New breakthrough in quantum computing error correction first cubic phase state

Non-classical states carrying light in three-dimensional microwave cavities have emerged as a promising paradigm for quantum information processing in continuous variables (CVs). Quantum technology researchers at Chalmers University of Technology have successfully developed a technique for high-fidelity generation of controlled optical quantum states in three-dimensional cavities, which include Schrödinger cat states, binomial states, Gottesman-Kitaev-Preskill states, and cubic phase states [1].

An illustration of the aluminum resonator on the right. The blue and red patterns show the quantum mechanical states that can be created and controlled by the Chalmers researchers. Counting from top to bottom, these states are: the Gottesman-Kitaev-Preskill (GKP) state, the Cubic phase state, the Binomial state, the Fock state, and the Cat state.

01First demonstration of Cubic phase state

In addition to creating previously known states, the researchers have demonstrated for the first time the long-sought cubic phase state. This breakthrough is an important step toward efficient error correction for quantum computers.

Simone Gasparinetti, head of the Experimental Quantum Physics research group at Chalmers University and one of the study's senior authors, said, "We have shown that our technology is on par with the best in the world."

Just as conventional computers are based on bits that can take on the value of 0 or 1, the most common approach to building quantum computers takes a similar approach. Quantum mechanical systems with two different quantum states, called quantum bits (qubits), are used as building blocks. One of the quantum states is assigned a value of 0 and the other a value of 1. However, due to the superposition of states in quantum mechanics, qubits can be a combination of both 0 and 1 states, allowing quantum computers to handle large amounts of data and potentially solve problems that are beyond the reach of current supercomputers.

A major obstacle to the realization of practical quantum computers is that the quantum systems used to encode information are susceptible to noise and interference, which can lead to errors. Correcting these errors is a key challenge in the development of quantum computers. One promising approach is to use resonators instead of quantum bits - quantum systems have a very large number of other states in addition to the two defined ones. These states can be compared to a guitar string, which can vibrate in many different ways. This approach is called continuous variable (CV) quantum computing, and it makes it possible to encode the values of 1 and 0 in several quantum mechanical states of a resonator.

(a) Pulse sequence used to prepare and describe the state. Denote by C, Q and R the cavity, the quantum bit and the readout resonator, respectively. (b) The two optimization steps performed to find the ideal displacement and SNAP gate. (c) Diagram of the geometric cavity coupled to the trans-quantum bit. (d) A zoomed-in view of the chip, which includes strip lines to read out the resonator and transmon quantum bits.

However, controlling the state of the resonator is a challenge that quantum researchers around the world are struggling to solve. And Chalmers' results provide a way to do just that. The newly developed technique allows researchers to generate almost all previously demonstrated optical quantum states, such as the Schrödinger cat state or the Gottesman-Kitaev-Preskill (GKP) state, as well as the cubic phase state, which was previously described only theoretically.

The cubic phase state is something that many quantum researchers have been trying to create in practice for two decades. We have now succeeded in doing this for the first time, which is a testament to how well our technique works," said Marina Kudra, a PhD student in the Department of Microtechnology and Nanoscience and lead author of the study. But the most important advance is that there are so many states of varying complexity that we've found a technique that can create any of them."

02Increased gate speed

The quantum mechanical properties of photons are controlled by applying a set of electromagnetic pulses called gates. The researchers first successfully used an algorithm to optimize specific sequences of simple displacement gates and complex SNAP gates to generate the states of the photon. When the operation times of the complex gates proved to be too long, the researchers found a way to optimize the electromagnetic pulses using optimal control methods to make them shorter.

"The dramatic increase in the speed of our SNAP gates allows us to mitigate the effects of decoherence in quantum controllers, taking this technology a step forward." Simone Gasparinetti said, "We have shown success in fully controlling our quantum mechanical system."

Achieving this result also depends on a high-quality physical system (the aluminum resonator itself and the superconducting circuit.) Marina Kudra has previously shown how the aluminum cavity was created: it was first milled and then made extremely clean by methods that included heating it to 500 degrees Celsius and cleaning it with acids and solvents. The electronics for applying electromagnetic gates to the cavity were developed in collaboration with the Swedish company Intermodulation Products [2].

Experimentally generated quantum states. Top row: experimental data; bottom row: target states. (a) two-photon Focker state; (b) binomial state, and (c) cat state. These three states have on average two photons, created with two SNAP gates and displacement gates (displacements). Next, (d) the GKP state with an average of four photons and (e) the cubic phase state. the GKP state is prepared with three SNAP gates and four displacement gates, and the cubic phase state is created with three SNAP gates and three displacement gates.

The state fidelity of the generated quantum states.

Simulated fidelity and calibration parameters for optimized and "standard" SNAP gates. The distance between the dashed lines represents the parameter span, where the fidelity is within 1% of the maximum. The optimized SNAP gate is compared to the "standard" SNAP gate, which is a superposition of 4-μs long pulses centered on a quantum bit frequency related to the number of photons.

The research was conducted in Chalmers within the framework of the Wallenberg Centre for Quantum Technologies (WACQT), a comprehensive research program that aims to make Swedish research and industry a leader in quantum technology. The program is led by Prof. Per Delsing and a major goal is to develop quantum computers.

Reference links.

[1]https://phys.org/news/2022-09-quantum-technology-unprecedented-captured.html

[2]https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.030301