# First Simulation of Quantum Tunneling on a Quantum Computer

Quantum tunneling had always been thought too complex to simulate on today’s simple quantum computers. Now a new approach to quantum computing has changed that and opens the door to more complex simulations.

The exploitation of quantum weirdness for computing is one of the great goals of modern physics. It’s promise is dramatic for a wide range of number-crunching tasks.

But quantum computers have another trick up their sleeves which is sometimes forgotten–the ability to simulate other quantum systems. Physicists have already shown how quantum computers of various types can simulate phenomenon such as quantum phase transitions and the dynamics of entanglement–things that classical computers simply cannot handle.

There is one quantum phenomenon, however, that has never been simulated–tunnelling. This is the ability of quantum particles to cross a barrier without seeming to have passed through it.

There’s no reason in principle why quantum computers can’t simulate tunnelling. The problem is the complexity of the task.

The simulations performed so far have all involved so-called analogue processes which are relatively straightforward. The idea here is that the mathematical description of one system, its Hamiltonian, is exactly reproduced in another system.

So watching one system tells you exactly how the other would behave. This is known as analogue quantum particle simulation and it works well provided you can find systems that match in required way. Watching quantum phase transitions is good example because many systems share the same mathematical description.

For more complex problems, physicists have recently been thinking about another approach. The idea here is to break the mathematical system into different parts and simulate them separately. This is known as digital quantum particle simulation and it has huge potential for events that involve more than one object, such as quantum chemistry and tunneling.

The problem is the sheer complexity of these calculations, which require numerous quantum logic gates processing dozens of qubits. That’s always been beyond the state-of-the-art for quantum computing.

Earlier this year, however, Andrew Sornborger at the University of Georgia in Athens showed how the case of a single particle tunnelling through a barrier could be made simple enough to simulate on today’s quantum computers. Such a demonstration would be the first example of a digital quantum simulation.

And today Guan Ru Feng and pals at Tsinghua University in Beijing say they’ve done it. To simulate tunnelling, these guys used a quantum computer that relies on nuclear magnetic resonance to manipulate qubits in encoded in the carbon and hydrogen atoms that make up chloroform molecules. They say this is the ﬁrst demonstration of a quantum tunnelling simulation using an NMR quantum computer.

That should open the floodgates for more digital quantum simulations in future. It’s significant because this approach has the potential to simulate much more complex quantum phenomenon than is currently possible. Expect to see more of it.

Ref: arxiv.org/abs/1205.2421: Experimental Digital Simulation of Quantum Tunneling in a NMR Quantum Simulator