Faster Computers Unlocked: Energy Scale Boosts Processing

The fundamental limits of information processing remain a central question in physics and computer science, and recent work explores these boundaries through the lens of complexity growth rate. Mojtaba Shahbazi and Mehdi Sadeghi, both from Ayatollah Boroujerdi University, investigate abrupt changes in this growth rate, revealing a surprising connection to concepts from high-energy physics. Their research demonstrates that these changes, or ‘jumps’, are governed by properties analogous to those found in bulk materials, specifically relating to energy momentum, viscosity, and anomalies on the boundary of a system. Importantly, the team discovers that complexity growth rate obeys an equation similar to the Callan-Symanzik equation used in quantum field theory, suggesting that processing speed can be altered by manipulating energy scales, potentially paving the way for computers significantly faster than those available today.

Holographic Complexity and Phase Transitions

This research explores holographic complexity, linking the complexity of a quantum system to the geometry of a corresponding gravitational theory. Researchers demonstrate that changes in complexity relate to phase transitions and are influenced by the Weyl squared tensor. This allows for a deeper understanding of how these transitions occur and what factors influence them. The team proposes that the Weyl squared tensor plays a crucial role in generalizing the surfaces used to calculate complexity, revealing connections to the divergence of the energy-momentum tensor, shear viscosity, and the Weyl anomaly of the boundary theory.

These factors control the phase transitions and the magnitude of changes in complexity. Complexity exhibits behavior analogous to a Callan-Symanzik-like equation, suggesting that complexity is scale-dependent and that the phase transitions are universal. This universality implies that the underlying principles governing complexity are fundamental and apply broadly across different systems, potentially optimizing information processing beyond current quantum computers.

Complexity Growth Rate and Gravitational Dynamics

This research investigates the growth rate of computational complexity, exploring how it arises from gravitational systems and relates to information processing. Researchers examine how changes in the complexity growth rate correlate with dynamics in the bulk gravitational system, identifying the factors that determine jumps observed in the growth rate. The team employs a method drawing an analogy between the growth of complexity and the motion of a classical particle, deriving equations of motion for a particle moving within an effective potential. This allows them to connect the behavior of the complexity growth rate to the properties of the potential and the particle’s trajectory, influenced by characteristics of the bulk gravitational system, such as the energy-momentum tensor, shear viscosity, and Weyl anomaly.

A key innovation lies in mapping properties of the boundary theory to dynamics within the bulk gravitational system, showing that the location of jumps in the complexity growth rate is dynamically influenced by these bulk fields. The amplitude of these jumps is linked to the renormalization group flow of the boundary theory, revealing how the system scales with changes in energy. The analysis reveals that transitions in complexity growth rate exhibit critical phenomena, displaying scaling behavior and universality, governed by a Callan-Symanzik-like equation. This equation suggests that the speed of information processing can be altered by changing the energy scale, potentially enabling faster computation. The late-time behavior of the complexity growth rate is determined by the local maximum of the effective potential, providing a crucial point for understanding the limits and potential of complexity growth.

Complexity Jumps Link to Boundary Field Dynamics

Researchers have discovered a connection between complexity growth rate and the dynamics of fields existing on the boundary of a theoretical spacetime. Jumps in the complexity growth rate are not random occurrences, but are instead directly linked to physical phenomena occurring on the boundary, signaled by a particle-like entity reaching a local maximum potential energy. These jumps in complexity growth rate are governed by three key properties of the boundary theory: the Weyl anomaly, shear viscosity, and the flow of matter. The magnitude of these jumps is determined by the interplay of these three factors, suggesting a deep connection between information processing and the fundamental properties of the boundary system.

The complexity growth rate can be described by an equation similar to the Callan-Symanzik equation, suggesting that the speed of information processing can be altered by changing the energy scale of the system. This has profound implications for computing, potentially offering a pathway to create processors that are significantly faster than those currently available. The research establishes a clear link between bulk spacetime dynamics and boundary theory properties, offering a new framework for understanding the fundamental limits of information processing and potentially paving the way for novel computational architectures.

Complexity Jumps Link Gravity and Computation

This research investigates the growth rate of computational complexity, revealing connections between jumps in this growth rate and properties of bulk fields in a theoretical framework linking gravity and quantum mechanics. These jumps are linked to the divergence of energy-momentum tensor, shear viscosity, and the Weyl anomaly on the boundary of the system, suggesting a physical basis for transitions in computational complexity. The complexity growth rate satisfies an equation analogous to the Callan-Symanzik equation, implying that the speed of information processing can be altered by changing the scale of energy. This suggests a potential pathway for enhancing computational speed, not by improving the quantum gates themselves, but by manipulating the energy scale at which they operate.