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Quantum Electronics and Laser Science Conference

Scalable entanglement of trapped ions

Charles A. Sackett, D. Kielpinski, C. Langer, V. Meyer, M. Röwe, Q. A. Turchette, Wayne M. Itano, Christopher R. Monroe, David J. Wineland

Published May 12, 2000• 3 citations
OpenAlex

Abstract

Summary form only given. Quantum entanglement is a fundamental element of schemes for quantum communication, cryptography, and computation. In a previous experiment, we demonstrated that two-particle entanglement could be generated in a deterministic way using trapped ions. However, that scheme also could not easily be applied to more particles in a single trap, because it relied on the particular behavior of two ions in a quadrupole RF trap. We have now demonstrated a truly scalable entanglement technique. The scheme is that of a recent proposal by Molmer and Sorensen. Twog /sup 9/Be/sub +/ ions are confined in a linear RF trap, and laser-cooled to near their motional ground state. Lasers are then used to drive Raman transitions between two ground-state hyperfine levels, which are separated by energy hw/sub o/.

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Summary form only given. We have laser-cooled all modes of two ions and select modes of three ions to the ground state, thereby paving the way for subsequent quantum logic operations. We have also used quantum logic on two ions to engineer the Bell entangled states, representing the first source of entanglement not relying on a selection process. This type of deterministic entanglement is a crucial requirement for large-scale quantum computation.

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We review recent experiments on entanglement, Bell's inequality, and decoherence-free subspaces in a quantum register of trapped {9Be+} ions. We have demonstrated entanglement of up to four ions using the technique of Molmer and Sorensen. This method produces the state ({|\uparrow\uparrow\rangle}+{|\downarrow\downarrow\rangle})/\sqrt{2} for two ions and the state ({\downarrow}{\downarrow}{\downarrow}{\downarrow} \rangle + | {\uparrow}{\uparrow}{\uparrow}{\uparrow} \rangle)/\sqrt{2} for four ions. We generate the entanglement deterministically in each shot of the experiment. Measurements on the two-ion entangled state violates Bell's inequality at the 8\sigma level. Because of the high detector efficiency of our apparatus, this experiment closes the detector loophole for Bell's inequality measurements for the first time. This measurement is also the first violation of Bell's inequality by massive particles that does not implicitly assume results from quantum mechanics. Finally, we have demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a decoherence-free subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective dephasing noise and retains coherence under ambient conditions 3.6 times longer than does an unencoded qubit. The encoding method, which uses single-ion gates and the two-ion entangling gate, demonstrates all the elements required for two-qubit universal quantum logic.

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We review recent experiments on entanglement, Bell's inequality, and decoherence-free subspaces in a quantum register of trapped \be ions. We have demonstrated entanglement of up to four ions using the technique of Mølmer and Sørensen. This method produces the state |down down> + |up up> for two ions and the state |down down down down> + |up up up up> for four ions. We generate the entanglement deterministically in each shot of the experiment. Measurements on the two-ion entangled state violates Bell's inequality at the $8σ$ level. Because of the high detector efficiency of our apparatus, this experiment closes the detector loophole for Bell's inequality measurements for the first time. This measurement is also the first violation of Bell's inequality by massive particles that does not implicitly assume results from quantum mechanics. Finally, we have demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a decoherence-free subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective dephasing noise and retains coherence under ambient conditions 3.6 times longer than does an unencoded qubit. The encoding method, which uses single-ion gates and the two-ion entangling gate, demonstrates all the elements required for two-qubit universal quantum logic.

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Quantum Entanglement Generation in Trapped Ions Using Coherent and Dissipative Methods

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Entangled states are a key resource in fundamental quantum physics, quantum cryptography, and quantum computation. In this thesis, we focus on the demonstrations of two novel methods to generate entanglement. First, we implement dissipative production of a maximally entangled steady state on two trapped ions. Dissipative and coherent processes are combined and implemented in a continuous time-independent fashion, analogous to optical pumping of atomic states, continuously driving the system towards the steady entangled state. With this method, we obtain a Bell state fidelity up to 0.89(2). Second, we propose and demonstrate a novel coherent process to confine quantum evolution in a subspace between an initial separable state and the target entangled state. We demonstrate this scheme on two and three ions obtaining a Bell state fidelity up to 0.992(2). Both of these methods are robust against certain types of experimental noise and decoherence. Additionally, we demonstrate sympathetic cooling of ion chains to near the ground\nstate of motion with an electromagnetically-induced-transparency (EIT) method. This results in roughly an order of magnitude faster cooling time while using significantly lower laser power compared to the conventional resolved sideband cooling method. These techniques may be helpful for scaled-up quantum computing.

•Jan 1, 2015•1 citation

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All of the essential elements for a trapped ion quantum computer have been demonstrated in previous experiments. There are, however, many technical challenges to scaling the number of quantum bits from the current state-of-the-art (about 8) to the number of qubits needed for practical quantum computing. Although there is experimental evidence supporting one possible method (using cw laser pulses and common motional modes as the ion interaction) for deterministic ion entanglement, it is not known if that will ultimately be the most practical method for building a large-scale quantum computer. One model for scalable quantum computing with trapped ions calls for large interconnected arrays of small traps. Several advancements reported in this work include the development of three layer alumina traps as well as MEMS fabricated microtraps. Other models for scalable trapped ion quantum computing do not call for local entanglement or call for relaxed constraints on the motional control of the ions. These proposals require the use of ultrafast laser pulses interacting with the ions. This work reviews several experiments that explore the interaction between the ultrafast laser and single tripped ions including early indication of ultrafast control and entanglement between a single ion and a single photon frequency qubit.

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Quantum control methods for robust entanglement of trapped ions

Christophe H. Valahu, I Apostolatos, S Weidt +1 more

Abstract A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to sources of noise. Nevertheless, it may be difficult to identify an appropriate quantum control technique for a particular need given the breadth of work pertaining to robust entanglement. To this end, we attempt to consolidate the literature by providing a non-exhaustive summary and critical analysis. The quantum control methods are separated into two categories: schemes which extend the robustness to (i) spin or (ii) motional decoherence. We choose to focus on extensions of the σ x ⊗ σ x Mølmer–Sørensen interaction using microwaves and a static magnetic field gradient. Nevertheless, some of the techniques discussed here can be relevant to other trapped ion architectures or physical qubit implementations. Finally, we experimentally realize a proof-of-concept interaction with simultaneous robustness to spin and motional decoherence by combining several quantum control methods presented in this manuscript.

arXiv:2206.06064•Journal of Physics B Atomic Molecular and Optical Physics•Sep 2, 2022•29 citations
Summary form only given. Quantum entanglement is a fundamental element of schemes for quantum communication, cryptography, and computation. In a previous experiment, we demonstrated that two-particle entanglement could be generated in a deterministic way using trapped ions. However, that scheme also could not easily be applied to more particles in a single trap, because it relied on the particular behavior of two ions in a quadrupole RF trap. We have now demonstrated a truly scalable entanglement technique. The scheme is that of a recent proposal by Molmer and Sorensen. Twog /sup 9/Be/sub +/ ions are confined in a linear RF trap, and laser-cooled to near their motional ground state. Lasers are then used to drive Raman transitions between two ground-state hyperfine levels, which are separated by energy hw/sub o/.
We review recent experiments on entanglement, Bell's inequality, and decoherence-free subspaces in a quantum register of trapped {9Be+} ions. We have demonstrated entanglement of up to four ions using the technique of Molmer and Sorensen. This method produces the state ({|\uparrow\uparrow\rangle}+{|\downarrow\downarrow\rangle})/\sqrt{2} for two ions and the state ({\downarrow}{\downarrow}{\downarrow}{\downarrow} \rangle + | {\uparrow}{\uparrow}{\uparrow}{\uparrow} \rangle)/\sqrt{2} for four ions. We generate the entanglement deterministically in each shot of the experiment. Measurements on the two-ion entangled state violates Bell's inequality at the 8\sigma level. Because of the high detector efficiency of our apparatus, this experiment closes the detector loophole for Bell's inequality measurements for the first time. This measurement is also the first violation of Bell's inequality by massive particles that does not implicitly assume results from quantum mechanics. Finally, we have demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a decoherence-free subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective dephasing noise and retains coherence under ambient conditions 3.6 times longer than does an unencoded qubit. The encoding method, which uses single-ion gates and the two-ion entangling gate, demonstrates all the elements required for two-qubit universal quantum logic.
We review recent experiments on entanglement, Bell's inequality, and decoherence-free subspaces in a quantum register of trapped \be ions. We have demonstrated entanglement of up to four ions using the technique of Mølmer and Sørensen. This method produces the state |down down> + |up up> for two ions and the state |down down down down> + |up up up up> for four ions. We generate the entanglement deterministically in each shot of the experiment. Measurements on the two-ion entangled state violates Bell's inequality at the 8σ8σ8σ level. Because of the high detector efficiency of our apparatus, this experiment closes the detector loophole for Bell's inequality measurements for the first time. This measurement is also the first violation of Bell's inequality by massive particles that does not implicitly assume results from quantum mechanics. Finally, we have demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a decoherence-free subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective dephasing noise and retains coherence under ambient conditions 3.6 times longer than does an unencoded qubit. The encoding method, which uses single-ion gates and the two-ion entangling gate, demonstrates all the elements required for two-qubit universal quantum logic.
Entangled states are a key resource in fundamental quantum physics, quantum cryptography, and quantum computation. In this thesis, we focus on the demonstrations of two novel methods to generate entanglement. First, we implement dissipative production of a maximally entangled steady state on two trapped ions. Dissipative and coherent processes are combined and implemented in a continuous time-independent fashion, analogous to optical pumping of atomic states, continuously driving the system towards the steady entangled state. With this method, we obtain a Bell state fidelity up to 0.89(2). Second, we propose and demonstrate a novel coherent process to confine quantum evolution in a subspace between an initial separable state and the target entangled state. We demonstrate this scheme on two and three ions obtaining a Bell state fidelity up to 0.992(2). Both of these methods are robust against certain types of experimental noise and decoherence. Additionally, we demonstrate sympathetic cooling of ion chains to near the ground\nstate of motion with an electromagnetically-induced-transparency (EIT) method. This results in roughly an order of magnitude faster cooling time while using significantly lower laser power compared to the conventional resolved sideband cooling method. These techniques may be helpful for scaled-up quantum computing.
All of the essential elements for a trapped ion quantum computer have been demonstrated in previous experiments. There are, however, many technical challenges to scaling the number of quantum bits from the current state-of-the-art (about 8) to the number of qubits needed for practical quantum computing. Although there is experimental evidence supporting one possible method (using cw laser pulses and common motional modes as the ion interaction) for deterministic ion entanglement, it is not known if that will ultimately be the most practical method for building a large-scale quantum computer. One model for scalable quantum computing with trapped ions calls for large interconnected arrays of small traps. Several advancements reported in this work include the development of three layer alumina traps as well as MEMS fabricated microtraps. Other models for scalable trapped ion quantum computing do not call for local entanglement or call for relaxed constraints on the motional control of the ions. These proposals require the use of ultrafast laser pulses interacting with the ions. This work reviews several experiments that explore the interaction between the ultrafast laser and single tripped ions including early indication of ultrafast control and entanglement between a single ion and a single photon frequency qubit.
Abstract A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to sources of noise. Nevertheless, it may be difficult to identify an appropriate quantum control technique for a particular need given the breadth of work pertaining to robust entanglement. To this end, we attempt to consolidate the literature by providing a non-exhaustive summary and critical analysis. The quantum control methods are separated into two categories: schemes which extend the robustness to (i) spin or (ii) motional decoherence. We choose to focus on extensions of the σ x ⊗ σ x Mølmer–Sørensen interaction using microwaves and a static magnetic field gradient. Nevertheless, some of the techniques discussed here can be relevant to other trapped ion architectures or physical qubit implementations. Finally, we experimentally realize a proof-of-concept interaction with simultaneous robustness to spin and motional decoherence by combining several quantum control methods presented in this manuscript.