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arXiv:2509.14331 · Quantum Science and Technology

Full programmable quantum computing with trapped-ions using semi-global fields

Yakov Solomons, Yotam Kadish, Lee Peleg, Jonathan Nemirovsky, Amit Ben Kish, Yotam Shapira

Published Mar 25, 2026• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2058-9565/ae573c

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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.
Abstract We study the use of global drives with multiple frequency components to improve the efficiency of trapped ion quantum simulations and computations. We show that such ‘multi-mode’ global drives, when combined with a linear number of single-qubit rotations, generate universal Ising-type interactions with shorter overall runtimes than corresponding two-qubit gate implementations. Further, we show how this framework may be extended to efficiently generate n − body interactions between any subset n of the ion qubits. Finally, we apply these techniques to encode the Quantum Fourier Transform using quadratically-fewer entangling operations, with quadratically smaller runtime, compared with traditional approaches.
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, NNN, 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 N2N^2N2, the gate duration scales as NNN, 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.
Quantum computing represents an exciting frontier in the realm of information processing; it is a promising technology that may provide future advances in a wide range of fields, from quantum chemistry to optimization problems. This thesis discusses experimental results for several quantum algorithms performed on a programmable quantum computer consisting of a linear chain of five or seven trapped 171Yb+ atomic clock ions with long coherence times and high gate fidelities. We execute modular one- and two-qubit computation gates through Raman transitions driven by a beat note between counter-propagating beams from a pulsed laser. The system's individual addressing capability provides arbitrary single-qubit rotations as well as all possible two-qubit entangling gates, which are implemented using a pulse-segmentation scheme. The quantum computer can be programmed from a high-level interface to execute arbitrary quantum circuits, and comes with a toolbox of many important composite gates and quantum subroutines. We present experimental results for a complete three-qubit Grover quantum search algorithm, a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database, and report better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. All quantum solutions are shown to outperform their classical counterparts. Performing parallel operations will be a powerful capability as deeper circuits on larger, more complex quantum computers present new challenges. Here, we perform a pair of 2-qubit gates simultaneously in a single chain of trapped ions. We employ a pre-calculated pulse shaping scheme that modulates the phase and amplitude of the Raman transitions to drive programmable high-fidelity 2-qubit entangling gates in parallel by coupling to the collective modes of motion of the ion chain. Ensuring the operation yields only spin-spin interactions between the desired pairs, with neither residual spin-motion entanglement nor crosstalk spin-spin entanglement, is a nonlinear constraint problem, and pulse solutions are found using optimization techniques. As an application, we demonstrate the quantum full adder using a depth-4 circuit requiring the use of parallel 2-qubit operations.
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 N 2 , 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 toward scaling up quantum computers based on ion-crystals with hundreds of qubits.
The universality theorem in quantum computing states that any quantum computational task can be decomposed into a finite set of logic gates operating on one and two qubits. However, the process of such decomposition is generally inefficient, often leading to exponentially many gates to realize an arbitrary computational task. Practical processor designs benefit greatly from availability of multi-qubit gates that operate on more than two qubits to implement the desired circuit. In 1995, Cirac and Zoller proposed a method to realize native multi-qubit controlled-ZZZ gates in trapped ion systems, which has a stringent requirement on ground-state cooling of the motional modes utilized by the gate. An alternative approach, the Mølmer-Sørensen gate, is robust against residual motional excitation and has been a foundation for many high-fidelity gate demonstrations. This gate does not scale well beyond two qubits, incurring additional overhead when used to construct many target algorithms. Here, we take advantage of novel performance benefits of long ion chains to realize fully programmable and scalable high-fidelity Cirac-Zoller gates.
The prevalent approach to executing quantum algorithms on quantum computers is to break down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers are still a prominent challenge. Here we propose and investigate multiqubit entangling gates for trapped ions. Our gates couple many qubits at once, allowing us to decrease the total number of gates used while retaining a high gate fidelity. Our method employs all of the normal modes of motion of the ion chain, which allows us to operate outside of the adiabatic regime and at rates comparable to the secular ion-trapping frequency. Furthermore we extend our method for generating Hamiltonians which are suitable for quantum analog simulations, such as a nearest-neighbor spin Hamiltonian or the Su-Schrieffer-Heeger Hamiltonian.