The End of Moore’s Law

In 1965, Gordon E. Moore, the co-founder of Intel, observed that every two years the amount of transistors that could fit on a single microchip was doubling, whilst the cost of computers was halving. Moore’s Law, a projection of this historic trend, has been used since 1975 for forecasting and goal-setting in the semiconductor industry.

Today, the record for the smallest transistor in the world is held by IBM, who have created a one at just 2nm wide. To put this into perspective, this would allow you to pack 50 billion of these tiny transistors onto a chip the size of your fingernail. You may be thinking this seems small enough, why do we want to make them smaller still? The answer is simple; the more transistors that we can cram into a device, the greater the processing power and the faster the computer.

Moore’s Law will soon fail to predict the future prospects of computing power as we eventually manage to create a transistor of the minimum possible size of a transistor. To understand where this minimum size comes from and thus why we are now investing into an alternative approach, we must first understand the key components of a transistor.

Transistors

Transistors are switches that can be turned on using a magnetic field. They are composed of two electrodes separated by a small gap, as depicted below. Above these, sits an insulating layer, which lies under a metal plate. Applying a positive voltage to this metal plate attracts electrons from the silicon electrodes toward the metal plate, where they are blocked by the insulating material. This halts the electrons at the surface of the insulator, creating a current between the electrodes; in this state, the transistor is ‘switched on’.

Fig. 1: Simplified schematic diagram of a transistor

The size of a transistor is measured as the size of the gap between the electrodes. When the positive voltage is removed from the metal plate, electrons retreat from the gap and there is no current flow; this represents ‘off’ state of the transistor. However, as you decrease the size of the gap, eventually a quantum effect known as quantum tunnelling allows electrons to jump across the gap. A higher potential barrier between the electrodes of a transistor reduces the chance of quantum tunnelling – but eventually we reach a point where quantum effects effectively prevent our ability to stop current flow between the electrodes, at which point Moore’s Law will no longer apply. 

Qubits

Quantum computers are being developed as a new, more powerful way of computing. Instead of making use of 2 states represented by an on/off switch, as done in transistors, quantum computers make use of the 2 quantum states of an electron – spin up and spin down. An electron can exist in a superposition of both of these states simultaneously; these spin states are known as quantum bits, or ‘qubits’. These are essentially the quantum version of the classical ‘bit’ that is currently used in computers to store information.

Quantum Entanglement

An electron spin produces a magnetic field, which makes it energetically favourable for the neighbouring electron spin to align in the opposite direction, so that it aligns with the magnetic field. As a result, although superposition prevents us knowing the direction of either spin, we can be sure that the 2 electrons will always have opposite spin. This means that upon measuring the spin state of one of the electrons, we instantly know the spin state of the other. 

This phenomenon, quantum entanglement, is essential to understanding information storage in quantum computing. Researchers are able to generate entangled pairs of qubits that work in this way, allowing us to instantaneously know the state of the other qubit depending on the measured properties of its entangled qubit, regardless of how far apart the two are separated.

Information Density

A pair of entangled qubits can be used to encode four possible states (shown below): up-up, down-down, up-down or parallel, but not pointing in the up/down plane. To describe the two entangled quantum bits, we require four numerical coefficients representing the respective likelihoods of measuring each of the four possible states. If we had three quantum bits, eight coefficients would be required to describe their superposed states. 

Fig. 2: The different possible states of a quantum-entangled pair.

In this way, the density of information stored in a set of n quantum bits is ‘2n’ as opposed to ‘n’ for a classical computer. This exponential, rather than linear, dependency explains why quantum computers have the potential to drive computational power to new level that was previously unachievable with classical computers.

Decoherence

The quantum state of a qubit is delicate, and when qubits interact with their environment, this causes the decay of their quantum properties. This is known as ‘decoherence’ and it is the biggest challenge we face in the current development of quantum computer technology. Noise refers to anything that can affect the quantum states of qubits to cause this decoherence, encompassing a vast range of sources, from slight temperature changes to changes in electric or magnetic fields. Any one of these factors results in large amounts of information loss, simultaneously making  quantum computers more error-prone than classical computers. 

Applications

Once barriers such as decoherence have been overcome and quantum computing technology reaches mainstream implementation, it will transform all types of industries, from drug development to artificial intelligence to cryptography. The limitless potential of this new technology is apparent in predictions from the business insider, which predict that the quantum computing market will be worth $64.98 billion by 2030.

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