Towards fault-tolerant quantum computing with trapped ions

Abstract

Today, ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics 1,2 . For the implementation of arbitrary operations, a quantum computer requires a universal set of quantum logic gates. As in classical models of computation, quantum error correction techniques 3,4 enable rectification of small imperfections in gate operations, thus enabling perfect computation in the presence of noise. For fault-tolerant computation 5 , it is believed that error thresholds ranging between 10 −4 and 10 −2 will be required-depending on the noise model and the computational overhead for realizing the quantum gates 6-8 -but so far all experimental implementations have fallen short of these requirements. Here, we report on a Mølmer-Sørensen-type gate operation 9,10 entangling ions with a fidelity of 99.3(1)%. The gate is carried out on a pair of qubits encoded in two trapped calcium ions using an amplitudemodulated laser beam interacting with both ions at the same time. A robust gate operation, mapping separable states onto maximally entangled states is achieved by adiabatically switching the laser-ion coupling on and off. We analyse the performance of a single gate and concatenations of up to 21 gate operations.For ion traps, all building blocks necessary for the construction of a universal quantum computer 1 have been demonstrated over the past decade. Currently, the most important challenges consist of scaling up the present systems to a higher number of qubits and raising the fidelity of gate operations up to the point where quantum error correction techniques can be successfully applied. Although single-qubit gates are easily carried out with high quality, the realization of high-fidelity entangling two-qubit gates 11-16 is much more demanding because the inter-ion distance is orders of magnitude bigger than the characteristic length scale of any state-dependent ion-ion interaction. Apart from quantum gates of the Cirac-Zoller type 2,12 , where a laser couples a single qubit with a vibrational mode of the ion string at a time, most other gate realizations entangling ions have relied on collective interactions of the qubits with the laser control fields 11,[13][14][15] . These gate operations entangle transiently the collective pseudospin of the qubits with the vibrational mode and produce either a conditional phase shift 17 or a collective spin flip 9,10,18 of the qubits. Whereas the highest fidelity F = 97% reported until now 13 has been achieved with a conditional phase gate acting on a pair of hyperfine qubits in 9 Be + , spin-flip gates have been limited so far to F ≈ 85% (refs 11,14). All of these experiments have used qubits encoded in hyperfine or Zeeman ground states and a Raman transition mediated by an electric-dipole transition for coupling the qubits. Whereas spontaneous scattering from the mediating short-lived levels degrades the gate fidelity owing to the limited amount of laser power available in current experi...

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

“…[8][9][10][11][12][13][14][15][16] However, quantum superposition and correlation are fragile in an open quantum system. Notorious decoherence, [17][18][19] which is caused by interactions with noisy environments, is a major hurdle in the realization of fault-tolerant coherent operation 20,21 and scalable quantum computation. To further expand the implementation of QIP in open quantum systems, full understanding and control of environmental interactions are required.…”

The “arch” of simulating quantum spin systems with trapped ions

“…Even though there appear to be no fundamental obstacles for scaling the ion trap approach from six or eight ions/qubits in state of the art experiments [8,9] at impressive operational fidelities of >99% [10], there is challenging technology to be developed.…”

Trapped Ions Make Impeccable Qubits

“…They also increase the complexity of the required quantum hardware, since they require additional qubits. Recent calculations [2] suggest that an error probability of less than 1% would enable fault-tolerant codes, and that lower error probabilities dramatically decrease the number of qubits required for such codes.The quality of qubit manipulation in a number of physical systems has dramatically improved in the past few years [3,4], raising hopes that a quantum computer, at a large enough scale to carry out meaningful computations, might be within reach. Now, Thomas Harty at the University of Oxford, UK, and colleagues [5] are reporting an important contribution to this goal with the demonstration that qubits consisting of trapped 43 Ca + ions can be manipulated with record high fidelities (in quantum information theory, fidelity is a measure of the "closeness" of two quantum states).…”

“…In the last decade, researchers have demonstrated trapped-ion qubits with long coherence times [6], highfidelity state preparation and readout [7], and singleand two-qubit logic gate operations with low error rates [3,8]. Yet each of these properties was demonstrated individually in different systems.…”