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Probing qubit memory errors at the 10^−5 level

J. E. Tarlton

Published Feb 1, 2018• 3 citations
Publisher

Abstract

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.

DOI
10.25560/60650

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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.
Robust qubit memory is essential for quantum computing, both for near-term devices operating without error correction, and for the long-term goal of a fault-tolerant processor. We directly measure the memory error ${\ensuremath{\epsilon}}_{m}$ for a 43Ca+^{43}{\mathrm{Ca}}^{+}43Ca+ trapped-ion qubit in the small-error regime and find ${\ensuremath{\epsilon}}_{m}<{10}^{\ensuremath{-}4}$ for storage times $t\ensuremath{\lesssim}50\text{ }\text{ }\mathrm{ms}$. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at t=1  mst=1\text{ }\text{ }\mathrm{ms}t=1  ms we measure ${\ensuremath{\epsilon}}_{m}=1.2(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, around ten times smaller than that extrapolated from the T2∗{T}_{2}^{*}T2∗​ time, and limited by instability of the atomic clock reference used to benchmark the qubit.
Trapped ions, together with superconducting qubits, are one of the two leading hardware platforms for scalable quantum information processing. The development of quantum computers represents a major technological breakthrough comparable to the introduction of classical computing. The benefits of this technology are currently limited by the technical capability to perform high fidelity entangling operations on the qubits. When gate fidelities surpass the fault-tolerance threshold it becomes possible, through error correction, to increase the system size to an arbitrary number of qubits. In this cumulative thesis we address some of the issues in the scalability of the trapped-ion quantum computer based on microwave near-fields. In this approach, gate operations on one or multiple ions are driven by an oscillating magnetic field generated by a current flowing through a conductor. In the first part of this work we discuss the design of traps toward the implementation of large scale systems. We introduce the basic design of a surface-electrode ion trap with embedded microwave conductors. The oscillating magnetic field required to perform the operations is generated by a single optimized conductor. We discuss the simulation and characterization of the magnetic field pattern, which is fixed by the microwave conductor design. In addition, we demonstrate the capability to simulate, fabricate and characterize a multilayer surface ion trap. Multilayer traps are a key aspect for scalability since they are necessary to achieve large system sizes, with many `ion registers', where the registers are interconnected by physically transporting ions between them. In the second part of this thesis we demonstrate the implementation of a two-qubit entangling gate and we explore the possibilities offered by quantum control methods to improve its fidelity. We perform an entangling gate on two 9Be+ ions and measure a Bell state fidelity of 98.2(1.2)%. Error characterization shows that the gate result is limited by technical issues connected to the ions' motional states. To reduce these errors we apply amplitude modulation of the gate microwave drive. After stabilization of the ions' radial modes, we obtain an amplitude modulated gate with infidelity in the 10^-3 range. The result is confirmed by analyzing the data using three different methods. Using additional dynamic decoupling techniques, these results could bring microwave near-field gates past the fault-tolerance threshold.
This thesis reports high-fidelity near-field spatial microwave addressing of long-lived 43Ca+ "atomic clock" qubits performed in a two-zone single-layer surface-electrode ion trap. Addressing is implemented by using two of the trap's integrated microwave electrodes, one in each zone, to drive single-qubit rotations in the zone we choose to address whilst interferometrically cancelling the microwave field at the neighbour (non-addressed) zone. Using this field-nulling scheme, we measure a Rabi frequency ratio between addressed and non-addressed zones of up to 1400, from which we calculate an addressing error (or a spin-flip probability on the qubit transition) of 1e-6. Off-resonant excitation out of the qubit state is a more significant source of error in this experiment, but we also demonstrate polarisation control of the microwave field at an error level of 2e-5, which, if combined with individual-ion addressing, would be sufficient to suppress off-resonant excitation errors to the 1e-9 level. Further, this thesis presents preliminary results obtained with a micron-scale coupled-microstrip differential antenna probe that can be scanned over an ion-trap chip to map microwave magnetic near fields. The probe is designed to enable the measurement of fields at tens of microns above electrode surfaces and to act as an effective characterisation tool, speeding up design-fabrication-characterisation cycles in the production of new prototype microwave ion-trap chips. Finally, a new multi-layer design for an ion-trap chip which displays, in simulations, a 100-fold improvement in addressing performance, is presented. The chip electrode structure is designed to use the cancelling effect of microwave return currents to produce Rabi frequency ratios of order 1000 between trap zones using a single microwave electrode (i.e. without the need for nulling fields). If realised, this chip could be used to drive individually addressed single-qubit operations on arrays of memory qubits in parallel and with high fidelity.
We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of ^{43}Ca^{+}. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of T_{2}^{*}=50 sec, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.
Quantum systems promise to revolutionize information processing science and technology [1-3]. The preservation of quantum coherence, the defining property of qubits, fundamentally constrains the performance of quantum information processing with quantum memories [4]. While trapped atomic ions theoretically support million-year coherence based on spontaneous emission [5-7], experimental demonstrations have reached far less, only about an hour [8-13]. Here we combine clock-state qubits with decoherence-free subspace (DFS) encoding to achieve coherence exceeding ten hours. Using correlation-based phase tracking in 171Yb+ ion pairs sympathetically cooled by 138Ba+ ion, we demonstrate this without magnetic shielding or enhanced microwave phase stabilization that previously limited coherence times. DFS encoding references the qubit phase to the inter-ion energy difference to reject microwave phase noise and common-mode magnetic fluctuations, while clock states provide environmental insensitivity. Throughout measurements extended to 1600 seconds, we observe minimal coherence decay, with exponential fits yielding a coherence time of (3.77 +/- 1.09) x 10^4 seconds. Our results establish DFS encoding as a form of passive error correction that eliminates technical noise constraints, unlocking the million-year coherence potential of atomic ions for scalable quantum information processing.
With a 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ trapped-ion hyperfine-state qubit, we demonstrate an error probability per randomized single-qubit gate of $2.0(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, below the threshold estimate of ${10}^{\ensuremath{-}4}$ commonly considered sufficient for fault-tolerant quantum computing. The 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ion is trapped above a microfabricated surface-electrode ion trap and is manipulated with microwaves applied to a trap electrode. The achievement of low single-qubit-gate errors is an essential step toward the construction of a scalable quantum computer.