Researchers Mediate Interactions Between 8 Qubits Using Magnetic-Field Gradients and Motional Modes

Scientists are exploring new methods for creating entanglement between qubits, a crucial process for quantum computation. Modesto Orozco-Ruiz and Florian Mintert, both from the Physics Department, Blackett Laboratory, Imperial College London, demonstrate a novel scheme for achieving this, utilising a time-dependent magnetic-field gradient to mediate interactions. This research circumvents the limitations of conventional approaches which require precise spectral addressing of individual modes, becoming increasingly complex and slow with larger qubit numbers. By employing all axial motional modes in a nonperturbative manner, their framework promises faster and more robust multi-qubit gate operations and two-qubit gates between any pair within a linear string, representing a significant advance in scalable quantum information processing.

Researchers have developed a novel method for entangling qubits, the fundamental building blocks of quantum computers, using trapped ions, circumventing limitations that have hindered scaling up these systems. Conventional approaches to linking qubits rely on precisely controlling a single vibrational mode of the ion chain, a technique that becomes increasingly difficult and slow as the number of ions increases. This work introduces a scheme that leverages all vibrational modes simultaneously, creating a more robust and efficient pathway to multi-qubit interactions. Trapped ions are considered a leading platform for building quantum processors, with information encoded in the internal states of individual ions and interactions mediated by their collective motion. As the ion chain lengthens, the coupling to any single mode weakens, necessitating stronger driving forces to maintain gate speed, creating a trade-off between achieving fast and high-fidelity operations. This research overcomes these limitations by harnessing the collective dynamics of all motional modes within the ion chain. By employing a carefully tailored, time-dependent magnetic-field gradient, the team engineered qubit-qubit interactions that are not reliant on spectral addressing, the need to individually resolve and control each vibrational mode. The framework presented is applicable to both multi-qubit gates and two-qubit gates between any pair of ions in a linear chain, addressing the need for gate schemes designed for larger systems, as experiments with ion strings containing up to a few dozens of ions are now commonplace. Unlike previous magnetic-gradient schemes, this method avoids perturbative approximations, allowing for stronger and faster interactions. The strength of the qubit-motion coupling is proportional to the magnetic field gradient, and the team demonstrated that by modulating this gradient, they could significantly enhance the qubit-qubit interaction, promising to overcome key limitations of conventional gate schemes. A time-dependent magnetic-field gradient forms the core of this work, enabling the manipulation of multiple qubits simultaneously and circumventing limitations inherent in conventional qubit entanglement methods that rely on addressing individual motional modes of ion strings. By employing a gradient that varies over time, the research activates all axial motional modes, fostering a nonperturbative interaction between qubits. This approach contrasts with perturbative schemes, which can restrict gate speed and fidelity, and complex driving schemes needed for numerous modes. The methodology prioritises precise control over the ions’ motional states through careful boundary condition management. Initial and final conditions for the gradient are meticulously defined to ensure consistency with both static and oscillating gradient methods previously established in the field. For static gradients, the boundary conditions maintain the dressed-qubit basis, preventing alterations to ion motion during gate operation. When utilising oscillating gradients, the conditions enforce the cancellation of net motional displacement, isolating spin dynamics and yielding a pure spin-spin interaction. Gate synthesis relies on a sequence of global driving segments, each modulated by the time-dependent magnetic-field gradient and interleaved with π-pulses. These π-pulses, applied before and after each gradient modulation, extend the range of achievable effective couplings between ions. The process is formulated as a mixed discrete, continuous optimisation problem, where continuous parameters define the waveforms and segment durations, while discrete choices determine the application of π-pulses to each ion. An iterative procedure jointly optimises these parameters, ensuring both boundary condition satisfaction and the approach to target pairwise phase shifts. The chosen parametrization employs 2N + 1 basis functions to describe each segment, providing sufficient flexibility for high-fidelity gates in smaller registers and scalable optimisation for larger systems. Scientists have demonstrated a novel gate scheme for controlling multiple qubits using ion strings, achieving gate times as short as 23 microseconds for a target coupling strength of π/4. This represents a significant advancement in the field of trapped-ion quantum computing. The research introduces a time-dependent magnetic-field gradient technique where all axial motional modes participate in mediating qubit interactions, circumventing limitations of existing methods. The optimised protocol achieves a gate time scaling similar to a single-tone approach, with T ∝ η−1 C, but crucially avoids the associated fidelity loss. Specifically, for a common-mode coupling of ηC = 0.3, achieved with a magnetic field gradient of approximately 250 Tesla per metre and a trap frequency of 100 kilohertz, the gate is completed in just two oscillation cycles of the common mode. This corresponds to a total gate time of approximately 2.3times the period of the first motional mode, or 23 microseconds, comparable to the fastest multi-qubit gate implementations currently reported. Gate fidelity is limited only by the numerical precision of the pulse shaping, set to 10−9, exceeding the accuracy of existing protocols by several orders of magnitude. The framework enables the direct construction of drive waveforms that simultaneously satisfy qubit-motion decoupling conditions for all motional modes and generate the desired collective qubit interaction. Furthermore, the study shows that at least five interaction windows are required to approximate a homogeneous Ising interaction with vanishingly small infidelity, demonstrating precise control over qubit entanglement. The research also details a rainbow coupling pattern, achieved with a magnetic field gradient of approximately 125 Tesla per metre and a coupling of ηj1 ≃0.15, resulting in a longer gate duration of T = 8.125/2πν. This capability is especially valuable in the strong-coupling regime, where conventional protocols are least effective, yet where fast gate operations become possible. Scientists are edging closer to scalable quantum computing with a new approach to controlling interactions between qubits. For years, building larger and more stable quantum processors has been hampered by the difficulty of precisely manipulating the delicate connections between quantum bits, particularly as their number increases. This research introduces a method for entangling qubits using time-dependent magnetic field gradients, effectively harnessing all available motional modes within an ion string to mediate these interactions. The significance lies in the potential to overcome a fundamental bottleneck in quantum processor design. Existing methods struggle with weakening coupling as ion strings grow, necessitating complex and slow gate operations. By utilising a non-perturbative approach, this technique promises faster and more reliable gate construction, even with dozens of qubits. Practical implementation remains a considerable challenge, however, as translating the theoretical framework into robust, error-resistant hardware will require significant engineering advances. Maintaining the precise magnetic field gradients and minimising external noise are critical hurdles, and scalability beyond a few dozen qubits needs to be demonstrated. Looking ahead, this work could inspire new architectures for quantum processors, potentially moving beyond linear ion strings to more complex, interconnected topologies. The principles explored here may also be applicable to other qubit modalities, such as trapped neutral atoms or superconducting circuits.