Quantum bits, or qubits, which are required for building quantum computers, come in different kinds. In recent years, many research institutes and companies have focused on superconducting circuits and trapped ions. However, neutral atoms trapped with laser light also have a lot going for them: since they carry no electric charge, they are less sensitive to disturbances. Moreover, trapping with laser light makes it easy to realize several thousand qubits in a single system – using superconductors or ions this is much more difficult.

Nevertheless, neutral atoms have their own problems. In quantum computers, qubits exist in superposition states of the logic values 0 and 1. To perform calculations with them, one needs to execute quantum logic operations, also known as quantum gates.

For such quantum gates, until now highly excited electronic states (Rydberg atoms) or collisions between atoms, as well as the tunnel effect, have mostly been used. However, particularly the tunnel effect, whereby particles can go through obstacles that would be unsurmountable according to classical physics, depends very strongly on the intensity of the laser light. Even tiny imperfections or fluctuations can, therefore, strongly diminish the quality of the quantum gate.

Very robust against experimental noise

A team of researchers at ETH Zurich led by Tilman Esslinger, professor at the Institute for Quantum Electronics, has now succeeded in realising a so-called swap gate, or a quantum exchange, with extremely high quality using only a geometric phase. This geometric phase causes the state of the particles to switch depending on the path they take, and not because of external disturbances. This makes the system very robust against experimental noise.

Moreover, the researchers were able to demonstrate that the gate can be applied to several thousands of qubits simultaneously. The results, which were recently published in the scientific journal external page Nature, pave the way for future progress in quantum computers with neutral atoms.

Quantum exchange with abstract phases

A swap gate exchanges the quantum states of two qubits. For example, if initially qubit A is in state 0 and qubit B in state 1, after the execution of the swap gate qubit A will be in state 1 and qubit B in state 0. Swap gates are important for the routing of quantum information within a large quantum computer.

“A few years ago, researchers managed to realise such gates using neutral atoms in their lowest energy state, albeit by exploiting dynamical phases due to tunnelling and collisions”, says postdoc Yann Kiefer. Dynamical phases arise when particles move in space or interact with each other. These phases then determine the oscillatory state of the particles’ quantum mechanical wave function, which influences the probability with which particles are observed in a particular quantum state.

Geometric phases, by contrast, are more abstract. They come about, for example, when the direction of an electron spin is changed. When the spin is rotated by 360 degrees, it ends up pointing in the same direction, but the phase of its wavefunction now differs by 180 degrees.

In a similar fashion, Esslinger and his team were able to realize a swap gate. To do so, they trapped extremely cold potassium atoms in optical lattices, in which the atoms are held in place inside a kind of artificial crystal of light. By cleverly manipulating the laser beams they were now able to bring pairs of atoms, whose spin states acted as qubits, so close together that their wavefunctions overlapped in space.

Robust gates for 17,000 qubits

Since the potassium atoms used were fermions, which according to the laws of quantum mechanics are not allowed to be in exactly the same quantum state, the manipulation resulted in a geometric phase. “Unlike dynamical phases, this geometric phase is largely independent of the speed with which we manipulate the atoms, or how strongly the laser intensity fluctuates during the process”, explains Konrad Viebahn, junior group leader for the experiment. The result: an extremely robust swap gate that exchanges the states of the two qubits in less than a millisecond with a precision of 99,91 percent – simultaneously for 17,000 qubit pairs!

“We can now make lots of swap gates with neutral atoms”, says Tilman Esslinger, “but of course we still need a few other ingredients to build a working quantum computer.” According to Esslinger, one of the next steps is combining the swap gates with a quantum gas microscope. It would then be possible to make individual qubit pairs visible and to selectively manipulate them. In this way, swap gates could be applied only to specific qubits.

Moreover, the researchers have already demonstrated that they can realise “half”-swap gates by adding collisions between the atoms. Such gates cause the qubits to become quantum mechanically entangled, which is a prerequisite for executing quantum algorithms.