Abstract We experimentally study the real-time susceptibility of trapped-ion quantum systems to small doses of ionizing radiation. We expose an ion-trap apparatus to a variety of α , β , and γ sources and measure the resulting changes in trapped-ion qubit lifetimes, coherence times, gate fidelities, and motional heating rates. We found no quantifiable degradation of ion trap performance in the presence of low-dose radiation sources for any of the measurements performed. This finding is encouraging for the long-term prospects of using ion-based quantum information systems in extreme environments, indicating that much larger doses may be required to induce errors in trapped-ion quantum processors.
Abstract We experimentally study the real-time susceptibility of trapped-ion quantum systems to small doses of ionizing radiation. We expose an ion-trap apparatus to a variety of α , β , and γ sources and measure the resulting changes in trapped-ion qubit lifetimes, coherence times, gate fidelities, and motional heating rates. We found no quantifiable degradation of ion trap performance in the presence of low-dose radiation sources for any of the measurements performed. This finding is encouraging for the long-term prospects of using ion-based quantum information systems in extreme environments, indicating that much larger doses may be required to induce errors in trapped-ion quantum processors.
We demonstrate long-lived coherence in internal hyperfine states of a single \Ca{43} trapped-ion qubit $[T_2=1.2(2)\s]$, and in external motional states of a single \Ca{40} trapped-ion qubit $[T_2'=0.18(4)\s]$, in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state T2 time that we observe in \Ca{43}, which has not previously been used as a trapped-ion qubit, is about one thousand times longer than that of physical qubits based on \Ca{40} ions. Using a single spin-echo pulse to ``re-phase'' the internal state, we can detect no decoherence after 1\s, implying an effective coherence time $T_2^{\mbox{\tiny SE}} \gtish 45\s$. This compares with timescales in this trap for single-qubit operations of \ish 1\us, and for two-qubit operations of \ish 10\us.
Trapped atomic ions are a promising candidate system for developing a quantum computer. All elementary operations for quantum information processing have al- ready been achieved in trapped-ion systems with errors below the “fault-tolerant threshold”, meaning that these errors are sufficiently small to be removed with quan- tum error correction. However, the preservation of quantum information over the short timescales that are relevant for quantum computing has not, to our knowledge, been measured before in trapped-ion qubits. Previous investigations have measured decoherence over long times and extrapolated an exponential decay model to short times. We directly measure the qubit memory error rate over short timescales, which is made possible by the high-fidelity single-qubit gates and state preparation and mea- surement in our system. Our qubit is a hyperfine “atomic clock” transition in 43Ca+, and gates are applied with near-field microwaves. We find that the assumption of exponential decay of qubit state coherence does not apply in our system. The data is fit well by a model of 1/f frequency noise with a low-frequency cutoff. The small- est memory error that we measure is 3(1)×10−6 over 2ms. The time at which our qubit memory error is 1×10−3, an important threshold for viable quantum error correction, is ≈400ms. We also present a design study into a new ion trap electrode geometry for applying near-field microwave two-qubit gates. This design features an ‘S’-shaped meander electrode to passively null the microwave field at the ions’ locations. It has improved isolation between the meander and other electrodes compared to previous work on this, which should reduce the sensitivity of the microwave field distribution to the boundary conditions of these electrodes. We show that the trap would allow for ion chains to be trapped, transported and split with feasible DC and RF voltages.
While quantum information processing offers a tantalizing possibility of a significant speedup in execution of certain algorithms, as well as enabling previously unmanageable simulations of large quantum systems, it remains extremely difficult to realize experimentally. Recently, fundamental building blocks of a quantum computer, including one and two qubit gates, teleportation and error correction, were demonstrated using trapped atomic ions. Scaling to a larger number of qubits requires miniaturization of the ion traps, currently limited by the sharply increasing motional state decoherence at sub-100 μm ion-electrode distances. This thesis explores the source and suppression of this decoherence at cryogenic temperatures, and demonstrates fundamental logic gates in a surface electrode ion trap.
Construction of the apparatus requires the development of a number of experimental techniques. Design, numerical simulation and implementation of a surface electrode ion trap is presented. Cryogenic cooling of the trap to near 4 K is accomplished by contact with a bath cryostat. Ions are loaded by ablation or photoionization, both of which are characterized in terms of generated stray fields and heat load.
The bulk of new experimental results deals with measurements of electric field noise at the ion's position. Upon cooling to 6 K, the measured rates are suppressed by up to 7 orders of magnitude, more than two orders of magnitude below previously published data for similarly sized traps operated at room temperature. The observed noise depends strongly on fabrication process, which suggests further improvements are possible. The measured dependence of the electric field noise on temperature is inconsistent with published models, and can be explained using a continuous spectrum of activated fluctuators.
The fabricated surface electrode traps are used to demonstrate coherent operations and the classical control required for trapped ion quantum computation. The necessary spectral properties of coherent light sources are achieved with a novel design using optical feedback to a triangular, medium finesse, cavity, followed by electronic feedback to an ultra-high finesse reference cavity. Single and two qubit operations on a single ion are demonstrated with classical fidelity in excess of 95%. Magnetic field gradient coils built into the trap allow for individual addressing of ions, a prerequisite to scaling to multiple qubits. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
Abstract We experimentally study the heating of trapped atomic ions during measurement of their internal qubit states. During measurement, ions are projected into one of two basis states and discriminated by their state-dependent fluorescence. We observe that ions in the fluorescing state rapidly scatter photons and heat at a rate of n¯˙≳2×104 quanta s−1, which is orders of magnitude faster than typical anomalous ion heating rates. We introduce a quantum trajectory-based framework that accurately reproduces the experimental results and provides a unified description of ion heating for both continuous and discrete sources.
This thesis describes experimental work on implementing single and two qubit gates in ¹7¹Yb+ ions using methods suitable for a large scale quantum computer. By combining a magnetic field gradient with microwave and radiofrequency radiation, the spin and motional states of the ions are coupled which allows multi-qubit operations to be performed, as well as providing individual addressing of ions in frequency space. A dressed state qubit is used which exhibits an increase of over two orders of magnitude in the coherence time for a qubit that it is sensitive to the magnetic field gradient. Using this system, single qubit gates are characterised using the technique of randomised benchmarking, resulting in a measured average error per gate of 9(3)x10¯4. A new type of two qubit gate is experimentally demonstrated, which in comparison to a standard two qubit gate shows significantly increased resilience to two major sources of gate infidelity: heating of the motional mode of the ions during gate operations, and incorrectly set gate field frequencies. These types of errors are expected to become increasingly important with the move towards quantum processors with large numbers of qubits. Using this same technique, a two qubit gate is also demonstrated at a higher initial temperature with a significantly improved fidelity compared to standard methods. These gate techniques are used to demonstrate work towards implementing positiondependent quantum logic, a method which could remove the correlation between the number of ions and the number of gate fields required in a large scale quantum computing architecture. A method to move the dressed state qubit through a magnetic field gradient while preserving quantum information is demonstrated, as well as a method to optimise the phase of a two qubit gate of unknown phase in order to implement a CNOT logic gate. This provides a path forwards to demonstrating a CNOT gate using position-dependent quantum logic.
Physical qubits in experimental quantum information processors are inevitably exposed to different sources of noise and imperfections, which lead to errors that typically accumulate hindering our ability to perform long computations reliably. Progress towards scalable and robust quantum computation relies on exploiting quantum error correction (QEC) to actively battle these undesired effects. In this work, we present a comprehensive study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level. Finally, we study the impact of residual crosstalk errors on the performance of fault-tolerant QEC numerically, identifying the experimental target values that need to be achieved in near-term trapped-ion experiments to reach the break-even point for beneficial QEC with low-distance topological codes.