Physicists produce symmetry-protected Majorana edge modes on a quantum computer

Google Quantum AI physicists have used their quantum computer to study an efficient type of particle that is more resilient to environmental disturbances that can degrade quantum computations. These effective particles, known as Majorana edge modes, form as a result of collective excitation of many individual particles, much like ocean waves form from the collective motions of water molecules. Majorana edge modes are of particular interest in quantum computing applications because they exhibit special symmetries that can shield otherwise fragile quantum states from noise in the environment.

Condensed matter physicist Philip Anderson once wrote, “It is only a slight exaggeration to say that physics is the study of symmetry.” Indeed, the study of physical phenomena and their relationship to underlying symmetries has been the primary focus of physics for centuries. Symmetries are simply statements about the transformations a system can undergo – such as translation, rotation, or inversion through a mirror – and remain unchanged. They can simplify problems and elucidate underlying physical laws. And, as new research shows, symmetries can even prevent the seemingly inexorable quantum process of decoherence.

When performing a calculation on a quantum computer, we generally want the quantum bits, or “qubits”, of the computer to be in a single, pure quantum state. But decoherence occurs when external electric fields or other environmental noises disturb these states by mixing them with other states to create unwanted states. If a state has some symmetry, then it might be possible to isolate it, creating an island of stability that is impossible to mix with the other states that also don’t have the special symmetry. Thus, the noise can no longer link the symmetric state to the others, it could preserve the coherence of the state.

In 2000, physicist Alexei Kitaev devised a simple model for generating symmetry-protected quantum states. The model consisted of a chain of interconnected particles called fermions. They could be connected in such a way that two effective particles appear at the ends of the chain. But these were no ordinary particles – they were delocalized in space, each appearing simultaneously at both ends of the chain.

These were Majorana Edge Modes (MEM). The two modes had markedly different behaviors under what is called the parity transformation. A mode looked identical under this transformation, so it was a symmetry of the state. The other took a minus sign. The parity difference between these two states meant that they could not be mixed by many external noise sources (i.e. those that also had parity symmetry).

In their new article published in Science and titled “Noise-tolerant Majorana Edge Modes on a String of Superconducting Qubits”, Xiao Mi, Pedram Roushan, Dima Abanin, and their colleagues at Google realized these MEMs with superconducting qubits for the first time. They used a mathematical transformation called the Jordan-Wigner transformation to map the model Kitaev had considered to the one they could achieve on their quantum computer: the kicked-Ising 1D model. This model connects each qubit in a 1D string to each of its two nearest neighbors, so that neighboring qubits interact with each other. Then a “kick” periodically disrupts the chain.

Mi and his colleagues looked for the signatures of the MEMs by comparing the behavior of the peripheral qubits with those in the middle of the chain. While the states of the middle qubits decayed quickly, the states of the edge ones lasted much longer. Mi says this was “a preliminary indication of the resilience of MEMs to external decoherence.”

The team then conducted a series of systematic studies on the noise resilience of MEMs. First, they measured the energies corresponding to the different quantum states of the system and observed that they corresponded exactly to the classic example of Kitaev’s model. In particular, they found that the two MEMs at opposite ends of the chain are exponentially more difficult to mix as the size of the system increases, a hallmark feature of the Kitaev model.

Next, the team perturbed the system by adding low-frequency noise to control operations in quantum circuits. They found that MEMs were immune to such perturbations, in stark contrast to other generic edge modes without symmetries. Surprisingly, the team also found that MEMs are even resistant to some noises that break the symmetries of Ising’s model. This is due to a mechanism called “prethermization”, which stems from the high energy cost required to transform MEMs into other possible excitations in the system.

Finally, the team measured the complete wave functions of the MEMs. To do this, it was necessary to simultaneously measure the states of varying numbers of qubits near each end of the chain. Here they made another startling discovery: no matter how many qubits were included in a measurement, its decay time was the same. In other words, measurements involving even up to 12 qubits degraded on the same time scale as those of a single qubit. This was contrary to the intuitive expectation that larger quantum observables decay faster in the presence of noise, and further highlighted the collective nature and noise resilience of MEMs.

Mi and Roushan think that in the future, they might be able to use MEMs to activate symmetry-protected quantum gates. Their work demonstrates that MEMs are insensitive to both low-frequency noise and small errors, so this is a promising way to create more robust gates in a quantum processor.

The researchers plan to continue improving the level of protection of these MEMs, hopefully to rival some of the leading techniques used to combat decoherence in quantum computers. Abanin says, “A key question for future work is whether these techniques can be extended to achieve levels of protection comparable to active error-correcting codes.”