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Journal of Optics B Quantum and Semiclassical Optics

A small trapped-ion quantum register

D. Kielpinski

Published Apr 11, 2003• 11 citations
Publisher

Abstract

We review experiments performed at the National Institute of Standards and Technology on entanglement, Bell's inequality and decoherence-free subspaces (DFSs) in a quantum register of trapped 9 Be + ions. The group of Dr David Wineland has demonstrated entanglement of up to four ions using the technique of Mølmer and Sørensen. This method produces the state (|↓↓ ⟩ + |↑↑ ⟩)/√2 for two ions and the state (|↓↓↓↓ ⟩ + |↑↑↑↑ ⟩)/√2 for four ions. The entanglement was generated deterministically in each shot of the experiment. Measurements on the two-ion entangled state violate Bell's inequality at the 8σ level. Because of the high detector efficiency of the 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. The group also demonstrated measurement of an interferometric phase with precision better than the shot-noise limit using a two-ion entangled state. A large-scale version of this scheme could improve the signal-to-noise ratio of atomic clocks by orders of magnitude. Further experiments demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a 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. Finally, we describe an architecture for a large-scale ion trap quantum computer. By performing logic gates on small numbers of ions trapped in separate regions of the array, we take advantage of existing techniques for manipulating small trapped-ion quantum registers while enabling massively parallel gate operation. Encoding the quantum information in the DFS removes decoherence associated with ion transport and imperfect clock synchronization.

DOI
10.1088/1464-4266/5/3/201

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We review experiments performed at the National Institute of Standards and Technology on entanglement, Bell's inequality and decoherence-free subspaces (DFSs) in a quantum register of trapped 9 Be + ions. The group of Dr David Wineland has demonstrated entanglement of up to four ions using the technique of Mølmer and Sørensen. This method produces the state (|↓↓ ⟩ + |↑↑ ⟩)/√2 for two ions and the state (|↓↓↓↓ ⟩ + |↑↑↑↑ ⟩)/√2 for four ions. The entanglement was generated deterministically in each shot of the experiment. Measurements on the two-ion entangled state violate Bell's inequality at the 8σ level. Because of the high detector efficiency of the 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. The group also demonstrated measurement of an interferometric phase with precision better than the shot-noise limit using a two-ion entangled state. A large-scale version of this scheme could improve the signal-to-noise ratio of atomic clocks by orders of magnitude. Further experiments demonstrated reversible encoding of an arbitrary qubit, originally contained in one ion, into a 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. Finally, we describe an architecture for a large-scale ion trap quantum computer. By performing logic gates on small numbers of ions trapped in separate regions of the array, we take advantage of existing techniques for manipulating small trapped-ion quantum registers while enabling massively parallel gate operation. Encoding the quantum information in the DFS removes decoherence associated with ion transport and imperfect clock synchronization.
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.
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 demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace (DFS) of a pair of trapped 9Be+ ions, we protect the qubit from environment-induced dephasing that limits the storage time of a qubit composed of a single ion. We measured the storage time under ambient conditions and under interaction with an engineered noisy environment and observed that encoding into the DFS increases the storage time by up to an order of magnitude. The encoding reversibly transfers an arbitrary qubit stored in a single ion to the DFS of two ions.
We demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace (DFS) of a pair of trapped 9Be+ ions, we protect the qubit from environment-induced dephasing that limits the storage time of a qubit composed of a single ion. We measured the storage time under ambient conditions and under interaction with an engineered noisy environment and observed that encoding into the DFS increases the storage time by up to an order of magnitude. The encoding reversibly transfers an arbitrary qubit stored in a single ion to the DFS of two ions.
Quantum entangling logic gates are key ingredients for the implementation of a quantum information processing device. In this thesis, we focus on experimental implementations of three types of entangling geometric-phase gates with trapped ions, which rely on the effective spin-spin interactions generated with state-dependent forces. First, a mixed-species entangling gate is demonstrated using a 9Be+ and a 25Mg+ ion to create a Bell state with a fidelity of 0.979(1). Combined with single-qubit gates, we use this mixed-species gate to implement controlled-NOT and SWAP gates. Second, we implement a high-fidelity universal gate set with 9Be+ ions. Single-qubit gates with error per gate of 3.8(1)x10-5 are achieved. By creating a Bell state with a deterministic two-qubit entangling gate, we deduce a gate error as low as 8(4)x10-4. Third, a novel two-qubit entangling gate with dynamical decoupling built-in is demonstrated with a fidelity of 0.974(4). This gate is robust against qubit dephasing errors and offers simplifications in experimental implementation compared to some other gates with trapped ions. Errors in the above implementations are evaluated and methods to further reduce imperfections are discussed. In a separate experiment, correlated measurements made on pairs of ions violate a "chained" Bell inequality obeyed by any local-realistic theory. The lowest chained Bell inequality parameter determined from our measurements is 0.296(12), this value is significantly lower than 0.586, the minimum value derived from a perfect Clauser-Horne-Shimony-Horne (CHSH) Bell inequality experiment. Furthermore, our CHSH Bell inequality results provide a device-independent certification of the deterministically created Bell states.
Experiments with two entangled trapped 9Be+ ions are discussed. In one type of experiments we used entanglement to increase the precision of rotation angle measurements. For “spin-squeezed" and maximally entangled states we observed a reduction in uncertainty of rotation angle below the standard quantum limit. In a second experiment we demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace of two ions, we protect it from environment-induced dephasing. We increased the storage time by up to an order of magnitude compared to an unprotected qubit.