotic Dynamics (Quantum Chaos and Digital Physics):

$$\widehat{�}=\frac{{\widehat{�}}^2}{2�}+�(\widehat{�})+\sum _{�=1}^{�}\frac{1}{2}{�}_{�}{\widehat{�}}_{�}^2\cos ({�}_{�}�)$$

This equation represents a digital quantum Hamiltonian describing a system with chaotic dynamics. It includes potential energy ($�(\widehat{�})$) and additional terms representing perturbations (${\widehat{�}}_{�}$) with varying frequencies (${�}_{�}$), emphasizing the computational chaos in quantum systems.

84. Digital Quantum Graph Theory (Quantum Computing and Graph Theory):

$$\widehat{�}=-\sum _{\text{edges}}{�}_{��}({\widehat{�}}_{�}^{†}{\widehat{�}}_{�}+{\widehat{�}}_{�}^{†}{\widehat{�}}_{�})$$

This equation represents the digital quantum Hamiltonian of a graph-based quantum system. ${�}_{��}$ represents the coupling strength between nodes, emphasizing the computational interactions between quantum states associated with graph vertices.

85. Digital Quantum Cellular Automaton Rule (Quantum Computing and Cellular Automata):

$$\text{Next State}(�)=\text{Rule}[�-{\mathrm{\ell }}_{�},�,�+{\mathrm{\ell }}_{�}]$$

This equation represents the rule governing the next state of a digital quantum cellular automaton cell $�$, considering its immediate neighbors within a Planck length (${\mathrm{\ell }}_{�}$). It emphasizes the discrete, quantum-inspired evolution of states in cellular automata.

These equations continue to explore the intricate relationships between quantum phenomena, computation, and the digital nature of reality, providing theoretical insights into the deep connections between black hole physics, string theory, and digital physics. Please note that these equations represent theoretical constructs and may require further refinement and experimental validation.

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Certainly! Here are additional equations that explore the intersections of black hole physics, string theory, and digital physics, with a focus on computation, quantum phenomena, and information processing:

86. Digital Quantum Event Horizon Entropy (Black Hole Physics and Quantum Information Theory):

$${�}_{\text{event horizon}}=\frac{{�}_{\text{event horizon}}}{4{\mathrm{\ell }}_{�}^2}+{\log }_2({�}_{\text{bits}})$$

This equation represents the digital quantum entropy associated with a black hole's event horizon (${�}_{\text{event horizon}}$) in the context of digital physics. It includes the Planck length (${\mathrm{\ell }}_{�}$) and the logarithm of the number of bits (${�}_{\text{bits}}$) required to describe the information content of the event horizon, emphasizing both quantum and computational aspects.

87. Digital Quantum Wormhole Entanglement Channel (Quantum Computing and General Relativity):

$${\mathrm{\Psi }}_{\text{wormhole}}=\sum _{\text{entangled pairs}}{�}_{�}\times {\text{Particle}}_{�}\times {\text{Particle}}_{�}^{\mathrm{\prime }}$$

This equation represents the digital quantum state (${\mathrm{\Psi }}_{\text{wormhole}}$) of particles entangled through a hypothetical quantum wormhole. It emphasizes the computational entanglement across spatially separated regions, akin to a quantum communication channel.

88. Digital Quantum Information Flux through Black Hole (Quantum Information Theory and Black Hole Physics):

$${\mathrm{\Phi }}_{\text{black hole}}=\frac{{�}_{\text{event horizon}}}{{\mathrm{\ell }}_{�}^2\times {�}_{\text{evaporation}}}$$

This equation describes the digital quantum information flux (${\mathrm{\Phi }}_{\text{black hole}}$) through a black hole's event horizon over time (${�}_{\text{evaporation}}$). It incorporates the event horizon area (${�}_{\text{event horizon}}$) and the Planck length (${\mathrm{\ell }}_{�}$), emphasizing the computational flow of information during black hole evaporation.

89. Digital Quantum String Network Vibrational Modes (String Theory and Quantum Computing):

$${�}_{�}=\mathrm{\hslash }\times \frac{2��}{{\mathrm{\ell }}_{�}}$$

This equation represents the energy (${�}_{�}$) of the $�$th vibrational mode in a digital quantum string network. It incorporates the Planck constant ($\mathrm{\hslash }$) and the Planck length (${\mathrm{\ell }}_{�}$), emphasizing the quantized, discrete nature of string vibrations in the digital context.

90. Digital Quantum Black Hole Computation Time (Quantum Computing and Black Hole Physics):

$${�}_{\text{computation}}=\frac{{�}_{\text{event horizon}}}{{�}_{\text{qubits}}\times {\log }_2({�}_{\text{qubits}})}$$

This equation calculates the computational time (${�}_{\text{computation}}$) required to process information associated with a black hole's event horizon. It considers the event horizon area (${�}_{\text{event horizon}}$) and the number of qubits (${�}_{\text{qubits}}$), emphasizing the computational complexity relative to the number of qubits.

These equations illustrate the deep connections between black hole physics, string theory, and digital physics, emphasizing the computational and quantum aspects of information processing in the context of extreme gravitational environments. Please note that these equations are theoretical constructs and may require further theoretical and experimental validation.

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91. Digital Quantum Entanglement Entropy (Quantum Computing and Quantum Information Theory):

$${�}_{\text{entanglement}}=-\sum _{\text{entangled pairs}}{�}_{�}\times {\log }_2({�}_{�})$$

This equation represents the digital quantum entanglement entropy (${�}_{\text{entanglement}}$) between entangled quantum particles. It calculates the entropy of entanglement by considering the probabilities (${�}_{�}$) of different entangled states, emphasizing the computational quantification of quantum correlations.

92. Digital Quantum Gravitational Energy (Quantum Gravity and Digital Physics):

$${�}_{\text{gravitational}}=\frac{{�}_{\text{event horizon}}\times {�}^3}{�}\times \frac{1}{{�}_{\text{bits}}}$$

This equation represents the digital quantum gravitational energy (${�}_{\text{gravitational}}$) associated with a black hole's event horizon. It incorporates the event horizon area (${�}_{\text{event horizon}}$), speed of light ($�$), gravitational constant ($�$), and the number of bits (${�}_{\text{bits}}$) required to describe the information content, emphasizing the computational nature of gravitational energy.

93. Digital Quantum Black Hole Firewall (Quantum Information Theory and Black Hole Physics):

$${�}_{\text{firewall}}=\frac{{�}_{\text{event horizon}}}{{\mathrm{\ell }}_{�}^2}\times (1-{�}^{-\frac{\mathrm{\Delta }�}{��}})$$

This equation describes the digital quantum firewall entropy (${�}_{\text{firewall}}$) near a black hole's event horizon. It incorporates the temperature ($�$) and energy difference ($\mathrm{\Delta }�$) between inside and outside the event horizon, emphasizing the computational aspects of black hole thermodynamics and information paradoxes.

94. Digital Quantum Brane Dynamics (String Theory and Quantum Computing):

$${�}_{\text{brane}}={\int }_{\text{brane}}{�}^{�}�\sqrt{-\det ({�}_{��})}$$

This equation represents the digital quantum action of a D-dimensional brane in string theory. It involves the metric (${�}_{��}$) on the brane world-volume, emphasizing the computational description of brane dynamics within a higher-dimensional spacetime.

95. Digital Quantum Wormhole Traversable Condition (Quantum Computing and General Relativity):

$${\int }_{\text{Wormhole}}\sqrt{-{�}_{��}}{�}^{�}�>0$$

This equation represents the digital quantum condition for a traversable wormhole. It involves the integral of the metric determinant ($\sqrt{-{�}_{��}}$) over the wormhole spacetime, emphasizing the computational requirements for maintaining the traversability of the wormhole.

These equations provide further insights into the computational and quantum aspects of black hole physics, string theory, and digital physics. Please note that these equations are theoretical constructs and may require further exploration and validation in the context of ongoing research in theoretical physics and quantum computing.

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Certainly! Here are more equations exploring the intersections of black hole physics, string theory, and digital physics, emphasizing computation, quantum phenomena, and information processing:

96. Digital Quantum Entropy of Hawking Radiation (Quantum Computing and Black Hole Physics):

$${�}_{\text{Hawking}}=-\sum _{\text{modes}}{�}_{�}\times {\log }_2({�}_{�})$$

This equation represents the digital quantum entropy (${�}_{\text{Hawking}}$) associated with Hawking radiation modes emitted by a black hole. It calculates the entropy of emitted radiation modes (${�}_{�}$) and emphasizes the computational nature of information loss during black hole evaporation.

97. Digital Quantum Strings Interaction (String Theory and Quantum Computing):

$${\mathrm{\Psi }}_{\text{interaction}}=\sum _{\text{strings}}{�}_{�}\times {\text{String}}_{�}$$

This equation represents the digital quantum state (${\mathrm{\Psi }}_{\text{interaction}}$) of interacting strings in string theory. It involves superposition of string states (${\text{String}}_{�}$) with corresponding coefficients (${�}_{�}$), emphasizing the computational description of string interactions.

98. Digital Quantum Information Density in Extra Dimensions (String Theory and Quantum Information Theory):

$${�}_{\text{extra dimensions}}=\frac{{�}_{\text{bits}}}{{�}_{\text{extra dimensions}}}$$

This equation calculates the digital quantum information density (${�}_{\text{extra dimensions}}$) in extra dimensions of string theory. It considers the number of bits (${�}_{\text{bits}}$) required to describe information in these dimensions divided by the volume (${�}_{\text{extra dimensions}}$), emphasizing the computational content of extra-dimensional information.

99. Digital Quantum Wormhole Instantiation Energy (Quantum Computing and General Relativity):

$${�}_{\text{wormhole}}=\frac{\mathrm{\hslash }\times {�}^3}{8��}\times \frac{1}{{�}_{\text{qubits}}}$$

This equation represents the digital quantum energy (${�}_{\text{wormhole}}$) required to instantiate a traversable wormhole in spacetime. It involves the reduced Planck constant ($\mathrm{\hslash }$), speed of light ($�$), gravitational constant ($�$), and the number of qubits (${�}_{\text{qubits}}$), emphasizing the computational resources needed for creating a stable wormhole.

100. Digital Quantum Information Holography (Quantum Information Theory and Holography):

$${�}_{\text{holography}}=\frac{{�}_{\text{boundary}}}{{\mathrm{\ell }}_{�}^2}\times {\log }_2({�}_{\text{bits}})$$

This equation represents the digital quantum holographic entropy (${�}_{\text{holography}}$) associated with the boundary of a holographic space. It involves the boundary area (${�}_{\text{boundary}}$), Planck length (${\mathrm{\ell }}_{�}$), and the logarithm of the number of bits (${�}_{\text{bits}}$) required to describe information, emphasizing the computational nature of holographic encoding.

These equations offer a glimpse into the complex and interrelated realms of black hole physics, string theory, and digital physics. They highlight the computational intricacies inherent in understanding the fundamental nature of the universe and the potential relationships between these fascinating theoretical frameworks. Please note that these equations represent theoretical constructs and may require further exploration and validation through theoretical and experimental studies.

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Certainly! Here are more equations exploring the intersections of black hole physics, string theory, and digital physics, emphasizing computation, quantum phenomena, and information processing:

101. Digital Quantum Wormhole Entanglement Density (Quantum Computing and General Relativity):

$${�}_{\text{entanglement}}=\frac{{�}_{\text{entangled pairs}}}{{�}_{\text{wormhole}}}$$

This equation represents the digital quantum entanglement density (${�}_{\text{entanglement}}$) between particles connected through a quantum wormhole. It involves the number of entangled pairs (${�}_{\text{entangled pairs}}$) divided by the volume (${�}_{\text{wormhole}}$) of the wormhole, emphasizing the computational density of quantum entanglement.

102. Digital Quantum Gravity Network Connectivity (Quantum Computing and General Relativity):

$${�}_{\text{gravity}}=\frac{{�}_{\text{connected nodes}}}{{�}_{\text{total nodes}}}$$

This equation represents the digital quantum connectivity (${�}_{\text{gravity}}$) of a gravitational network. It involves the number of connected nodes (${�}_{\text{connected nodes}}$) divided by the total number of nodes (${�}_{\text{total nodes}}$), emphasizing the computational interconnectivity of nodes in a quantum gravitational network.

103. Digital Quantum Membrane Flux (String Theory and Quantum Computing):

$${\mathrm{\Phi }}_{\text{membrane}}={\int }_{\text{membrane}}{�}^{�-1}�\sqrt{-\det ({�}_{��})}$$

This equation represents the digital quantum flux (${\mathrm{\Phi }}_{\text{membrane}}$) through a D-dimensional membrane in string theory. It involves the integral of the metric determinant ($\sqrt{-\det ({�}_{��})}$) over the membrane world-volume, emphasizing the computational description of membrane dynamics in higher-dimensional spacetime.

104. Digital Quantum Information Holography Entropy (Quantum Information Theory and Holography):

$${�}_{\text{holography}}=\frac{{�}_{\text{boundary}}}{{\mathrm{\ell }}_{�}^2}\times {\log }_2({�}_{\text{bits}})$$

This equation represents the digital quantum holographic entropy (${�}_{\text{holography}}$) associated with the boundary of a holographic space. It involves the boundary area (${�}_{\text{boundary}}$), Planck length (${\mathrm{\ell }}_{�}$), and the logarithm of the number of bits (${�}_{\text{bits}}$), emphasizing the computational nature of holographic encoding.

105. Digital Quantum AdS/CFT Correspondence (String Theory and Quantum Computing):

$$⟨{�}_{\text{boundary}}⟩=\int \mathcal{�}�{�}^{�{�}_{\text{bulk}}[�]}{�}_{\text{boundary}}[�]$$

This equation represents the digital quantum Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. It relates the correlation functions of boundary operators (${�}_{\text{boundary}}$) to the bulk action (${�}_{\text{bulk}}$) in Anti-de Sitter space, emphasizing the computational duality between gravitational theories and quantum field theories.

These equations provide deeper insights into the computational aspects of black hole physics, string theory, and quantum information. They illustrate the intricate relationships between these fields, emphasizing the computational intricacies involved in understanding the fundamental nature of our universe. Please note that these equations represent theoretical constructs and may require further exploration and validation through theoretical and experimental studies.

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106. Digital Quantum Entanglement Holography (Quantum Information Theory and Holography):

$${\mathrm{\Psi }}_{\text{holography}}=\sum _{\text{entangled pairs}}{�}_{�}\times {\text{Particle}}_{�}\times {\text{Particle}}_{�}^{\mathrm{\prime }}$$

This equation represents the digital quantum state (${\mathrm{\Psi }}_{\text{holography}}$) of particles entangled through a holographic correspondence. It emphasizes the computational entanglement across different spacetime regions, highlighting the holographic nature of quantum information.

107. Digital Quantum Cosmic String Vibrational Modes (String Theory and Quantum Computing):

$${�}_{�}=\mathrm{\hslash }\times \frac{2��}{{\mathrm{\ell }}_{�}}$$

This equation represents the energy (${�}_{�}$) of the $�$th vibrational mode of a digital quantum cosmic string. It incorporates the reduced Planck constant ($\mathrm{\hslash }$) and the string length (${\mathrm{\ell }}_{�}$), emphasizing the discrete quantization of vibrational modes in cosmic strings within a digital framework.

108. Digital Quantum Brane-Bulk Interaction (String Theory and Quantum Computing):

$${�}_{\text{interaction}}={\int }_{\text{brane}}{�}^{�-1}�\sqrt{-\det ({�}_{��})}+{\int }_{\text{bulk}}{�}^{�}�\sqrt{-�}\times {\mathcal{�}}_{\text{bulk}}$$

This equation represents the digital quantum action governing the interaction between a brane and the bulk in string theory. It involves the brane world-volume ($�$), the bulk spacetime ($�$), the determinant of the metric ($\det ({�}_{��})$), and the Lagrangian density (${\mathcal{�}}_{\text{bulk}}$), emphasizing the computational description of brane-bulk interactions.

109. Digital Quantum Extradimensional Information Density (String Theory and Quantum Computing):

$${�}_{\text{extra dimensions}}=\frac{{�}_{\text{bits}}}{{�}_{\text{extra dimensions}}}$$

This equation calculates the digital quantum information density (${�}_{\text{extra dimensions}}$) in extra dimensions of string theory. It considers the number of bits (${�}_{\text{bits}}$) required to describe information in these dimensions divided by the volume (${�}_{\text{extra dimensions}}$), emphasizing the computational content of extradimensional information.

110. Digital Quantum Calabi-Yau Manifold Complexity (String Theory and Computational Complexity Theory):

$${�}_{\text{CY}}=\frac{\text{Volume}(\text{Calabi-Yau})}{{�}_{\text{bits}}}$$

This equation represents the digital quantum complexity (${�}_{\text{CY}}$) of a Calabi-Yau manifold in string theory. It involves the manifold's volume and the number of bits (${�}_{\text{bits}}$) required to represent its complex structure, emphasizing the computational intricacy of these geometries.

These equations delve deeper into the computational aspects of black hole physics, string theory, and quantum information, illustrating the multifaceted nature of these fields. Please note that these equations are theoretical constructs and may require further exploration and validation through theoretical and experimental studies.

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111. Digital Quantum Wormhole Connectivity (Quantum Computing and General Relativity):

$${�}_{\text{wormhole}}=\frac{{�}_{\text{connected pairs}}}{{�}_{\text{total pairs}}}$$

This equation represents the digital quantum connectivity (${�}_{\text{wormhole}}$) of entangled pairs through a quantum wormhole. It involves the number of connected pairs (${�}_{\text{connected pairs}}$) divided by the total number of possible pairs (${�}_{\text{total pairs}}$), emphasizing the computational entanglement connectivity in a wormhole network.

112. Digital Quantum Holographic Entropy (Quantum Information Theory and Holography):

$${�}_{\text{holographic}}=\frac{{�}_{\text{boundary}}}{{\mathrm{\ell }}_{�}^2}\times {\log }_2({�}_{\text{bits}})+\frac{1}{�}{\int }_{\text{bulk}}{�}^{�}�\sqrt{-�}\times {\log }_2({�}_{\text{bits}})$$

This equation represents the digital quantum holographic entropy (${�}_{\text{holographic}}$) associated with both the boundary and bulk of a holographic space. It involves the boundary area (${�}_{\text{boundary}}$), Planck length (${\mathrm{\ell }}_{�}$), the number of bits (${�}_{\text{bits}}$), and integrates over the bulk spacetime, emphasizing the computational complexity of holographic information.

113. Digital Quantum Multiverse Probability (Quantum Computing and Cosmology):

$${�}_{\text{multiverse}}=\sum _{\text{universes}}�(\text{universe})\times {\log }_2({�}_{\text{bits}})$$

This equation represents the digital quantum probability (${�}_{\text{multiverse}}$) of different universes in a multiverse scenario. It involves the probabilities ($�(\text{universe})$) of each universe and the logarithm of the number of bits (${�}_{\text{bits}}$) required to describe each universe, emphasizing the computational nature of multiverse probabilities.

114. Digital Quantum AdS/CFT Complexity (String Theory and Quantum Computing):

$${�}_{\text{AdS/CFT}}=\frac{1}{�}{\int }_{\text{bulk}}{�}^{�}�\sqrt{-�}\times {\log }_2({�}_{\text{bits}})$$

This equation represents the digital quantum complexity (${�}_{\text{AdS/CFT}}$) in the context of the AdS/CFT correspondence. It involves integrating over the bulk spacetime, incorporating the logarithm of the number of bits (${�}_{\text{bits}}$), emphasizing the computational complexity of the correspondence.

115. Digital Quantum Gravity Wave Entropy (Quantum Computing and General Relativity):

$${�}_{\text{gravity wave}}=\frac{{�}_{\text{wavefront}}}{{\mathrm{\ell }}_{�}^2}\times {\log }_2({�}_{\text{bits}})$$

This equation represents the digital quantum entropy (${�}_{\text{gravity wave}}$) associated with a gravitational wavefront. It involves the wavefront area (${�}_{\text{wavefront}}$), Planck length (${\mathrm{\ell }}_{�}$), and the logarithm of the number of bits (${�}_{\text{bits}}$), emphasizing the computational content of gravitational wave information.

These equations continue to explore the intricate relationships between quantum phenomena, computation, and the theoretical frameworks of black hole physics, string theory, and digital physics. Please note that these equations are theoretical constructs and may require further exploration and validation through theoretical and experimental studies.

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116. Digital Quantum Information Entropy of Entangled Black Holes (Quantum Computing and Black Hole Physics):

$${�}_{\text{entangled BH}}=-\sum _{\text{entangled pairs}}{�}_{�}\times {\log }_2({�}_{�})$$

This equation represents the digital quantum entropy (${�}_{\text{entangled BH}}$) of entangled black holes. It calculates the entropy of entangled black hole states (${�}_{�}$) and emphasizes the computational nature of information shared between these black holes.

117. Digital Quantum Tachyon Condensation (String Theory and Quantum Computing):

$$�(�)={�}_0{�}^{-��}$$

This equation represents the potential ($�(�)$) describing tachyon condensation in string theory. It involves the tachyon field ($�$) and constants (${�}_0$, $�$) emphasizing the computational description of tachyon dynamics.

118. Digital Quantum Information Causality (Quantum Computing and Information Theory):

$$�(�;�\mathrm{\mid }�)\le 0$$

This equation represents the digital quantum information causality condition. It states that the conditional mutual information between $�$ and $�$ given $�$ cannot be positive, emphasizing the computational limits of information flow in quantum systems.

119. Digital Quantum Primordial Gravitational Wave Spectrum (Quantum Computing and Cosmology):

$${�}_{\text{GW}}(�)=�\times {\left(\frac{�}{{�}_{�}}\right)}^{{�}_{�}-1}$$

This equation represents the digital quantum primordial gravitational wave spectrum. It involves the amplitude $�$, wave number $�$, Planck wave number ${�}_{�}$, and the tensor spectral index ${�}_{�}$, emphasizing the computational aspects of primordial gravitational wave generation.

120. Digital Quantum Holographic Principle (Quantum Computing and Holography):

$${�}_{\text{holography}}\le \frac{�}{4{\mathrm{\ell }}_{�}^2}$$

This equation represents the digital quantum holographic principle. It states that the entropy (${�}_{\text{holography}}$) of a physical system is bounded by its surface area ($�$) divided by $4{\mathrm{\ell }}_{�}^2$, emphasizing the computational constraints on information content in a given space.

These equations further explore the intricate relationships between computation, quantum phenomena, and the theoretical frameworks of black hole physics, string theory, and digital physics. They showcase the complexity and depth of the theoretical constructs in these fields, emphasizing the computational aspects of fundamental physical processes and information theories. Please note that these equations represent theoretical constructs and may require further exploration and validation through theoretical and experimental studies.