Physicists are discovering the infinite possibilities of quantum states

Spin (blue ball with arrow) interacts with surrounding bosons described by non-Gaussian states – a new computational method that allows us to precisely describe what is happening inside quantum devices. Source: Jiří Minář

A new method developed by researchers in Amsterdam uses non-Gaussian states to efficiently describe and configure quantum spin-bosonic systems, representing a promising advance in the field quantum computing and sensing.

Many modern quantum devices operate on groups of qubits, or spins, that have only two energy states: “0” and “1.” However, in real devices, these spins also interact with photons and phonons, collectively called bosons, which significantly complicates the calculations. In a recent study published in Physical inspection lettersresearchers from Amsterdam have developed a method to effectively describe these spin-boson systems. This breakthrough could help in efficiently configuring quantum devices to achieve specific desired states.

Quantum devices use the bizarre behavior of quantum particles to perform tasks beyond the capabilities of “classical” machines, including quantum computing, simulation, sensing, communications and metrology. These devices can take many forms, such as a collection of superconducting circuits or a network of atoms or ions held in place by lasers or electric fields.

Regardless of their physical implementation, quantum devices are usually described simplistically as a collection of interacting two-level quantum bits or spins. However, these spins also interact with other elements in their environment, such as light in superconducting circuits or oscillations in a lattice of atoms or ions. Examples of bosons are light particles (photons) and lattice vibrational modes (phonons).

Innovative descriptions of quantum states

Unlike spins, which have only two possible energy levels (“0” or “1”), the number of levels of each boson is infinite. As a result, there are very few computational tools for describing boson-coupled spins. In their new work, physicists Liam Bond, Arghavan Safavi-Naini and Jiří Minář from the University of Amsterdam, QuSoft and Centrum Wiskunde & Informatica get around this limitation by describing systems composed of spins and bosons using so-called non-Gaussian states. Every non-Gaussian state is a combination (superposition) of much simpler Gaussian states.

Each blue-red pattern in the image above represents a possible quantum state of the spin-boson system. “The Gaussian state would look like a plain red circle without any interesting blue-red patterns,” explains PhD student Liam Bond. An example of the Gaussian state is laser light, in which all light waves are perfectly synchronized. “If we take many of these Gaussian states and start superimposing them (so that they form a superposition), these beautifully complex patterns emerge. We were particularly excited because these non-Gaussian states allow us to retain much of the powerful mathematical machinery that exists for Gaussian states, while allowing us to describe a much more diverse set of quantum states.”

Bond continues: “There are so many possible patterns that classical computers often have difficulty calculating and processing them. Instead, in this paper we use a method that identifies the most important of these patterns and ignores the rest. This allows us to study these quantum systems and design new ways to prepare interesting quantum states.”

The new approach can be used to efficiently prepare quantum states in a way that outperforms other traditionally used protocols. “Fast preparation of a quantum state could be useful for a wide range of applications, such as quantum simulation and even quantum error correction,” notes Bond. Scientists have also shown that they can use non-Gaussian states to prepare “critical” quantum states, which correspond to a system undergoing a phase transition. Beyond basic interest, such states can significantly increase the sensitivity of quantum sensors.

While these results are very encouraging, they are only a first step towards more ambitious goals. So far, the method has been demonstrated for a single spin. A natural but challenging extension is to consider multiple spins and multiple bosonic modes simultaneously. A parallel direction is to take into account the influence of the environment disturbing spin-boson systems. Both of these approaches are under active development.

Reference: “Fast quantum state preparation and bath dynamics using non-Gaussian variation Ansatz and Quantum Optimal Control” by Liam J. Bond, Arghavan Safavi-Naini and Jiří Minář, April 23, 2024, Physical inspection letters.
DOI: 10.1103/PhysRevLett.132.170401