Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

European Quantum Electronics Conference (EQEC)

Realisation of the Cirac-Zoller controlled-NOT quantum gate

Ferdinand Schmidt‐Kaler, Hartmut Häffner, Mark Riebe, S. Gulde, C.P.T. Lancaster, T. Deuschle, Christoph Becher, Christian F. Roos, Jürgen Eschner, R. Blatt

Published Jan 1, 2003• 1 citation
Publisher

Abstract

Realisation of controlled-NOT gate (CNOT) operation between two individual ions as a universal two-bit quantum gate based from the proposals of Cirac and Zoller, is presented. Two single /sup 40/Ca/sup +/ ions are held in a linear Paul trap and are individually addressed with focused laser beams. Superpositions of the S/sub 1/2 /and the D/sub 5/2/ long lived electronic states represent a qubit. A sequence of well suited laser pulses flips the state of the target ion conditional to the state of the control ion.

DOI
10.1109/eqec.2003.1314241

Related papers

Simplified quantum logic with trapped ions

Christopher R. Monroe, Dietrich G. Leibfried, B. E. King +3 more

We describe a simplified scheme for quantum logic with a collection of laser-cooled trapped atomic ions. Building on the scheme of Cirac and Zoller, we show how the fundamental controlled-NOT gate between a collective mode of ion motion and the internal states of a single ion can be reduced to a single laser pulse, and the need for a third auxiliary internal electronic state can be eliminated.

arXiv:quant-ph/9612042•Physical Review A•Apr 1, 1997•116 citations

Quantum gate using qubit states separated by terahertz

Kenji Toyoda, Shinsuke Haze, Rekishu Yamazaki +1 more

A two-qubit quantum gate is realized using electronically excited states in a single ion with an energy separation on the order of a terahertz times the Planck constant as a qubit. Two phase-locked lasers are used to excite a stimulated Raman transition between two metastable states ${D}_{3/2}$ and ${D}_{5/2}$ separated by $1.82$ THz in a single trapped $^{40}\mathrm{Ca}$${}^{+}$ ion to construct a qubit, which is used as the target bit for the Cirac-Zoller two-qubit controlled NOT gate. Quantum dynamics conditioned on a motional qubit is clearly observed as a fringe reversal in Ramsey interferometry.

arXiv:1001.4600•Physical Review A•Mar 24, 2010•16 citations

Demonstration of a quantum logic gate in a cryogenic surface-electrode ion trap

Shannon X. Wang, Jaroslaw Labaziewicz, Yufei Ge +2 more

We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of ${\mathrm{Sr}}^{+}$ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. ac Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminating the need for an additional laser. Quantum process tomography is implemented on atomic and motional states by use of conditional pulse sequences. With these techniques, we demonstrate a Cirac-Zoller controlled-not gate in a single ion with a mean fidelity of $91(1)%$.

arXiv:0912.4892•Physical Review A•Jun 24, 2010•35 citations

Ion Trap Quantum Computers Part 2: The Universal 2-Qubit-CNOT Gate

Bernd Baumann

The Cirac-Zoller mechanism is generally used for the implementation of CNOT gates in ion trap quantum computers. We present here a highly detailed quantum physical description of this approach. To keep the presentation simple, the qubits are modeled as rigid rotors and the radiation field of each of the lasers is treated as a classical field. In combination with the corresponding first part (Ion Trap Quantum Computer Part 1: 1-Qubit Gates), this results in the complete quantum theory of a universal set of quantum gates. This presentation is intended for readers with basic knowledge of quantum physics and assumes familiarity with Part 1.

Scientific Insights•Dec 26, 2025•0 citations

Realization of Scalable Cirac-Zoller Multi-Qubit Gates

Fang, Chao, Ye Wang, Ke Sun +1 more

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.

arXiv:2301.07564•Jan 18, 2023•1 citation

Efficient Multi-Controlled Gate Implementation in Trapped-Ion Systems

Minhyeok Kang, Taejin Kim, Jungsoo Hong +1 more

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-$Z$ 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 $N$-controlled gates that use a single-controlled gate primitive and $\mathcal{O}(N)$ 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 $L$ unitaries can be reduced from $\mathcal{O}(L\log L)$ to $\mathcal{O}(L)$, which improves the efficiency and scalability of LCU-based quantum circuits.

quant-pharXiv:2605.04654•Quantum Science and Technology•May 7, 2026•0 citations
Realisation of controlled-NOT gate (CNOT) operation between two individual ions as a universal two-bit quantum gate based from the proposals of Cirac and Zoller, is presented. Two single /sup 40/Ca/sup +/ ions are held in a linear Paul trap and are individually addressed with focused laser beams. Superpositions of the S/sub 1/2 /and the D/sub 5/2/ long lived electronic states represent a qubit. A sequence of well suited laser pulses flips the state of the target ion conditional to the state of the control ion.
A two-qubit quantum gate is realized using electronically excited states in a single ion with an energy separation on the order of a terahertz times the Planck constant as a qubit. Two phase-locked lasers are used to excite a stimulated Raman transition between two metastable states D3/2{D}_{3/2}D3/2​ and D5/2{D}_{5/2}D5/2​ separated by 1.821.821.82 THz in a single trapped 40Ca^{40}\mathrm{Ca}40Ca+{}^{+}+ ion to construct a qubit, which is used as the target bit for the Cirac-Zoller two-qubit controlled NOT gate. Quantum dynamics conditioned on a motional qubit is clearly observed as a fringe reversal in Ramsey interferometry.
We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of Sr+{\mathrm{Sr}}^{+}Sr+ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. ac Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminating the need for an additional laser. Quantum process tomography is implemented on atomic and motional states by use of conditional pulse sequences. With these techniques, we demonstrate a Cirac-Zoller controlled-not gate in a single ion with a mean fidelity of 91(1)91(1)%91(1).
The Cirac-Zoller mechanism is generally used for the implementation of CNOT gates in ion trap quantum computers. We present here a highly detailed quantum physical description of this approach. To keep the presentation simple, the qubits are modeled as rigid rotors and the radiation field of each of the lasers is treated as a classical field. In combination with the corresponding first part (Ion Trap Quantum Computer Part 1: 1-Qubit Gates), this results in the complete quantum theory of a universal set of quantum gates. This presentation is intended for readers with basic knowledge of quantum physics and assumes familiarity with Part 1.
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.