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arXiv:2301.07564

Realization of Scalable Cirac-Zoller Multi-Qubit Gates

Fang, Chao, Ye Wang, Ke Sun, Jungsang Kim

Published Jan 18, 2023• 1 citation
arXivHTMLPDF

Abstract

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-$Z$ 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.

DOI
10.48550/arxiv.2301.07564

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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.
Multi-controlled gates are essential primitives in quantum algorithms, yet implementing them via standard gate-level decompositions remains resource-intensive. We develop efficient pulse-level implementations of multi-controlled gates in trapped-ion systems using the Cirac-Zoller scheme. We first show that the Cirac-Zoller construction admits a freedom in the sign choice of red-sideband (RSB) pulses, which leaves the logical operation invariant up to a local Pauli-ZZZ correction. By exploiting this freedom, we construct equivalent realizations of multi-controlled gates and develop pulse cancellation for more efficient implementations of successive gates. We perform numerical simulations and show that pulse cancellation reduces the gate time and improves the state fidelity. Furthermore, we propose ancilla-free circuits for general NNN-controlled gates that use a single-controlled gate primitive and O(N)\mathcal{O}(N)O(N) RSB pulses. As a key application, we apply our pulse cancellation to the linear combination of unitaries (LCU) method for block encoding. We show that the RSB-pulse cost of the select operator over LLL unitaries can be reduced from O(Llog⁡L)\mathcal{O}(L\log L)O(LlogL) to O(L)\mathcal{O}(L)O(L), which improves the efficiency and scalability of LCU-based quantum circuits.
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 Trapped-ion systems are one of the leading platforms for quantum information processing, where a key challenge is to scale up system size while maintaining high-fidelity two-qubit operations. A promising approach is to build high-performance modules interconnected via strong coupling. In particular, axial motional modes offer a practical mechanism to couple the ions in a chain, enabling the preparation of Greenberger–Horne–Zeilinger states with up to 24 ions using global operations, as well as high-fidelity two-qubit gates (96.6%–98.0%) in fully connected five-ion chains. Here, we demonstrate two-qubit quantum logic gates in a 5-ion 40 Ca + chain using axial modes, achieving fidelities exceeding 99% for adjacent pairs and over 98% for arbitrary pairs by carefully tackling dominant error sources. Our results are beneficial to the development of scalable ion-trap quantum processors, quantum simulation and quantum-enhanced metrology.
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.
The high-fidelity multi-ion entangled states and quantum gates are the basis for trapped-ion quantum computing. Among the developed quantum gate schemes, Mølmer-Sørensen gate is a relatively mature experimental technique to realize multi-ion entanglement and quantum logic gates. In recent years, there have also been schemes to realize ultrafast quantum entanglement and quantum logic gates that operate outside the Lamb-Dicke regime by designing ultrafast laser pulse sequences. In such a many-body quantum system, these entanglement gates couple the spin states between ions by driving either the phonon energy level or the motional state of the ion chain. To improve the fidelity of quantum gates, the modulated laser pulses or the appropriately designed pulse sequences are applied to decouple the multi-mode motional states. In this review, we summarize and analyze the essential aspects of realizing these entanglement gates from both theoretical and experimental points of view. We also reveal that the basic physical process of realizing quantum gates is to utilize nonlinear interactions in non-equilibrium processes through driving the motional states of an ion chain with laser fields.
High-fidelity two-qubit entangling gates play an important role in many quantum information processing tasks and are a necessary building block for constructing a universal quantum computer. Such high-fidelity gates have been demonstrated on trapped-ion qubits; however, control errors and noise in gate parameters may still lead to reduced fidelity. Here we propose and demonstrate a general family of two-qubit entangling gates which are robust to different sources of noise and control errors. These gates generalize the renowned Mølmer-Sørensen gate by using multitone drives. We experimentally implemented several of the proposed gates on ^{88}Sr^{+} ions trapped in a linear Paul trap and verified their resilience.