Quantum Computing Explained: How It Differs From Classical Computers and Why It Matters for Bitcoin

What exactly is quantum computing, and how does it differ from an ordinary computer? And why should Bitcoin users care?

Newcomers to Bitcoin regularly encounter these questions and must grapple with the concerns they raise about Bitcoin's vulnerability to what could become a genuine existential danger if a functional quantum computer is ever built.

The ability to own bitcoin depends on the fundamental premise that, unless a copy is directly leaked, only the holder of a private key can authorize transactions involving coins secured by that key. Quantum computing challenges that premise.

Quantum computers are not merely "computers, but faster." They operate on a profoundly different basis than classical computers, making them far more efficient at very particular types of calculations. Obviously, a detailed technical explanation of quantum computing is beyond the scope of this piece, but the core idea of how they differ from classical machines will be outlined.

Consider how each type of computer handles large cryptographic keys.

Classical Computers

Every piece of data in a classical computer is represented as a sequence of 1s and 0s. Each bit is unambiguously either a 1 or a 0. Data is stored, manipulated and modified bit by bit, step by step, one bit at a time.

A computer works linearly. It modifies discrete, unambiguous data pieces one step after another. It cannot jump ahead or take shortcuts in its step-by-step process; it must execute each computational step in order.

When a computer generates a private key, it obtains a random value and stores it in memory as 1s and 0s. It then multiplies that value by the elliptic curve's generator point to produce a public key. This is done via an algorithm — essentially instructions on which bits to take, how to modify them, and which physical circuits to use, eventually placing the new, altered value back into memory.

Additional steps are required to produce a valid address, but for this discussion they are not essential. They follow the same pattern: step-by-step instructions for modifying 1s and 0s in memory.

What if someone wanted to use a computer to guess another person's private key?

There are 2^256 possible private keys — that is 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936 distinct possibilities.

A computer would need to test every single one of those private keys, one after another (or as many in parallel as possible), following the exact key-generation instructions. The more keys checked in parallel, the more computing power is required, and there is no way around that cost.

Less computing power means more time; less time requires more computing power.

This is an impossible task for a classical computer. On one hand, the computational cost exceeds the combined capacity of every computer on Earth. On the other, the time required is so vast that every star in the universe would burn out before all keys were checked.

To succeed, a different approach is needed — one that does not rely on checking keys linearly or in parallel. That is where quantum computing enters the picture.

Quantum Computers

Quantum computers do not work with discrete states. While everything is still ultimately a 1 or a 0, the basic information unit is a qubit. Unlike a bit, a qubit exists in a superposition, simultaneously being both a 1 and a 0. It settles into one definite state only when observed.

Superposition is one key building block. The other is entanglement. Qubits are not stored in isolation; the physical atoms representing them become entangled. When observed and collapsed, entangled atoms collapse to the same state regardless of distance.

This is where the explanation becomes somewhat hand-wavy, but the essential intuition remains. A classical algorithm is a set of instructions that takes specific bits and modifies them step by step until a new set of bits is output. It transforms one discrete state into another.

Qubits do not store discrete states until observed. They store probabilities. When qubits of any given size are entangled — hypothetically 2^256 — each possible collapsed state has a certain probability of occurring.

Quantum algorithms are not step-by-step instructions for operating on discrete states. Instead, they are instructions for operating on entangled qubits to alter the probabilities of different outcomes. Constructive interference boosts the probability of a correct result, while destructive interference lowers the probability of incorrect ones. (This is not the same as the physical noise that makes building functional quantum computers difficult.)

A classical computer must check each private key individually to find the one matching a given public key. A quantum computer, using the right algorithm, can run a few times and arrive at the correct answer. It does not "check all possibilities at once." It simply adjusts the probabilities of what a superposition collapses into.

This explains why a quantum computer could break the assumptions behind elliptic curve cryptography while a classical computer cannot. It also explains why quantum computers are only useful for certain problems with a vast space of possible answers.

Don't Panic

This fundamental difference means that if a viable, correctly functioning quantum computer is ever built, the foundational assumption securing every Bitcoiner's coins is broken. All those funds become insecure.

Yes, this is a serious risk if such a device is actually manufactured and works. But the community is not entirely unprepared. The problem and the exposure are understood, and many potential solutions for various facets of the issue are taking shape.

Breathe and relax. The rest of this issue will walk through the entire problem.

This piece is featured in the latest Print edition of Bitcoin Magazine, The Quantum Issue. It is shared here as an early look at the ideas explored throughout the full issue.