New Circuits Harness ‘fraxons’ for Robust Quantum Data Storage

Scientists have developed a new superconducting circuit capable of encoding quantum information using qudits, extending beyond the traditional qubit paradigm. Luca Chirolli and colleagues from University of Florence, University of Rome, Quantum Research Centre, Max Planck Institute for Chemical Physics of Solids, Technology Innovation Institute, and 1 other institutions, detail a system using fractional fluxon states, termed ‘fraxons’, to create well-defined, low-lying energy levels protected from leakage errors. The research details the design and analysis of qudit systems with dimensions of four and five, with a particular focus on the qutrit case, and proposes a key gate protocol utilising stimulated Raman adiabatic passage. This platform represents a sharp advance in circuit engineering and offers new avenues for exploring quantum computation with increased information density.

Fraxon-based circuits enable stable multi-state qudit encoding

A superconducting circuit capable of encoding qudits with up to five states has been engineered, representing a significant advance beyond traditional qubits limited to two. Realising stable qutrits, a three-state qudit, previously suffered from leakage errors, where the quantum information escapes the intended computational subspace. The new design demonstrably mitigates these issues by utilising ‘fraxons’, localised states of electrical current that create well-defined, low-lying energy levels. These fraxons arise from the unique properties of Josephson junctions, non-linear circuit elements crucial to superconducting quantum devices. A Josephson junction consists of two superconducting materials separated by a thin insulating barrier, allowing Cooper pairs, pairs of electrons, to tunnel through the barrier, creating a supercurrent. The careful design of the circuit’s geometry and the application of magnetic fields allows for the creation of these fractional fluxon states, which are topologically protected and thus less susceptible to decoherence. This advancement stems from a carefully sculpted Josephson potential, achieved through Fourier engineering, which precisely controls the circuit’s energy field and prevents unwanted transitions to higher energy states.

Clear separation between these low-lying states enables strong quantum information processing and opens new possibilities for computation with increased information density. The Fourier engineering approach involves designing the circuit’s geometry such that the Josephson potential contains multiple harmonic frequencies. This creates a potential landscape with multiple minima, each corresponding to a stable energy level for the fraxon. By carefully choosing the frequencies and amplitudes of these harmonics, the researchers were able to tailor the potential to create the desired number of low-lying states and maximise the separation between them. Building on prior work with three-state qutrits, the team successfully created circuits for both a four-state ‘ququart’ and a five-state ‘ququint’ system. For the ququint, the lowest five states were localised around fractional phases of π/2, indicating the successful confinement of the fraxons within the designed potential wells. Detailed analysis of a three-state qutrit revealed a proposed gate protocol utilising stimulated Raman adiabatic passage, potentially offering a route to manipulating qudit states. Stimulated Raman adiabatic passage is a quantum control technique that allows for the coherent transfer of a quantum state between different energy levels without inducing unwanted transitions to other levels. This is particularly important for qudits, where the increased number of states makes it more difficult to achieve precise control.

Quantum processors of increasing complexity are now being built, moving beyond the simple two-state qubit to explore systems encoding multiple levels of information within a single quantum entity, known as a qudit. While this offers the potential for denser data storage and more efficient computation, realising stable and scalable qudits presents formidable challenges. The increased dimensionality of qudits introduces more degrees of freedom, making them more susceptible to noise and decoherence. Maintaining quantum coherence as dimensionality increases remains a significant hurdle to practical application, but a viable pathway towards building these systems using superconducting circuits and localised quantum states within a specifically engineered potential is now available. A qudit functions like a switch with more than two positions, unlike the qubit’s simple 0 or 1, and this circuit encodes quantum information using multiple quantum states simultaneously, offering the potential for increased computational power and data density. The potential benefits of qudits are substantial; algorithms that require exponential resources on a qubit-based computer may be solvable with polynomial resources on a qudit-based computer. Central to this design are these ‘fraxons’, acting as controllable valves within the circuit, carefully shaped using the technique to precisely control energy levels and minimise unwanted transitions. The low-lying states are well separated from the rest of the spectrum, providing inherent protection against leakage errors, a critical factor for maintaining the integrity of quantum computations. The ability to reliably create and manipulate these fraxon states represents a significant step towards building more powerful and versatile quantum computers.

The implications of this research extend beyond fundamental quantum information science. The precise control over superconducting circuits demonstrated here could also find applications in other areas, such as the development of highly sensitive sensors and novel electronic devices. Furthermore, the Fourier engineering approach used to design the Josephson potential could be adapted to create other types of quantum systems with tailored properties. Future work will focus on improving the coherence times of the qudit states and developing more sophisticated gate protocols for manipulating them. Scaling up the system to create larger and more complex qudit networks is also a key priority, paving the way for the realisation of fault-tolerant quantum computation with increased computational capabilities and efficiency.

Researchers successfully demonstrated a superconducting circuit hosting a qudit system with up to five states, utilising localised quantum states called fraxons. This represents a move beyond the standard qubit, potentially allowing for more efficient quantum computations as certain algorithms may require fewer resources on a qudit-based computer. The circuit design inherently protects against leakage errors, which is crucial for maintaining accurate calculations. The authors intend to focus on improving the stability of these states and developing more complex methods for controlling them, with the ultimate goal of creating larger qudit networks.