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.
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.
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.
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.
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.
Ion trap quantum computers are based on modulating the Coulomb interaction between atomic ion qubits using external forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals by using a small and fixed number of motional modes, simplifying the scaling of ion trap quantum computers. We present analytical work that shows that gate operations need not couple to the motion of distant ions, allowing parallel entangling gates with a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also experimentally demonstrate high-fidelity entangling gates on a fully connected set of seventeen 171Yb+ qubits using simple laser pulse shapes that primarily couple to just a few modes.
Entangling gates are an essential component of quantum computers. However, generating high-fidelity gates, in a scalable manner, remains a major challenge in all quantum information processing platforms. Accordingly, improving the fidelity and robustness of these gates has been a research focus in recent years. In trapped ions quantum computers, entangling gates are performed by driving the normal modes of motion of the ion chain, generating a spin-dependent force. Even though there has been significant progress in increasing the robustness and modularity of these gates, they are still sensitive to noise in the intensity of the driving field. Here we supplement the conventional spin-dependent displacement with spin-dependent squeezing, which creates a new interaction, that enables a gate that is robust to deviations in the amplitude of the driving field. We solve the general Hamiltonian and engineer its spectrum analytically. We also endow our gate with other, more conventional, robustness properties, making it resilient to many practical sources of noise and inaccuracies.
A universal quantum computer is an ultimate pursuit, which should possess the ability to perform entangling gate operations in parallel with high quality in a scalable fashion. However, for a long trapped-ion chain, the simultaneous implementation of two-qubit quantum gates is a challenging task due to the drastic increase of the crosstalk resulting from the collective motional modes. In this paper, by utilizing the structure of the localized motional modes in the long mixed-species ion chain, we propose a highly efficient linear iterative scheme to eliminate the crosstalk within the neighboring pairs. We show that this scheme allows the realization of high-fidelity, low-crosstalk, scalable, parallel two-qubit gates with only a few pulse segments for the long chain. In addition, by considering the practical experimental feasibility, we optimize the laser power and improve the robustness against the random static drifts of the motional frequencies.