#4342 16-Core CPU at 7.85 exahertz (EHz)

#4342 Describe a problem that takes quantum computers minutes to solve, but takes supercomputers thousands of years.

A classic example of this "Quantum Supremacy" (or quantum advantage) is Random Circuit Sampling.

This problem was specifically designed to demonstrate the point where a programmable quantum device can perform a task that no classical supercomputer can feasibly replicate.

The Problem: Random Circuit Sampling

In this task, a quantum computer is given a sequence of random quantum "gates" (operations). The goal is to execute these gates on a set of qubits and then measure the final state.

Because of quantum entanglement and superposition, the qubits exist in a complex probability distribution. To "solve" the problem, the computer must produce a set of samples (bitstrings) that follow this specific, incredibly complex probability distribution.

Why It’s Impossible for Supercomputers

As you add more qubits, the "state space" of the system grows exponentially.

For 53 qubits (like Google’s Sycamore processor), a classical computer must track $2^{53}$ different states simultaneously. This is roughly 9 quadrillion numbers.
To simulate just one operation, a supercomputer has to perform massive matrix-vector multiplications across that entire state space.
As the circuit gets "deeper" (more operations), the complexity of calculating the final probability distribution becomes so high that even the world's most powerful supercomputers, like Frontier or Summit, would need to run for millennia to produce the same results that a quantum computer generates in about 200 seconds.

Other Real-World Candidates

While Random Circuit Sampling is a "benchmarking" problem, there are two other famous examples that follow this same time-gap logic:

Problem	Quantum Time	Supercomputer Time
Shor’s Algorithm	Minutes/Hours	Billions of Years
Breaking 2048-bit RSA encryption by finding prime factors.
Boson Sampling	Minutes	Billions of Years
Calculating the distribution of photons passing through an optical network.
Molecular Simulation	Minutes/Hours	Decades/Centuries
Simulating the exact electron energy states of complex molecules (like FeMoco for nitrogen fixation).

The "Shortcut" Factor

The reason for this discrepancy isn't just "faster hardware." It's about the algorithm. Classical supercomputers use "brute force" to track every possibility one by one. Quantum computers use constructive interference to amplify the correct answer and destructive interference to cancel out the wrong ones, essentially "sifting" through the entire solution space at once.

Given 5 gigaherz CPUs today, what CPU rate would be required to match the quantum computer?

To match a quantum computer’s performance through raw clock speed alone, the numbers quickly enter the realm of science fiction.

Because quantum computers scale exponentially rather than linearly, the "required" GHz rate for a classical CPU doesn't just double or triple—it explodes.

The Comparison: 53-Qubit Sycamore vs. Frontier Supercomputer

Google’s 2019 "Sycamore" experiment (53 qubits) solved a random circuit sampling problem in 200 seconds.

The Supercomputer: Oak Ridge National Laboratory’s Frontier (the world's first exascale supercomputer) would theoretically take several days to 10,000 years (depending on the algorithm used) to solve the same problem.
The Hardware: Frontier has ~8.7 million CPU cores.

The Calculation

If we assume the "10,000 years" figure for a single hypothetical CPU to match what the quantum computer did in 200 seconds:

The Time Ratio: 10,000 years is approximately $3.15 \times 10^{11}$ seconds.
The Speedup: To shrink $3.15 \times 10^{11}$ seconds down to 200 seconds, you need a speedup factor of 1.57 billion times.
The Clock Rate: If your current CPU is 5 GHz ( $5 \times 10^9$ Hz), you would need a clock rate of:
$5 \text{ GHz} \times 1.57 \text{ billion} \approx 7.85 \text{ exahertz (EHz)}$

To put 7.85 Exahertz in perspective:

It is 7,850,000,000 GHz.
The frequency of X-rays starts at about 30 Petahertz. An Exahertz CPU would essentially be a Gamma-ray emitter, vibrating so fast that it would likely undergo spontaneous nuclear transitions or simply vaporize into pure energy.

Why GHz Doesn't Matter to a Quantum Computer

The reason you can't "clock speed" your way out of this is the State Space.

Qubits	Classical States to Track
10	1,024
30	1,073,741,824 (1 Billion)
53	9,007,199,254,740,992 (9 Quadrillion)
300	More states than there are atoms in the observable universe.

For a classical CPU, every time you add one qubit, you have to double the CPU speed (or the number of CPUs) just to keep up. By the time you reach 70 or 100 qubits, there isn't enough matter in the solar system to build a classical computer fast enough to compete, even if every atom was a 5 GHz processor.

In short, a quantum computer isn't just "faster"—it's taking a different path. While a classical computer is a mouse trying to solve a maze by running every possible path one by one, a quantum computer is the mist that fills the entire maze simultaneously and finds the exit.

So let's develop a 16-core CPU at 7.85 exahertz (EHz)

Designing a 16-core CPU that operates at 7.85 Exahertz (EHz) is a fascinating "thought experiment," but according to our current understanding of physics, it would likely be the most dangerous object ever constructed.

To build this, we have to bypass three "hard" physical walls. Here is the blueprint for your 16-core EHz processor:

1. The Material Wall: From Silicon to Dielectrics

At 7.85 EHz, silicon is useless. The electrons simply cannot move fast enough through a semiconductor to switch states at that frequency; they hit a "speed limit" (the Petahertz limit) due to the time it takes for quantum mechanical processes to generate a current.

The Solution: We must use dielectric materials (like lithium fluoride or specialized glass) and switch the state using ultrashort UV laser pulses instead of electrical voltage. This moves us into the realm of Attosecond Physics.
The Problem: At exahertz frequencies, the "clock signal" is no longer an electrical wave; it is a Gamma Ray.

2. The Speed of Light Wall: The "Atomic Scale" Core

This is the most rigid constraint. Information cannot travel faster than $c$ (the speed of light).

Calculation: At 7.85 EHz, one clock cycle lasts roughly 0.127 attoseconds.
Travel Distance: In one cycle, light travels only 0.038 nanometers ( $3.8 \times 10^{-11}$ meters).
The Design: For a 16-core processor to remain "synchronized," the distance between any two components must be smaller than the distance light travels in one cycle.
- Since 0.038 nm is smaller than the diameter of a Hydrogen atom (~0.1 nm), your 16-core CPU cannot exist as a multi-component chip.
- The entire 16-core architecture would have to be contained within a space smaller than a single atom. Essentially, your "CPU" would be a singular subatomic particle or a highly dense "quark-gluon" computational plasma.

3. The Thermal Wall: The "Star-in-a-Box" Problem

Every time a bit flips, it generates a tiny amount of heat (the Landauer Limit).

The Math: At room temperature, erasing one bit generates $2.9 \times 10^{-21}$ Joules.
The Result: If your 16-core CPU is processing data at 7.85 EHz, the energy dissipation would be so intense that the "chip" would have a power density significantly higher than the core of the Sun. It wouldn't just melt; it would instantly become a localized supernova.

Comparison: Your 16-Core EHz CPU vs. Reality

Feature	Your 5 GHz CPU	The 7.85 EHz "Quantum Match"
Clock Cycle	0.2 nanoseconds	0.127 attoseconds
Signal Carrier	Electrons	High-energy Gamma Rays
Size	~1-2 cm	Sub-atomic (smaller than 0.04 nm)
Cooling	Fans / Liquid Nitrogen	Impossible (Violates thermodynamics)
Stability	Years	Immediate nuclear explosion

The Verdict

To match a 53-qubit quantum computer using a classical CPU, you wouldn't be building a "computer" in the traditional sense. You would be trying to engineer a controlled singularity.

This is exactly why researchers are so excited about quantum computing: it allows us to solve these "impossible" problems using the weirdness of quantum mechanics (interference and entanglement) rather than trying to build a Gamma-ray-emitting, atom-sized super-processor that violates the laws of thermodynamics.

From <https://gemini.google.com/app/> Google Gemini 3.0 (Fast)

Search This Blog

Learning from ChatGPT