# Quantum computer coding in silicon now possible

## Quantum computer coding: entanglement in a silicon chip

*Nature Nanotechnology*.

*Nature Nanotechnology*paper.

With quantum bits, one can use a ‘quantum computing language’ that is vastly richer than standard digital codes, because it contains special code words that do not exist in normal computers. Accessing and elaborating these special codes is what gives quantum computers their superior power. This code comes into existence through the creation of quantum entanglement between multiple qubits.

While there has been tremendous progress in the construction and operation of single and multiple qubits in various types of hardware, creating entanglement between qubits remains an extremely challenging task, because of the inherent fragility of this quantum effect.

The UNSW team has now, for the first time, demonstrated the ability to entangle two quantum bits in silicon. The significance of this result is that silicon is the material routinely used in all modern electronic devices. Harnessing this quantum effect in such a technologically important platform widely used by the computer industry, and in which billions of dollars have been invested in research and development, will greatly facilitate the construction of practical quantum computers.

## Einstein, Bell and the predictions of quantum theory

Albert Einstein was famously disturbed by some of the predictions of quantum theory, with quantum entanglement perhaps the most puzzling one. In the classical world we perceive in our daily lives, we are used to seeing that certain objects are correlated to each other – for instance, a coin that shows a head on one side, will certainly have a tail on the other. But they nonetheless maintain their individual essence – if we slice the coin and separate the head from the tail, the images don’t change.

Quantum entanglement is a unique form of correlation, where each particle loses its individuality and begins to exist only in relation to the other. A ‘quantum coin’ would be one where each face is blank until it is observed, but it is, nonetheless, ‘the opposite of the other’. What disturbed Einstein the most was the prediction that, if one observes one side of a sliced quantum coin (finding, for instance, heads), the other side of the coin instantly acquires the opposite image (tails, in this case). And this happens no matter how far apart we have separated the two sides of the sliced coin. This is what Einstein called ‘spooky action at a distance’, and what he used as an argument to question the completeness of quantum theory.

In 1964, British physicist John Bell derived a remarkably simple theorem to address this. It quantifies, with a measurable number, the strength of correlation between particles. His theorem is based upon two seemingly obvious assumptions: (1) **Locality**, which means that what happens at one place can only be influenced by objects that are in its vicinity, and (2) **Realism**, which means that physical objects exist regardless of whether or not they are observed.

With these assumptions, he showed that a certain quantity (call it the ‘Bell number’) – which expresses the correlation between pairs of particles – can never be *larger* than 2, or *lower* than -2. This theorem is called Bell’s Inequality. The striking prediction of quantum theory is that, if one takes a pair of quantum entangled particles, the Bell number can be as large as 2.82, or as low as -2.82. An explanation of Bell’s theorem can be found in Episode 2 of the YouTube series “The quantum around you” created by Andrea Morello and produced by UNSWTV.

## The technological significance of violating Bell’s Inequality

Since the formulation of Bell’s theorem in 1964, scientists worldwide embarked in challenging experiments to demonstrate, in the laboratory, the ability to produce pairs of entangled particles that violate Bell’s Inequality. Nowadays, the existence of quantum entangled states that violate Bell’s Inequality is well established. Therefore, either Locality (the concept dear to Einstein) or Realism must break down in the quantum world.

From a technological standpoint, violating Bell’s Inequality represents the pinnacle of experimental quantum science. This is because the quantum entangled states necessary for the experiment are extremely delicate. Moreover, the Bell test is extremely sensitive to all possible imperfections that can afflict the experiment: from the preparation of the initial states of the particles, the creation of their entangled states, to the measurement of their correlations. Any tiny error will reduce the Bell number. It only takes the slightest inaccuracy to bring this number below 2, by which point one can no longer claim that an entangled state has been produced.

The UNSW experiment now claims a new experimental record of Bell number: 2.70, approaching very closely the theoretical ‘perfect’ value of 2.82. This result is the strongest possible indication that the Australian team has created the most accurate quantum bits, which will become the workhorse of future quantum computers. In their experiment, the UNSW engineers have used as qubits the electron and the nuclear spin of a single phosphorus atom, placed inside a silicon microelectronic chip.

**Entangled particles as quantum computer code**

Quantum entanglement plays a key role in quantum computing. One can think of entangled states as a form of new ‘quantum computer code’, which can only be written on a quantum machine.

For example, in a classical computer with two bits, one can write four possible digital codes: 00, 01, 10, or 11. However, a quantum machine can use a much wider set of code words, which are the quantum superpositions of the classical codes, such as 00+11, 00-11, 01+10 or 01-10. Strange as they may look, these are perfectly legitimate codes in a quantum computer, and are physically implemented by creating entanglement between the qubits. Each of these quantum computer code words would violate Bell’s Inequality.

The existence of these additional quantum code words is one of the reasons why quantum computers can be so powerful. By adding more and more qubits, the number of entangled code words that become allowed grows exponentially. In turn, one can write specific quantum algorithms which exploit the existence of this enormous vocabulary of codes. For certain applications, it is possible to run algorithms where the exponentially larger vocabulary of quantum codes can be used to arrive at a result in an exponentially smaller number of steps, compared to an ordinary computer. These are the classes of problems where quantum computers can make the biggest impact.

**Applications of quantum computing**

There are several classes of problems where the use of quantum algorithms, enabled by the creation of entangled qubit codes, can provide a massive speed up over their classical counterparts. This is particularly important where the problem at hand is intrinsically quantum. For example, modelling and designing a complex molecule, such as a drug, is an inherently quantum mechanical problem, because the chemical bonds that hold the molecule together are quantum effects. Similar considerations apply to complex materials, where the quantum behaviour of the electrons and atoms plays a crucial role. Quantum computers will harness the exponentially large vocabulary of quantum codes to efficiently simulate these systems.

Other examples include searching large databases, solving complex systems of equations, or finding optimal solutions to problems with multiple constrains, such as the decision on how to route traffic in a congested network.

**Entanglement in silicon: from spooky to practical**

The work published by the UNSW team in *Nature Nanotechnology* represents the first demonstration of Bell’s Inequality violation in silicon. It brings a spooky quantum phenomenon into the realm of microelectronic devices similar to those used in everyday computers and smartphones.

The single-atom qubit device used by Morello’s team is fabricated using the standard process where a silicon chip is covered with a layer of insulating silicon oxide, on top of which rests a pattern of metallic electrodes. Although it is operated at temperatures near absolute zero and in the presence of a very strong magnetic field, the device resembles the silicon transistors found in normal electronic chips. Therefore, the UNSW team expects that this type of device can be scaled up to many qubits by using the same industry-standard processes employed to make everyday computers.

## Timeline of the development of silicon quantum computing

**1994:** Peter Shor from Bell Labs (USA) shows that a quantum computer would be able to decrypt Public Key Encrypted codes (at the heart of modern secure communications) exponentially faster than today’s supercomputers. This triggers massive interest in quantum computing worldwide.

**1998:** Bruce Kane, then a postdoctoral researcher at UNSW (now a researcher at the U.S. Laboratory for Physical Sciences in Maryland), publishes a paper in *Nature* outlining the concept for a silicon-based quantum computer, in which the qubits are defined by single phosphorus atoms in an otherwise ultra-pure silicon chip. This is the first such scheme in silicon – the material used for all modern day microprocessors. Kane’s paper attracts great interest because: (a) Silicon is ‘industrially relevant’; (b) Silicon electron ‘spins’ have very long ‘coherence times’ (hence, low error rates). This paper has now generated over 2,000 citations.

**2000: **Bob Clark establishes the ARC Special Research Centre for Quantum Computer Technology (CQCT), headquartered at UNSW, to attempt to build a quantum computer. The centre has now expanded to become an ARC Centre of Excellence – with more than 150 researchers in Australia, and major collaborations world-wide. Andrew Dzurak develops the silicon nanofabrication capabilities necessary for the construction of the hardware.

**2006:** Andrea Morello joins UNSW and CQCT, working in close collaboration with Andrew Dzurak on the construction of a silicon-based quantum computer. The technology they choose is based upon using the spin of phosphorus atoms, implanted within a silicon chip which is fabricated along industry-standard methods.

**2010:** Andrea Morello and Dzurak publish in *Nature* a paper describing the “Single shot readout of an electron spin in silicon” – the first-ever demonstration of measuring a silicon qubit.

**2012:** Paper in *Nature* by Morello and Dzurak groups: “A single-atom electron spin qubit in silicon” – the crucial step of writing information on an electron to operate the first silicon qubit.

**2013:** Paper in *Nature* by Morello and Dzurak groups: “High-fidelity readout and control of a nuclear spin qubit in silicon” – the first demonstration of read-write quantum operations on the nucleus of an atom in silicon, which is exceptionally well isolated from its environment.

**2014:** Paper in *Nature Nanotechnology* by Morello’s group: “Storing quantum information for 30 seconds in a nanoelectronic device” – a new generation of qubit devices built on purified silicon. This device has set, for solid-state qubits, the new record of “coherence time”, which describes how long quantum information can be preserved on a qubit.

**2015:** Morello’s group, with lead authors Juan Pablo Dehollain and Stephanie Simmons, publishes in *Nature Nanotechnology *the paper “Bell’s Inequality violation with spins in silicon”. This work shows the ability to write two-qubit quantum computer code using the electron and the nucleus of a phosphorus atom. The outstanding accuracy with which this was achieved is demonstrated by the highest violation of Bell’s Inequality ever reported.

## Key research team members and their roles in the paper

**Professor Andrea Morello** (UNSW) – Research team leader. Developed over 2007-2015 the concept, design and fabrication technologies for silicon spin qubits based on modified silicon transistors. Director of Australian National Fabrication Facility at UNSW and co-leader of silicon quantum computing programs at CQC^{2}T.

**Dr Juan Pablo Dehollain and Dr Stephanie Simmons** (UNSW) – Post-doctoral researchers in Morello’s team at the UNSW School of Electrical Engineering & Telecommunications, and joint lead-authors on the *Nature Nanotechnology *paper. They designed and conducted the experiment that led to the landmark violation of Bell’s Inequality.

**Juha Muhonen, Rachpon Kalra, Arne Laucht, Fay Hudson** (UNSW) – Post-doctoral and PhD researchers in the teams of Morello and Dzurak at the UNSW School of Electrical Engineering & Telecommunications, who contributed key aspects of the nanofabrication and measurement capabilities deployed in this experiment.

**Scientia Professor Andrew Dzurak **(UNSW) – Expert on silicon nanofabrication, Director of the NSW node of ANFF. Long-time collaborator of Andrea Morello and key person in the development of the silicon-based qubits.

**Professor David Jamieson and Associate Professor Jeffrey McCallum** (University of Melbourne) – key collaborators of Morello’s group. They have developed the technology to implant individual phosphorus atoms in silicon, while using a process compatible with industry standards.

**Professor Kohei Itoh** (Keio University, Japan) – Collaborates with Morello and Dzurak by providing isotopically purified silicon wafers for device production at UNSW.

## Key stakeholders & funding bodies

**Centre of Excellence for Quantum Computation and Computer Technology (CQC2T):**Australian centre of research excellence, headquartered at UNSW, in which Morello leads the Quantum Spin Control Program. Founded in January 2000.**Australian Research Council (ARC):**Major funder of CQC2T via the ARC Centres of Excellence Scheme (a funder since 2000).**U.S. Army Research Office:**Funder of the Silicon Quantum Computer Program at UNSW and the University of Melbourne since 1999.**Australian National Fabrication Facility (ANFF):**Founded in 2006 under the Australian Government’s National Collaborative Research Infrastructure Scheme (NCRIS). Provides infrastructure and technical support at UNSW for fabrication of the qubit devices.**State Government of New South Wales:**Through the Office of Scientific Research at the NSW Department of Trade & Investment, provides significant co-funding to CQC2T (since 2003) and also to ANFF (since 2006).**Commonwealth Bank of Australia:**Has provided research funding to CQC2T, including Morello’s group, since 2013.**UNSW Australia:**Has provided core financial and infrastructure support to both CQC2T and ANFF since their establishment.