Trapped-ion Qubits Research Articles

Optimal quantum control of multimode couplings between trapped ion qubits for scalable entanglement.

We demonstrate entangling quantum gates within a chain of five trapped ion qubits by optimally shaping optical fields that couple to multiple collective modes of motion. We individually address qubits with segmented optical pulses to construct multipartite entangled states in a programmable way. This approach enables high-fidelity gates that can be scaled to larger qubit registers for quantum computation and simulation.

Speeding up conditional quantum logic of trapped ion qubits with overlapping pulses

We introduce two types of two-qubit controlled-phase gates, which operate with trapped ions in a linear Paul trap. Each ion is addressed individually with two sequential bichromatic laser pulses, the two frequency components of which are tuned on exact resonance with the first blue and red vibrational sidebands of the qubit transition frequency. For suitably chosen pulse areas and relative laser phases the dependence on the phonon number vanishes and the net effect is a controlled-phase gate between the electronic qubit states. In contrast to earlier gates, in which the pulses addressing the two ions are separated in time, we use partly overlapping pulses, which make the present gates faster, e.g., by about 26% for rectangular and over 50% for sinusoidal pulses.

Autonomously stabilized entanglement between two superconducting quantum bits

Quantum error correction codes are designed to protect an arbitrary state of a multi-qubit register from decoherence-induced errors, but their implementation is an outstanding challenge in the development of large-scale quantum computers. The first step is to stabilize a non-equilibrium state of a simple quantum system, such as a quantum bit (qubit) or a cavity mode, in the presence of decoherence. This has recently been accomplished using measurement-based feedback schemes. The next step is to prepare and stabilize a state of a composite system. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have been used for qubit reset, single-qubit state stabilization, and the creation and stabilization of states of multipartite quantum systems. Unlike conventional, measurement-based schemes, the autonomous approach uses engineered dissipation to counteract decoherence, obviating the need for a complicated external feedback loop to correct errors. Instead, the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building block for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, as demonstrated by the accompanying paper on trapped ion qubits, will be an essential tool for the implementation of quantum error correction.

Dissipative production of a maximally entangled steady state of two quantum bits

Entangled states are a key resource in fundamental quantum physics, quantum cryptography and quantum computation. Introduction of controlled unitary processes--quantum gates--to a quantum system has so far been the most widely used method to create entanglement deterministically. These processes require high-fidelity state preparation and minimization of the decoherence that inevitably arises from coupling between the system and the environment, and imperfect control of the system parameters. Here we combine unitary processes with engineered dissipation to deterministically produce and stabilize an approximate Bell state of two trapped-ion quantum bits (qubits), independent of their initial states. Compared with previous studies that involved dissipative entanglement of atomic ensembles or the application of sequences of multiple time-dependent gates to trapped ions, we implement our combined process using trapped-ion qubits in a continuous time-independent fashion (analogous to optical pumping of atomic states). By continuously driving the system towards the steady state, 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. 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.

Individual-Ion Addressing with Microwave Field Gradients

Individual-qubit addressing is a prerequisite for many instances of quantum information processing. We demonstrate this capability on trapped-ion qubits with microwave near fields delivered by electrode structures integrated into a microfabricated surface-electrode trap. We describe four approaches that may be used in quantum information experiments with hyperfine levels as qubits. We implement individual control on two 25Mg+ ions separated by 4.3 μm and find spin-flip crosstalk errors on the order of 10(-3).

Transparent ion trap with integrated photodetector

Fluorescence collection sets the efficiency of state detection and the rate of entanglement generation between remote trapped ion qubits. Despite efforts to improve light collection using various optical elements, solid angle capture is limited to ≈10% for implementations that are scalable to many ions. We present an approach based on fluorescence detection through a transparent trap using an integrated photodetector, combining collection efficiency approaching 50% with scalability. We microfabricate transparent surface traps with indium tin oxide and verify stable trapping of single ions. The fluorescence from a cloud of ions is detected using a photodiode sandwiched with a transparent trap.

Creation of arbitrary Dicke and NOON states of trapped-ion qubits by global addressing with composite pulses

We propose a fast and efficient technique to create classes of highly entangled states of trapped ions, such as arbitrary Dicke states and superpositions of them, e.g. NOON states. The ions are initialized in the phonon ground state and are addressed globally with a composite pulse that is resonant with the first motional sideband. The technique is fairly robust to parameter fluctuations and operates on comparatively short time scales, as resonant interactions allow one to use the minimum laser pulse area. The number of single pulses from the composite sequence is equal to the number of ions; thus the implementation complexity grows only linearly with the size of the system. The approach does not require individual addressing of the ions in the trap and can be applied both inside and outside the Lamb–Dicke regime.

A microfabricated ion trap with integrated microwave circuitry

We describe the design, fabrication, and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators, and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to give a large microwave field gradient to allow state-dependent manipulation of the ions' motional degrees of freedom, the key to multi-qubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled 43Ca+ ion.

Scalable architecture for a room temperature solid-state quantum information processor

The realization of a scalable quantum information processor has emerged over the past decade as one of the central challenges at the interface of fundamental science and engineering. Here we propose and analyse an architecture for a scalable, solid-state quantum information processor capable of operating at room temperature. Our approach is based on recent experimental advances involving nitrogen-vacancy colour centres in diamond. In particular, we demonstrate that the multiple challenges associated with operation at ambient temperature, individual addressing at the nanoscale, strong qubit coupling, robustness against disorder and low decoherence rates can be simultaneously achieved under realistic, experimentally relevant conditions. The architecture uses a novel approach to quantum information transfer and includes a hierarchy of control at successive length scales. Moreover, it alleviates the stringent constraints currently limiting the realization of scalable quantum processors and will provide fundamental insights into the physics of non-equilibrium many-body quantum systems.

Near-ground-state transport of trapped-ion qubits through a multidimensional array

We have demonstrated transport of Be+ ions through a 2D Paul-trap array that incorporates an X-junction, while maintaining the ions near the motional ground-state of the confining potential well. We expand on the first report of the experiment [1], including a detailed discussion of how the transport potentials were calculated. Two main mechanisms that caused motional excitation during transport are explained, along with the methods used to mitigate such excitation. We reduced the motional excitation below the results in Ref. [1] by a factor of approximately 50. The effect of a mu-metal shield on qubit coherence is also reported. Finally, we examined a method for exchanging energy between multiple motional modes on the few-quanta level, which could be useful for cooling motional modes without directly accessing the modes with lasers. These results establish how trapped ions can be transported in a large-scale quantum processor with high fidelity.

Scalable uniform construction of highly conditional quantum gates

We present a scalable uniform technique for construction of highly conditional C$^n$-NOT quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.

Combing a qubit

A trick for modulating optical frequency combs will enable more flexible control over trapped-ion qubits.

On the transport of atomic ions in linear and multidimensional ion trap arrays

Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.

On the transport of atomic ions in linear and multidimensional ion trap arrays

Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.

Towards a scalable quantum computer/simulator based on trapped ions

We describe the concept and experimental demonstration of the basic building blocks of a scalable quantum computer using trapped-ion qubits. The trap structure is divided into subregions where ion qubits can either be held as memory or subjected to individual rotations and multi-qubit gates in processor zones. Thus, ion qubits can become entangled in one trapping zone, then separated and distributed to separate zones (by switching control-electrode potentials) where subsequent single- and two-ion gates, and/or detection is performed. Recent work using these building blocks includes (1) demonstration of a dense-coding protocol, (2) demonstration of enhanced qubit-detection efficiency using quantum logic, (3) generation of GHZ states and their application to enhanced precision in spectroscopy, and (4) the realization of teleportation with atomic qubits. In the final section an analog quantum computer that could provide a shortcut towards quantum simulations under requirements less demanding than those for a universal quantum computer is also described.

Observation of entanglement between a single trapped atom and a single photon.

An outstanding goal in quantum information science is the faithful mapping of quantum information between a stable quantum memory and a reliable quantum communication channel. This would allow, for example, quantum communication over remote distances, quantum teleportation of matter and distributed quantum computing over a 'quantum internet'. Because quantum states cannot in general be copied, quantum information can only be distributed in these and other applications by entangling the quantum memory with the communication channel. Here we report quantum entanglement between an ideal quantum memory--represented by a single trapped 111Cd+ ion--and an ideal quantum communication channel, provided by a single photon that is emitted spontaneously from the ion. Appropriate coincidence measurements between the quantum states of the photon polarization and the trapped ion memory are used to verify their entanglement directly. Our direct observation of entanglement between stationary and 'flying' qubits is accomplished without using cavity quantum electrodynamic techniques or prepared non-classical light sources. We envision that this source of entanglement may be used for a variety of quantum communication protocols and for seeding large-scale entangled states of trapped ion qubits for scalable quantum computing.

Atomic qubit manipulations with an electro-optic modulator.

We report new techniques for driving high-fidelity stimulated Raman transitions in trapped-ion qubits. An electro-optic modulator induces sidebands on an optical source, and interference between the sidebands allows coherent Rabi transitions to be efficiently driven between hyperfine ground states separated by 14.53 GHz in a single trapped 111Cd+ ion.