When Moore’s Law meets quantum mechanics

In 1965, Gordon Moore, co-founder of one of the world’s largest computer companies, first described what has now become known as Moore’s Law. An observation rather than a physical law, Moore noticed that the number of components that could fit on a computer chip doubled roughly every two years, and this observation has proven to hold true over the decades. Accordingly, the processing power and memory capacity of computers has doubled every two years as well.

Starting from computer chips that held a few thousand components in the 1960s, chips today hold several billion components. There is a physical limit to how small these components can get, and as they get near the size of an atom, the quirky rules that govern quantum mechanics come into play. These rules that govern the quantum world are so different from those of the macro world that our traditional understanding of binary logic in a computer doesn’t really work effectively any more. Quantum laws are based on probabilities, so a computer on this scale no longer works in a ‘deterministic’ manner, which means it gives us a definite answer. Rather, it starts to behave in a ‘probablistic’ way—the answer the computer would give us is based on probabilities, each result could fluctuate and we would have to try several times to get a reliable answer.

So if we want to keep increasing computer power, we are going to have to find a new way. Instead of being stymied or trying to avoid the peculiarities of quantum mechanics, we must find ways to exploit them.

Bits and qubits

In the computer that sits on your desk, your smartphone, or the biggest supercomputer in the world, information, be it text, pictures or sound is stored very simply as a number. The computer does its job by performing arithmetic calculations upon all these numbers. For example, every pixel in a photo is assigned numbers that represents its colour or brightness, numbers that can then be used in calculations to change or alter the image.

The computer saves these numbers in binary form instead of the decimal form that we use every day. In binary, there are only two numbers: 0 and 1. In a computer, these are known as ‘bits’, short for ‘binary digits’. Every piece of information in your computer is stored as a string of these 0s and 1s. As there are only two options, the 1 or the 0, it’s easy to store these using a number of different methods—for example, as magnetic dots on a hard drive, where the bit is either magnetised one way (1) or another (0), or where the bit has a tiny amount of electrical charge (1) or no charge (0). These combinations of 0s and 1s can represent almost anything, including letters, sounds and commands that tell the computer what to do.

• How does binary counting work?

  Binary counting works on the same logic as decimal counting, but it takes some getting used to. In decimal counting, each digit in a number represents a factor of ten—there are 1s, 10s, 100s and so on. Each digit can be between 0 and 9, and represents how many of that particular factor of 10 unit are in the final number.

  In binary counting, you do the same thing but each digit is the next factor of 2. It starts at 1, then 2, 4, 8, 16 and so on. Each can only be 0 or 1, representing how many of that factors of 2 there are in the number.

  In the table, you can see how the number 54 in decimal counting is 5 tens plus 4 ones. The number 99 is made up of 9 tens and 9 ones.

  In binary, 54 is made up of 1 thirty-two, 1 sixteen, no eights, 1 four, 1 two and no ones. It looks more confusing for us, but it really is easier for computers to deal with the two options of 1 and 0 rather than ten options from 0 to 9.

Instead of binary bits, a quantum computer uses qubits. These are particles, such as an atom, ion or photon, where the information is stored by manipulating the particles’ quantum properties, such as spin or polarisation states.

In a normal computer the many steps of a calculation are carried out one after the other. Even if the computer might work on several calculations in parallel, each calculation has to be done one step at a time. A quantum computer works differently. The qubits are programmed with a complex set of conditions, which formulates the question, and these conditions then evolve following the rules of the quantum world—Schrödinger’s wave equation—to find the answer. Each programmed qubit evolves simultaneously; all the steps of the calculation are taken at the same time. Mathematicians have found that this approach can solve a number of computational tasks that are very hard or time consuming on a classical computer. The speed advantage is enormous—and grows with the complexity we can program (i.e. the number of qubits the quantum computer has).

Superposition

Individually, each qubit has its own quantum properties, such as spin. This has two values +1 and -1, but can also be in what’s called a superposition: partly +1 and partly -1. If you think of a globe, you can point to the North Pole (+1) or the South Pole (-1) or any other point in between: London, or Sydney. A quantum particle can be a in a state that is part North Pole and part South Pole.

A qubit with superposition is in a much more complex state than the simple 1 or 0 of a binary bit. More parameters are required to describe that state, and this translates to the amount of information a qubit can hold and process.

Entanglement

Even more interesting is the fact that we can link many particles, each in their state of superposition, together. We can create a link, called entanglement, where all of these particles are dependent upon each other, all their properties exist at the same time. All the particles together are in one big state that evolves, according to the rules of quantum mechanics, as a single system. This is what gives quantum computers their power of parallel processing—the qubits all evolve, individual yet linked, simultaneously.

Imagine the complexity of all these combinations, all the superpositions. The number of parameters needed to fully describe N qubits grows as 2 to the power N. Basically, this means that for each qubit you add to the computer, the information required to describe the assembly of qubits doubles. Just 50 qubits would require more than a billion numbers to describe their collective states or contents. This is where the supreme power of a quantum computer lies, since the evolution in time of these qubits corresponds to a bigger calculation, without costing more time.

For the particular tasks suited to quantum computers, a quantum computer with 30 qubits would be more powerful than the world’s most powerful supercomputer, and a 300 qubit quantum computer would be more powerful than every computer in the world connected together.

A delicate operation

An important feature of these quantum rules is that they are very sensitive to outside interference. The qubits must be kept completely isolated, so they are only being controlled by the laws of quantum mechanics, and not influenced by any environmental factors. Any disturbance to the qubits will cause them to leave their state of superposition—this is called decoherence. If the qubits decohere, the computation will break down. Creating a totally quiet, isolated environment is one of the great challenges of building a quantum computer.

Another challenge is transferring information from the quantum processor to some sort of quantum memory system that can preserve the information so that we can then read the answer. Researchers are working on developing ‘non-demolition’ readouts—ways to read the output of a computation without breaking the computation.

What are quantum computers useful for?

A lot of coverage of the applications of quantum computers talk about the huge gains in processing power over classical computers. Many statements have been made about being able to effortlessly solve hard problems instantaneously but it’s not clear if all the promises will hold up. Rather than being able to solve all of the world’s financial, medical and scientific questions at the press of a button, it’s much more likely that, as with many major scientific projects, the knowledge gain that comes from building the computers will prove just as valuable as their potential applications.

The nearest term and most likely applications for quantum computers will be within quantum mechanics itself. Quantum computers will provide a useful new way of simulating and testing the workings of quantum theory, with implications for chemistry, biochemistry, nanotechnology and drug design. Search engine optimisation for internet searches, management of other types of big data and optimising other systems, such as fleet routing and manufacturing processes could also be impacted by quantum computing.

Another area where large scale quantum computers are predicted to have a big impact is that of data security. In a world where so much of our personal information is online, keeping our data—bank details or our medical records—secure is crucial. To keep it safe, our data is protected by encryption algorithms that the recipient needs to ‘unlock’ with a key. Prime number factoring is one method used to create encryption algorithms. The key is based on knowing the prime number factors of a large number. This sounds pretty basic, but it’s actually very difficult to figure out what the prime number factors of a large number are.

Classical computers can very easily multiply two prime numbers to find their product. But their only option when performing the operation in reverse is a repetitive process of checking one number after another. Even performing billions of calculations per second, this can take an extremely long time when the numbers get especially large. Once numbers reach over 1000 digits, figuring out its prime number factors is generally considered to take too long for a classical computer to calculate—the data encryption is ‘uncrackable’ and our data is kept safe and sound.

However, the superposed qubits of quantum computers change everything. In 1994, mathematician Peter Shor came up with an algorithm that would enable quantum computers to factor large prime numbers significantly faster than by classical methods. As quantum computing advances we may need to change the way we secure our data so that quantum computers can’t access it.

Beyond these applications that we can foretell, there will undoubtedly be many new applications appearing as the technology develops. With classical computers, it was impossible to predict the advances of the internet, voice recognition and touch interfaces that are today so commonplace. Similarly, the most important breakthroughs to come from quantum computing are likely still unknown.

Quantum computer research in Australia

There are several centres of quantum computing research in Australia, working all over the country on a wide range of different problems. The Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (CQC2T) and the Centre of Excellence for Engineered Quantum Systems (EQuS) are both at the forefront of research in this field.

Two teams from the University of NSW (UNSW) are using silicon to create extremely coherent qubits in new ways, which opens the door to creating quantum computers using easy to manufacture components. One team is focussing on using silicon transistors like those in our laptops and smartphones.

The other UNSW-led team is working to create qubits from phosphorus atoms embedded in silicon. In 2012, this team created atom-sized components ten years ahead of schedule by making the world’s smallest transistor.

They placed a single phosphorus atom on a sheet of silicon with all the necessary atomic-sized components that would be needed to apply a voltage to the phosphorus atom, giving it its spin state in order to function as a qubit.

The nuclear spins of single phosphorus atoms have been shown to have the highest fidelity (>99%) and longest coherence time (>35 seconds) of any qubit in the solid state making them extremely attractive for a scalable system.

A team at the University of Queensland is working to develop quantum computing techniques using single photons as qubits. In 2010, this team has also conducted the first quantum chemistry simulation. This sort of a task involves computing the complex quantum interactions between electrons and requires such complicated equations that performing the calculations with a classical computer necessarily requires a trade-off between accuracy and computational feasibility. Qubits, being in a quantum state themselves, are much more capable of representing these systems, and so offer great potential to the field of quantum chemistry.

This group has also performed a demonstration of a quantum device using photons  capable of performing a task that is factorially difficult—i.e. one of the specific tasks that classical computers get stuck with.

Large sums of money are being invested into Australian quantum computing research. In 2014, the Commonwealth Bank made an investment of $5 million towards the Centre of Excellence for Quantum Computation and Communication Technology at the University of New South Wales. Microsoft has invested more than $10M in engineered quantum systems at University of Sydney, also in 2014.

It’s not very likely that in 20 years we’ll all be walking around with quantum devices in our pockets. Most likely, the first quantum computers will be servers that people will access to undertake complex calculations. However, it is not easy to predict the future, who would have thought fifty years ago, that we would enjoy the power and functionality of today’s computers, like the smartphones that so many of us now depend upon? Who can tell what technology will be at our beck and call if the power of quantum mechanics can be harvested?