This paper explores the ultimate physical limits of computation, focusing on the speed and memory capacity of computers. Seth Lloyd, from MIT, argues that the laws of physics, particularly the speed of light ($c$), Planck's reduced constant ($\hbar$), and the gravitational constant ($G$), set the boundaries for what can be achieved in terms of computational power. The paper calculates the maximum computational capacity of a "ultimate laptop" with a mass of one kilogram and a volume of one liter, considering the energy required for logical operations and the entropy of the system. Key findings include: 1. **Energy Limits Speed**: The speed of computation is limited by the energy available. A system with average energy $E$ can perform a maximum of $2E / \pi \hbar$ logical operations per second. For a one-kilogram computer, this results in a maximum of $5.4258 \times 10^{50}$ operations per second. 2. **Entropy Limits Memory**: The amount of information that can be stored and processed is related to the system's entropy. The maximum entropy for a one-kilogram computer in a liter volume is estimated to be around $2.13 \times 10^{31}$ bits, allowing for approximately $10^{19}$ operations per bit per second. 3. **Parallelization and Serial computation**: The degree of parallelization in a computer is determined by the ratio of the time to communicate across the computer to the time to perform a logical operation. The ultimate laptop is highly parallel, with a ratio of about $10^{10}$. 4. **Black Hole Computation**: The paper discusses the theoretical possibility of a black hole computer, which would operate entirely in serial mode and have a maximum entropy of $3.827 \times 10^{16}$ bits, performing the same number of operations as the one-kilogram computer in a liter volume. The paper concludes by noting that while these physical limits are challenging to achieve, existing quantum computers already operate at or near these boundaries, and further advancements in technology and understanding of quantum mechanics could lead to even more powerful computational systems.This paper explores the ultimate physical limits of computation, focusing on the speed and memory capacity of computers. Seth Lloyd, from MIT, argues that the laws of physics, particularly the speed of light ($c$), Planck's reduced constant ($\hbar$), and the gravitational constant ($G$), set the boundaries for what can be achieved in terms of computational power. The paper calculates the maximum computational capacity of a "ultimate laptop" with a mass of one kilogram and a volume of one liter, considering the energy required for logical operations and the entropy of the system. Key findings include: 1. **Energy Limits Speed**: The speed of computation is limited by the energy available. A system with average energy $E$ can perform a maximum of $2E / \pi \hbar$ logical operations per second. For a one-kilogram computer, this results in a maximum of $5.4258 \times 10^{50}$ operations per second. 2. **Entropy Limits Memory**: The amount of information that can be stored and processed is related to the system's entropy. The maximum entropy for a one-kilogram computer in a liter volume is estimated to be around $2.13 \times 10^{31}$ bits, allowing for approximately $10^{19}$ operations per bit per second. 3. **Parallelization and Serial computation**: The degree of parallelization in a computer is determined by the ratio of the time to communicate across the computer to the time to perform a logical operation. The ultimate laptop is highly parallel, with a ratio of about $10^{10}$. 4. **Black Hole Computation**: The paper discusses the theoretical possibility of a black hole computer, which would operate entirely in serial mode and have a maximum entropy of $3.827 \times 10^{16}$ bits, performing the same number of operations as the one-kilogram computer in a liter volume. The paper concludes by noting that while these physical limits are challenging to achieve, existing quantum computers already operate at or near these boundaries, and further advancements in technology and understanding of quantum mechanics could lead to even more powerful computational systems.