Quantum mechanics allows systems to exist simultaneously in multiple states, a property famously illustrated by Schrödinger’s cat paradox, where the cat is both alive and dead until observed. Traditionally, this phenomenon has been harnessed in laboratories through the creation of qubits—quantum bits—capable of inhabiting superpositions of states labeled 0 and 1. However, quantum systems inherently possess richer structures beyond this binary paradigm. In particular, quantum harmonic oscillators, which model diverse phenomena such as trapped ion motion, vibrational modes, and electromagnetic fields, offer a complex landscape with many accessible energy states.

The research team exploited the quantum harmonic oscillator corresponding to the motion of a single trapped ion, an experimental platform that merges the discreetness of internal ion states with the continuous spectrum of motional states. This hybrid nature enables the faithful preparation and manipulation of intricate quantum states beyond simple qubits. Prior research commonly focused on “cat states” formed by superpositions of coherent states—localized wave packets akin to classical oscillations—displaced in opposite directions. In contrast, this breakthrough expands the toolbox by generating superpositions composed of trisqueezed components, which exhibit highly nonclassical statistical properties and richer phase-space structures.

Central to their experiment was the reconstruction of the Wigner function—a quasiprobability distribution offering a full phase-space portrait of a quantum state. The reconstructed Wigner functions demonstrated a distinctive sixfold rotational symmetry alongside pronounced regions of negativity, unambiguous hallmarks of quantum interference and the presence of genuine nonclassical states. These features attest that the constructed states cannot be mimicked by any classical probabilistic mixture, underscoring the experimental success in sculpting uniquely quantum superpositions with fine-tuned coherence and interference.

The method employed involves entangling the trapped ion’s internal electronic state with its motional modes through precisely engineered interactions. A mid-circuit projective measurement on the internal state effectively “selects” the ion’s motion into a programmable superposition of trisqueezed states. This innovative approach offers unprecedented control, enabling researchers to tailor the number, orientation, and displacement of component wave packets, allowing the realization of an expansive variety of exotic quantum states within the same physical platform.

Such programmable versatility is a significant stride forward because it transcends traditional superpositions arising from coherent states and squeezed states alone. The trisqueezed states used here redistribute quantum uncertainties across different quadratures more intricately than previous states, opening opportunities for enhanced quantum metrology and resource states for quantum information protocols that harness higher-order quantum correlations.

Additionally, the capability to engineering these states with a single trapped ion circumvents many scalability challenges faced by other quantum systems, offering a highly controllable and low-noise environment. This experiment serves as a blueprint for advancing quantum architectures that encode information not just in binary states but within multi-component superpositions across an extended Hilbert space—a crucial ingredient toward fault-tolerant quantum computing and resilient error-correction strategies.

The implications of this work ripple beyond applied quantum technologies. By enabling the construction and characterization of quantum states with unprecedented complexity, the researchers open a new experimental regime to investigate the quantum-to-classical transition—the fundamental question of how classical reality emerges from quantum underpinnings. The intricate interference patterns and Wigner negativities help illuminate the delicate interplay between coherence and decoherence, providing empirical data to test quantum decoherence models and theories of environmental impact on quantum systems.

Both Dr. Sebastian Saner, who spearheaded the research, and Dr. Raghavendra Srinivas, overseeing the project, emphasize that they have only begun to explore the vast landscape of nonclassical states accessible through their technique. Their approach is highly adaptable, and ongoing collaborations with theorists aim to rigorously quantify the degree of quantumness inherent to these states, refining our understanding of exotic quantum resources.

Looking forward, this experimental platform could be integral to next-generation quantum sensors that exploit these complex states to surpass classical limits in measuring fields, forces, and time. Moreover, the potential for these states to enhance error-resilient quantum computing paradigms is particularly exciting, as controlling multi-component superpositions could lead to more efficient decoding algorithms and novel qudit (multi-level quantum) architectures.

The team’s findings have been comprehensively detailed in a recent publication in Physical Review X, highlighting not only the technical sophistication of the implementation but also its conceptual novelty. This breakthrough represents a vibrant intersection of quantum control, fundamental physics, and technological innovation, cementing Oxford’s role at the forefront of experimental quantum science.

In sum, this achievement marks a transformative step from traditional two-state quantum systems toward a richer, multidimensional quantum fabric, enabling more powerful and nuanced quantum technologies. The ability to “sculpt” quantum superpositions in virtually any shape broadens the frontier of quantum state engineering, promising profound impacts across computing, sensing, and our fundamental understanding of the quantum world.

Subject of Research: Quantum superpositions beyond qubits in harmonic oscillators, specifically engineered nonclassical motional states of trapped ions.
Article Title: Generating Arbitrary Superpositions of Nonclassical Quantum Harmonic Oscillator States
Web References: DOI: 10.1103/k1xk-yt42
Image Credits: Department of Physics, University of Oxford

Keywords

Quantum mechanics, quantum superposition, Schrödinger’s cat states, trapped ions, quantum harmonic oscillator, nonclassical states, trisqueezed states, Wigner function, quantum interference, quantum computing, quantum sensing, quantum control

Quantum bits, or qubits, are notoriously fragile, susceptible to spontaneous errors that have long posed a barrier to the practical realization of reliable quantum machines. While error correction codes help mitigate this problem by encoding a single logical qubit into multiple physical qubits, the exponential increase in physical qubit resources—termed hardware overhead—has remained a daunting engineering challenge. The GKP codes present a theoretical framework to significantly alleviate this overhead by encoding logical qubits in continuous quantum variables, effectively translating the analog nature of quantum states into discrete, digital-like patterns that facilitate error detection and correction.

Until now, GKP codes have existed largely as a theoretical promise rather than an experimentally viable solution. The team led by Dr. Tingrei Tan has not only materialized these codes in the lab but has also engineered a universal set of quantum gates acting on GKP-encoded qubits. This universal set is fundamental because it means researchers can perform any quantum operation necessary for computation using qubits stored within the same physical quantum system. Their approach leverages exquisite control over the harmonic oscillations of a single trapped ytterbium ion, manipulating its motion in quantized vibrational modes to represent two logical qubits simultaneously.

Achieving entanglement between these logical qubits was a pivotal milestone. Entanglement, a uniquely quantum phenomenon where the state of one qubit instantaneously correlates with another regardless of distance, underpins the enhanced computational capabilities of quantum computers. Here, rather than entangling separate physical qubits, the researchers ingeniously entangled two distinct quantum vibrational modes—akin to quantized oscillations—within a single atom. This “quantum plumbing” not only conserves physical resources but also simplifies the traditionally complex architecture of quantum processors.

The logic gate constructed operates by precisely tuning the trapped ion’s quantum vibrations using advanced quantum control software developed by Q-CTRL, a spin-off from the laboratory itself. This control software employs physics-based models to minimize deleterious distortions to the delicate GKP code states throughout quantum operations. Maintaining the GKP code’s intricate structure during gate execution is paramount, as any degradation could negate the error-correcting advantages these codes provide. The experimental fidelity achieved in these control protocols demonstrates a crucial proof of concept for high-quality logical qubit manipulation within a practicable physical system.

A central experimental tool in this research is the Paul trap, a sophisticated device that confines charged ions using oscillating electric fields generated by precisely arranged electrodes. Unlike many quantum platforms requiring ultracold conditions, this trap operates at room temperature while maintaining stable control over the ion’s complex vibrational dynamics in three dimensions. By isolating and manipulating two specific motional modes of the ytterbium ion, the team effectively harnessed the continuous quantum variables necessary for GKP encoding, merging the mechanical quantum properties of the ion with state-of-the-art quantum error correction techniques.

This accomplishment represents more than a novel method; it acts as a blueprint for dramatically scaling quantum computers while overcoming one of their most formidable limitations: the physical qubit resource overhead. By embedding two error-correctable logical qubits within a single atom and demonstrating entanglement gates between them, the researchers have significantly lowered the barrier to hardware-efficient quantum computation. This efficiency is critical as the quantum computing community races to build devices with millions of logical qubits, which until now required unimaginably complex arrays of physical qubits.

The implications extend beyond mere hardware efficiency. The logical gates realized in this work establish a path toward more robust quantum information processing that leverages continuous-variable quantum systems. Unlike conventional qubits, which are two-state systems, continuous-variable qubits stored in harmonic oscillators enable richer encoding schemes and naturally integrate with quantum error correction protocols such as the GKP code. This hybrid approach effectively combines the benefits of discrete and continuous quantum systems, broadening the technological toolbox for quantum engineers.

Collaborator and lead author Vassili Matsos emphasizes the collaboration between theoretical and experimental quantum control, highlighting how the precisely engineered gate designs were made possible by integrating quantum control algorithms with physical modeling of GKP states. This synergy not only realized the first universal logical gate set for GKP qubits but also points toward a future in which complex quantum algorithms can be executed with unprecedented fidelity using these codes, reducing error rates that have historically limited the scale and reliability of quantum processors.

Looking forward, the researchers aim to expand their methods to entangle multiple logical qubits and integrate these gates into larger quantum circuits, laying foundational work for scalable, fault-tolerant quantum computers. As quantum devices continue to grow in both size and complexity, innovations like this will be instrumental in overcoming the resource bottleneck. They bring the theoretical promises of quantum error correction and continuous-variable qubits into tangible, programmable architectures, accelerating the timeline for quantum technologies capable of transformative applications in cryptography, materials science, and beyond.

This breakthrough, published in Nature Physics, not only validates longstanding theoretical models but raises compelling questions about the future architectures of quantum machines. By turning the abstract mathematical symmetries of the GKP code into a practical engineering reality, the University of Sydney researchers demonstrate how fundamental physics insights can revolutionize computing paradigms. Their achievement underscores the intricate dance between quantum theory, precision engineering, and control algorithms necessary to unlock quantum computing’s full potential.

The team acknowledges the critical role of international and interdisciplinary support, including funding from the Australian Research Council, the US Office of Naval Research, the US Army Research Office, the US Air Force Office of Scientific Research, Lockheed Martin, Sydney Quantum Academy, and private benefactors. Such collaboration and resources are essential as quantum research ventures deeper into uncharted scientific and technological territory, where each milestone requires the convergence of expertise and innovation at the highest level.

Media enquiries regarding this research can be directed to Marcus Strom at the University of Sydney. The detailed paper titled “Universal quantum gate set for Gottesman-Kitaev-Preskill logical qubits” offers comprehensive experimental data and technical discourse for those wishing to dive deeper into the mechanisms underpinning this advance.

Subject of Research: Not applicable

Article Title: Universal quantum gate set for Gottesman-Kitaev-Preskill logical qubits

News Publication Date: 21-Aug-2025

Web References:
– Quantum Control Laboratory: https://quantum.sydney.edu.au/research/quantum-control-laboratory/
– University of Sydney Nano Institute: https://www.sydney.edu.au/nano/
– Original article: https://www.nature.com/nphys/

References:
Matsos, V. et al ‘Universal quantum gate set for Gottesman-Kitaev-Preskill logical qubits’ (Nature Physics 2025) DOI: 10.1038/s41567-025-03002-8

Image Credits: Fiona Wolf/University of Sydney

Keywords

Quantum computing, quantum error correction, Gottesman-Kitaev-Preskill (GKP) code, logical qubits, trapped ion, quantum entanglement, Paul trap, quantum logic gates, harmonic oscillations, quantum control, continuous-variable quantum systems, scalable quantum computing