Trapped-ion systems have emerged as a leading platform for scalable quantum information processing owing to their high-fidelity operations and long-range entangling capabilities. As the number of ions in a trap increases, the growing density of collective motional modes makes the synthesis of multimode entangling gates increasingly challenging. Designing large-scale gates requires simultaneously realizing the desired spin-spin interactions, suppressing residual spin-motion entanglement, and limiting experimental control resources, leading to a high-dimensional non-convex optimization problem. Here we develop a numerical framework for multi-tone gate synthesis that directly searches for control fields satisfying these competing requirements. By employing an alternating-minimization strategy, the framework improves numerical stability and remains effective for large systems with many motional modes and target interactions. As representative demonstrations, we synthesize gates implementing all-to-all and nearest-neighbor interaction patterns in ion chains of up to N = 1000, using only global laser control. Across the parameter regimes explored here, the control resources required to maintain high-fidelity interactions do not exhibit rapid growth with system size. We extend the framework to individual addressing using a structured qLDPC target at N = 512 as an example. These results identify multimode gate synthesis as a viable route toward programmable interaction engineering in large-scale trapped-ion quantum processors.
Trapped-ion systems have emerged as a leading platform for scalable quantum information processing owing to their high-fidelity operations and long-range entangling capabilities. As the number of ions in a trap increases, the growing density of collective motional modes makes the synthesis of multimode entangling gates increasingly challenging. Designing large-scale gates requires simultaneously realizing the desired spin-spin interactions, suppressing residual spin-motion entanglement, and limiting experimental control resources, leading to a high-dimensional non-convex optimization problem. Here we develop a numerical framework for multi-tone gate synthesis that directly searches for control fields satisfying these competing requirements. By employing an alternating-minimization strategy, the framework improves numerical stability and remains effective for large systems with many motional modes and target interactions. As representative demonstrations, we synthesize gates implementing all-to-all and nearest-neighbor interaction patterns in ion chains of up to N = 1000, using only global laser control. Across the parameter regimes explored here, the control resources required to maintain high-fidelity interactions do not exhibit rapid growth with system size. We extend the framework to individual addressing using a structured qLDPC target at N = 512 as an example. These results identify multimode gate synthesis as a viable route toward programmable interaction engineering in large-scale trapped-ion quantum processors.
A central challenge in developing practical quantum processors is maintaining low control complexity while scaling to large numbers of qubits. Trapped-ion systems excel in small-scale operations and support rapid qubit scaling via long-chain architectures. However, their performance in larger systems is hindered by spectral crowding in radial motional modes, a problem that forces reliance on intricate pulse-shaping techniques to maintain gate fidelities. Here, we overcome this challenge by developing a novel trapped-ion processor with an individual-addressing system that generates steerable Hermite-Gaussian beam arrays. The transverse gradient of these beams couples qubits selectively to sparse axial motional modes, enabling to isolate a single mode as entanglement mediator. Leveraging this capability, we demonstrate addressable two-qubit entangling gates in chains up to six ions with fidelities consistently around 0.97, achieved without complex pulse shaping. Our method significantly reduces control overhead while preserving scalability, providing a crucial advance toward practical large-scale trapped-ion quantum computing.
Trapped-ion quantum simulators are powerful platforms for exploring many-body physics, yet engineering of arbitrary interaction graphs remains a central challenge. To leverage the intrinsic structure of native motional modes and thereby enhance programmability, a residual-guided optimization protocol is introduced for the systematic design of multi-tone global drive spectra. While the achievable interaction fidelity is fundamentally bounded by the available motional modes, this adaptive strategy converges on the theoretical limit using a number of laser tones that scales nearly linearly with system size. The versatility of this method enables the synthesis of both long-range and traditionally difficult short-range coupling topologies. Additionally, by incorporating a penalty for residual motional excitation, the algorithm effectively mitigates errors associated with incomplete closure of phase-space trajectories. Overall, this scalable framework significantly expands the programmable capabilities of trapped-ion architectures while maintaining low computational overhead and high potential for experimental implementation.
A central challenge in developing practical quantum processors is maintaining low control complexity while scaling to large numbers of qubits. Trapped-ion systems excel in small-scale operations and support rapid qubit scaling via long-chain architectures. However, their performance in larger systems is hindered by spectral crowding in radial motional modes, a problem that forces reliance on intricate pulse-shaping techniques to maintain gate fidelities. Here, we overcome this challenge by developing a trapped-ion processor with an individual-addressing system that generates steerable Hermite-Gaussian beam arrays. The transversal gradient of these beams couples qubits selectively to sparse axial motional modes, enabling to isolate a single or few modes as entanglement mediator. Leveraging this capability, we demonstrate addressable two-qubit entangling gates in chains up to six ions, with Bell-state preparation fidelities consistently around 0.97, achieved without complex pulse shaping. Our method substantially reduces control overhead while preserving scalability, providing a crucial advance toward practical large-scale trapped-ion quantum computing.
Abstract Trapped-ion quantum computing can utilize all motional modes of the ion-crystal, to entangle multiple qubits simultaneously, enabling universal computation with multi-qubit gates supplemented by single-qubit rotations. Using multiple tones to drive each ion individually induces Ising-type interactions, forming a multi-qubit gate, where the coupling matrix of all ion pairs is fully controllable. This reduces the total gate count while maintaining high fidelity, as opposed to traditional methods that rely on a single type of two-qubit gate, such as the well-known Mølmer–Sørensen gate. However, scaling to large ion chains, individual addressing can be technically challenging in terms of optical delivery and signal generation. We explore global and semi-global drives combined with single-qubit flips and show that these can reproduce the full set of multi-qubit gates. Although optimizing the combination of single-qubit flips is a computationally hard problem, we propose an efficient scheme to implement any desired couplings in large ion chains, yielding a concatenation scheme that uses at most N / 2 multi-qubit gates, with N being the number of ions. In addition, we show that by using B < N independent semi-global fields, each driving a set of N / B ions, the number of maximal multi-qubit gates is reduced to approximately N 2 B 2 ( N − 1 ) . We show how to design the driving fields that support these schemes and investigate their properties. Our results pave the way for efficient implementations of quantum algorithms in large-scale trapped-ion quantum systems.
The construction of entangling gates with individual addressing capability represents a crucial approach for implementing quantum computation in trapped-ion crystals. Conventional entangling gate schemes typically rely on laser beam wave vectors to couple the ions' spin and motional degrees of freedom. Here, we experimentally demonstrate an alternative method that employs a polarization gradient field generated by a tightly focused laser beam-an approach theoretically proposed as the Magnus effect for quantum logic gate design [Mazzanti et al., Phys. Rev. Res. 5, 033036 (2023)PPRHAI2643-156410.1103/PhysRevResearch.5.033036]. Using this technique, we perform Raman operations on hyperfine qubits encoded in ^{171}Yb^{+} ions, generating spin-dependent forces along axial motional modes in a linear trap. By utilizing an acousto-optic deflector to create arbitrary spot pairs for individual ion addressing in two-ion (four-ion) chains, we achieve Mølmer-Sørensen gates with Bell-state fidelities exceeding 98.7(1)% [and 97.2(4)%]. Further improvements in numerical aperture (NA) and laser power could reduce gate durations while enhancing fidelity by orders of magnitude. This method is compatible with-and can significantly simplify-optical tweezer gate proposals, where motional mode engineering enables scalable trapped-ion quantum computation. The technique can be readily extended to two-dimensional ion crystals, representing a key advancement toward large-scale trapped-ion quantum processors.
Quantum computers based on crystals of trapped ions are a prominent technology for quantum computation. A unique feature of trapped ions is their long-range Coulomb interactions, which can be exploited to realize large-scale multiqubit entanglement gates. However, scaling up the number of qubits, N, in these systems, while retaining high-fidelity and high-speed operations, is challenging. Specifically, designing multiqubit entanglement gates in long ion crystals of hundreds of ions involves an NP-hard optimization problem, rendering scale-up not only a technological challenge, but also a conceptual challenge. Here we introduce a method that mitigates this challenge, effectively allowing for a polynomial-time design of fast, robust, and programmable entanglement gates, acting on the entire ion-crystal. We show that while the number of simultaneous entanglement operations scales as N2, the gate duration scales as N, leading to a scaling advantage. We use our methods to investigate the drive-power requirements and susceptibility to noise and errors of these multiqubit gates. Our method delineates a path towards scaling up quantum computers based on ion-crystals with hundreds of qubits.