The first digital "quantum simulator" based on trapped ions has been built by physicists in Austria. The system, developed by Ben Lanyon and colleagues at the University of Innsbruck, comprises a number of trapped calcium ions that are manipulated using sequences of laser pulses. The team has used the system to simulate the time-evolution of several multi-particle systems.

A quantum simulator uses one quantum system to simulate the behaviour of another, less accessible system. For example, by carefully manipulating the laser light and magnetic fields trapping an ensemble of ultracold atoms, researchers can control the interactions between atoms – and therefore simulate interactions that occur between electrons in solids. But unlike electrons in solids, the strength of these interactions can be easily adjusted, allowing physicists to test theories of condensed-matter physics.

Analogue to digital

Most quantum simulators are "analogue" in the sense that the interactions between the trapped atoms are directly analogous to those between electrons. A digital quantum simulator, in contrast, contains an ensemble of interacting quantum particles that act as quantum bits (qubits) and can be used to create quantum logic gates. The quantum system to be simulated is then encoded into the system and the behaviour of the electrons is determined by performing a quantum calculation.

Unlike analogue simulators, which address specific systems, a digital simulator could be used to study a wide range of quantum systems. Furthermore, digital simulators can benefit from error-correction schemes, which means that physicists can be more confident in their results.

But while researchers have had some success creating digital quantum simulators using nuclear magnetic resonance (NMR) techniques, these work with just two or three qubits and it has proven difficult to scale up to the 40 or so qubits needed to do a useful quantum simulation. The new trapped-ion quantum simulator created Lanyon and colleagues means that it should, in principle, be much easier to scale up such a system to do useful simulations.

Easily scalable

The team's experiments begin with a small number of calcium ions (a maximum of six) that are lined up in a row in an electromagnetic trap. Each ion can exist in two electronic states – "0" and "1" – and can therefore act as a qubit. Interactions between individual ions can be controlled by firing carefully selected laser pulses at the trapped ions.

A calculation begins by putting the ions into a specific quantum state. In an experiment involving four ions, for example, each qubit was given the value "1". A series of laser pulses was then fired at the ions, which causes them to interact with each other creating a sequence of logic gates that process the quantum information held in the initial state.

It is this sequence that simulates the interactions that occur in a real (or imagined) quantum system. In this particular example, the qubits were used to simulate four spin-1/2 particles in which the spin of each particle can interact with the three other particles.

Approximate solutions

Lanyon and colleagues were interested in calculating the time evolution of the spins, which is particularly difficult to do using a classical computer. To do this, the team implement the "Trotter approximation" on their system. This is done by firing a series of pulses that simulates the evolution of the system over a certain period of time before the values of the qubits are read out. The system is then reset and an identical simulation is repeated many times to obtain average values for the qubits – which is an approximate solution to the problem being simulated.

This entire process is then repeated to simulate a number of different time periods, building up a map of the time evolution of the spins. Time evolution simulations were done for as many as six trapped-ion qubits and involving up to 100 quantum gates.

Towards quantum chemistry

"Six qubits and a 100 gates for quantum simulation is a feat that paves the way for more complex and rich digital quantum simulations in the future," says Alán Aspuru-Guzik of Harvard University in the US. "What Ben Lanyon and his colleagues did was to implement one of the most important building blocks for quantum simulation, what we call a 'Trotter step' in a generic or universal sense. This is one of the required and essential building blocks to do exact quantum chemistry on quantum computers, when they become powerful enough."

Lanyon told physicsworld.com that his team's next challenge is to perform the simulations with 10 or more ions. Creating such a system is not the problem – the team has already trapped and entangled as many as 14 ions. However, performing large numbers of operations on the ions is tricky because the qubits tend to lose their quantum nature over time as they interact with their surroundings.

The work is described in Science 10.1126/science.1208001