Beyond Ones and Zeroes

Superposition and Bell States

Sid
4 min readApr 16, 2024

The first thing most students learn when entering a computer science class is the concept of binary. All data stored, processed, and transmitted by computers is solely made up of 2 digits: 0s and 1s.

The core principle of digital information — a bit can only exist in one of two distinct states — underpins the entire domain of computer architecture.

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In the early 1980’s, noticing the limitations of classical computers, physicist Richard Feynman proposed an alternative — a computer which functioned based on the principles of quantum mechanics. Working off his vision, other scientists, including Paul Benioff and David Deustch, developed a theoretical framework for a potential quantum computer, built using a concept known as qubits.

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In classical physics, objects are in definite states — a coin can either be heads or tails, but never both.

The theory of quantum superposition states that a quantum system can exist in multiple states simultaneously.

When carrying out Young’s double-slit experiment with an electron beam, a characteristic interference pattern of alternating minima and maxima when diffracted through a double slits, showing that electrons behave like a wave.

When repeated with an observer, the electrons go back to behaving like a particle.

The interference pattern is no longer formed, instead, the electrons form 2 lines on the back screen corresponding to the position of the slits, showcasing the wave-particle duality of electrons.

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Superposition

The superposition principle demonstrated by electrons was the concept applied when developing quantum computers. Instead of existing in one of 2 states, a qubit has the ability to represent a 0, a 1, or any proportion of 0 and 1 in superposition of both states, with a certain probability of being a 0 and a certain probability of being a 1.

To make qubits, scientists make use of various physical systems that can exist in a superposition of 2 distinct quantum states. Some examples of physical qubits include

  1. Excitation states of atoms. As atoms absorb energy, electrons move up to higher energy levels. Each energy level can represent a different qubit state (ground state = 0, ionised = 1, and everything in between).
  2. Electron spins. Information is encoded in the intrinsic spin of trapped electrons.
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Entanglement

The existence of qubits is defined by the wave function (Ψ), which describes the probabilities of finding a qubit in a specific state (0, 1, or anything in between).

Entanglement occurs when the wave functions of 2 qubits become linked. When the state of a qubit is measured, its entangled partner is forced to remain in a specific state that is correlated with the initial measurement.

Even though the individual states of 2 entangled qubits seemed random, they are perfectly correlated.

One physical representation of a qubit, as mentioned above, are electron spins. In the context of entanglement, measuring one qubit to be in an “up” spin could guarantee the other qubit to be in a “down” spin. This is known as a Bell state. There are 4 unique Bell states for 2 entangled qubits.

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This area is at the forefront of scientific research. In 2022, the Nobel Prize in Physics was awarded to Alain Aspect, John F. Clauser, and Anton Zeilinger for their experiments that confirmed John Bell’s groundbreaking predictions about entanglement.

Because of superposition and entanglement, qubits can explore far more possibilities than regular bits can handle at the same time. The parallel processing capability of qubits increases exponentially as the number of qubits increases.

10 classical bits can represent 2¹⁰ unique states, with 1024 values.

A 10 qubit system can represent 1024 unique states in parallel — a system which can be achieved using 16 kilobytes of classical bits.

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The exponential growth of processing power of quantum computing systems has proven its worth already. In 2019, a mathematical problem that would take 10,000 years to solve on the world’s fastest supercomputer was solved by Google’s Sycamore quantum computer — in just 200 seconds.

This makes them extremely powerful for certain tasks including drug discovery, financial modelling, and possibly the most important of them all — breaking cryptographic encryption.

With continued development, quantum computers have the potential to solve some of humanity’s most pressing challenges. As research continues, the possibilities seem limitless.

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