We report high-fidelity laser-beam-induced quantum logic gates on magnetic-field-insensitive qubits comprised of hyperfine states in 9 Be + ions with a memory coherence time of more than 1 s. We demonstrate single-qubit gates with error per gate of 3.8(1) × 10 −5 . By creating a Bell state with a deterministic two-qubit gate, we deduce a gate error of 8(4) × 10 −4 . We characterize the errors in our implementation and discuss methods to further reduce imperfections towards values that are compatible with fault-tolerant processing at realistic overhead.Quantum computers can solve certain problems that are thought to be intractable on conventional computers. An important general goal is to realize universal quantum information processing (QIP), which could be used for algorithms having a quantum advantage over processing with conventional bits as well as to simulate other quantum systems of interest [1][2][3]. For large problems, it is generally agreed that individual logic gate errors must be reduced below a certain threshold, often taken to be around 10 −4 [4][5][6], to achieve fault tolerance without excessive overhead in the number of physical qubits required to implement a logical qubit. This level has been achieved in some experiments for all elementary operations including state preparation and readout, with the exception of two-qubit gates, emphasizing the importance of improving multi-qubit gate fidelities. [7,8]. As various ions differ in mass, electronic, and hyperfine structure, they each have technical advantages and disadvantages. For example, 9 Be + is the lightest ion currently considered for QIP, and as such, has several potential advantages. The relatively light mass yields deeper traps and higher motional frequencies for given applied potentials, and facilitates fast ion transport [9,10]. Light mass also yields stronger laser-induced effective spin-spin coupling (inversely proportional to the mass), which can yield less spontaneous emission error for a given laser intensity [11]. However, a disadvantage of 9 Be + ion qubits compared to some heavier ions such as 40 Ca + and 43 Ca + [12, 13] has been the difficulty of producing and controlling the ultraviolet (313 nm) light required to drive 9 Be + stimulated-Raman transitions. In the work reported here, we use an ion trap array designed for scalable QIP [14] and take advantage of recent technological developments with lasers and optical fibers that improve beam quality and pointing stability. We also implement active control of laser pulse intensities to re- duce errors. We demonstrate laser-induced single-qubit computational gate errors of 3.8(1) × 10 −5 and realize a deterministic two-qubit gate to ideally produce the Bell state |Φ + = 1 √ 2 (|↑↑ + |↓↓ ). By characterizing the effects of known error sources with numerical simulations and calibration measurements, we deduce an entangling gate infidelity or error of = 8(4) × 10 −4 , where = 1 -F, and F is the fidelity. Along with Ref.[13]; these appear to be the highest two-qubit gate fidelitie...

Entangled states are a key resource in fundamental quantum physics, quantum cryptography, and quantum computation [1]. To date, controlled unitary interactions applied to a quantum system, so-called "quantum gates", have been the most widely used method to deterministically create entanglement [2]. These processes require high-fidelity state preparation as well as minimizing the decoherence that inevitably arises from coupling between the system and the environment and imperfect control of the system parameters. Here, on the contrary, we combine unitary processes with engineered dissipation to deterministically produce and stabilize an approximate Bell state of two trapped-ion qubits independent of their initial state. While previous works along this line involved the application of sequences of multiple time-dependent gates [3] or generated entanglement of atomic ensembles dissipatively but relied on a measurement record for steady-state entanglement [4], we implement the process in a continuous time-independent fashion, analogous to optical pumping of atomic states. By continuously driving the system towards steady-state, the entanglement is stabilized even in the presence of experimental noise and decoherence. Our demonstration of an entangled steady state of two qubits represents a step towards dissipative state engineering, dissipative quantum computation, and dissipative phase transitions [5][6][7]. Following this approach, engineered coupling to the environment may be applied to a broad range of experimental systems to achieve desired quantum dynamics or steady states. Indeed, concurrently with this work, an entangled steady state of two superconducting qubits was demonstrated using dissipation [8].Trapped ions are one of the leading experimental platforms for quantum information processing. Here, advanced protocols using unitary quantum gates have been demonstrated, see for example Refs. [9, 10]. However, decoherence and dissipation from coupling to the environment remains a challenge. One approach to overcome this relies on active feedback [11][12][13][14][15][16][17]. Such feedback techniques may be extended to quantum error correction, which can stabilize entangled states or realize fault-tolerant quantum computations. This will, however, require high-fidelity quantum gates and large qubit overheads that are beyond the reach of current experiments [2]. Recently, a complementary approach has been proposed to create entangled states or perform quantum computing by engineering the continuous interaction of the system with its environment [5][6][7][18][19][20][21][22][23][24][25][26].In our experiment, we take a step towards harnessing dissipation for quantum information processing by producing an entangled state that is inherently stabilized against decoherence by the applied interactions in a setting fully compatible with quantum computation. With this technique, we realize maximally entangled steady states with a fidelity of F = 0.75(3) by simultaneously applying a combination of time-independent fiel...

We investigate the dynamics of single and multiple ions during transport between and separation into spatially distinct locations in a multizone linear Paul trap. A single 9Be+ ion in a ~2 MHz harmonic well was transported 370 μm in 8 μs, corresponding to 16 periods of oscillation, with a gain of 0.1 motional quanta. Similar results were achieved for the transport of two ions. We also separated chains of up to 9 ions from one potential well to two distinct potential wells. With two ions this was accomplished in 55 μs, with excitations of approximately two quanta for each ion. Fast transport and separation can significantly reduce the time overhead in certain architectures for scalable quantum information processing with trapped ions.

Precision control over hybrid physical systems at the quantum level is important for the realization of many quantum-based technologies. In the field of quantum information processing (QIP) and quantum networking, various proposals discuss the possibility of hybrid architectures where specific tasks are delegated to the most suitable subsystem. For example, in quantum networks, it may be advantageous to transfer information from a subsystem that has good memory properties to another subsystem that is more efficient at transporting information between nodes in the network. For trapped ions, a hybrid system formed of different species introduces extra degrees of freedom that can be exploited to expand and refine the control of the system. Ions of different elements have previously been used in QIP experiments for sympathetic cooling, creation of entanglement through dissipation, and quantum non-demolition measurement of one species with another. Here we demonstrate an entangling quantum gate between ions of different elements which can serve as an important building block of QIP, quantum networking, precision spectroscopy, metrology, and quantum simulation. A geometric phase gate between a (9)Be(+) ion and a (25)Mg(+) ion is realized through an effective spin-spin interaction generated by state-dependent forces induced with laser beams. Combined with single-qubit gates and same-species entangling gates, this mixed-element entangling gate provides a complete set of gates over such a hybrid system for universal QIP. Using a sequence of such gates, we demonstrate a CNOT (controlled-NOT) gate and a SWAP gate. We further demonstrate the robustness of these gates against thermal excitation and show improved detection in quantum logic spectroscopy. We also observe a strong violation of a CHSH (Clauser-Horne-Shimony-Holt)-type Bell inequality on entangled states composed of different ion species.