Roee Ozeri

Deterministic quantum teleportation of atomic qubits

Quantum teleportation provides a means to transport quantum information efficiently from one location to another, without the physical transfer of the associated quantum-information carrier. This is achieved by using the non-local correlations of previously distributed, entangled quantum bits (qubits). Teleportation is expected to play an integral role in quantum communication and quantum computation. Previous experimental demonstrations have been implemented with optical systems that used both discrete and continuous variables, and with liquid-state nuclear magnetic resonance. Here we report unconditional teleportation of massive particle qubits using atomic (9Be+) ions confined in a segmented ion trap, which aids individual qubit addressing. We achieve an average fidelity of 78 per cent, which exceeds the fidelity of any protocol that does not use entanglement. This demonstration is also important because it incorporates most of the techniques necessary for scalable quantum information processing in an ion-trap system.

Creation of a six-atom 'Schrödinger cat' state.

Among the classes of highly entangled states of multiple quantum systems, the so-called ‘Schrödinger cat’ states are particularly useful. Cat states are equal superpositions of two maximally different quantum states. They are a fundamental resource in fault-tolerant quantum computing and quantum communication, where they can enable protocols such as open-destination teleportation and secret sharing. They play a role in fundamental tests of quantum mechanics and enable improved signal-to-noise ratios in interferometry. Cat states are very sensitive to decoherence, and as a result their preparation is challenging and can serve as a demonstration of good quantum control. Here we report the creation of cat states of up to six atomic qubits. Each qubits state space is defined by two hyperfine ground states of a beryllium ion; the cat state corresponds to an entangled equal superposition of all the atoms in one hyperfine state and all atoms in the other hyperfine state. In our experiments, the cat states are prepared in a three-step process, irrespective of the number of entangled atoms. Together with entangled states of a different class created in Innsbruck, this work represents the current state-of-the-art for large entangled states in any qubit system.

Microfabricated surface-electrode ion trap for scalable quantum information processing.

Individual laser-cooled 24Mg+ ions are confined in a linear Paul trap with a novel geometry where gold electrodes are located in a single plane and the ions are trapped 40 microm above this plane. The relatively simple trap design and fabrication procedure are important for large-scale quantum information processing (QIP) using ions. Measured ion motional frequencies are compared to simulations. Measurements of ion recooling after cooling is temporarily suspended yield a heating rate of approximately 5 motional quanta per millisecond for a trap frequency of 2.83 MHz, sufficiently low to be useful for QIP.

Realization of quantum error correction

Scalable quantum computation and communication require error control to protect quantum information against unavoidable noise. Quantum error correction protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes. Error-correction protocols have been implemented in nuclear magnetic resonance experiments, but the inherent limitations of this technique prevent its application to quantum information processing. Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits). Errors are induced simultaneously in all qubits at various rates. The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state. In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.

Long-lived qubit memory using atomic ions

We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a magnetic field B approximately = 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 s, an improvement of approximately 5 orders of magnitude from previous experiments with 9Be+. We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.

Randomized benchmarking of quantum gates

A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized

Experimental purification of two-atom entanglement

\ensuremath{\pi}/2

Entangled mechanical oscillators

pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.

Errors in trapped-ion quantum gates due to spontaneous photon scattering

Entanglement is a necessary resource for quantum applications—entanglement established between quantum systems at different locations enables private communication and quantum teleportation, and facilitates quantum information processing. Distributed entanglement is established by preparing an entangled pair of quantum particles in one location, and transporting one member of the pair to another location. However, decoherence during transport reduces the quality (fidelity) of the entanglement. A protocol to achieve entanglement ‘purification’ has been proposed to improve the fidelity after transport. This protocol uses separate quantum operations at each location and classical communication to distil high-fidelity entangled pairs from lower-fidelity pairs. Proof-of-principle experiments distilling entangled photon pairs have been carried out. However, these experiments obtained distilled pairs with a low probability of success and required destruction of the entangled pairs, rendering them unavailable for further processing. Here we report efficient and non-destructive entanglement purification with atomic quantum bits. Two noisy entangled pairs were created and distilled into one higher-fidelity pair available for further use. Success probabilities were above 35 per cent. The many applications of entanglement purification make it one of the most important techniques in quantum information processing.

Simplified motional heating rate measurements of trapped ions

Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations as envisaged in the ‘Schrödinger’s cat’ thought experiment (where the cat exists in a superposition of alive and dead states entangled with a radioactive nucleus). Such situations are not observed in nature. This may be simply due to our inability to sufficiently isolate the system of interest from the surrounding environment—a technical limitation. Another possibility is some as-yet-undiscovered mechanism that prevents the formation of macroscopic entangled states. Such a limitation might depend on the number of elementary constituents in the system or on the types of degrees of freedom that are entangled. Tests of the latter possibility have been made with photons, atoms and condensed matter devices. One system ubiquitous to nature where entanglement has not been previously demonstrated consists of distinct mechanical oscillators. Here we demonstrate deterministic entanglement of separated mechanical oscillators, consisting of the vibrational states of two pairs of atomic ions held in different locations. We also demonstrate entanglement of the internal states of an atomic ion with a distant mechanical oscillator. These results show quantum entanglement in a degree of freedom that pervades the classical world. Such experiments may lead to the generation of entangled states of larger-scale mechanical oscillators, and offer possibilities for testing non-locality with mesoscopic systems. In addition, the control developed here is an important ingredient for scaling-up quantum information processing with trapped atomic ions.