T. P. Harty

High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits

We demonstrate laser-driven two-qubit and single-qubit logic gates with respective fidelities 99.9(1)% and 99.9934(3)%, significantly above the ≈99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed-fidelity trade-off for the two-qubit gate, for gate times between 3.8  μs and 520  μs, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.The generation of entanglement is a fundamental resource for quantum technology, and trapped ions are one of the most promising systems for storage and manipulation of quantum information. Here we study the speed/fidelity trade-off for a two-qubit phase gate implemented in Ca hyperfine trapped-ion qubits. We characterize various error sources contributing to the measured fidelity, allowing us to account for errors due to single-qubit state preparation, rotation and measurement (each at the ∼ 0.1% level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between 97.1(2)% (for a gate time tg = 3.8μs) and 99.9(1)% (for tg = 100μs), representing respectively the fastest and lowest-error two-qubit gates reported between trapped-ion qubits by nearly an order of magnitude in each case. We perform a two-qubit geometric phase gate in the σz basis [1], where the qubits are stored in the S 4,+4 1/2 and S 1/2 states of the ground hyperfine manifold of Ca. The two-qubit gate operation is implemented by a pair of Raman laser beams at a detuning ∆ from the 4S1/2 ↔ 4P1/2 transition. To vary tg we adjust ∆ while holding the Raman beam intensity constant (at 5 mW per beam in a spot size of w = 27μm); smaller ∆ enables a faster gate, at the cost of increased error due to photon scattering [2]. The Raman difference frequency is δ = νz + δg where δg = 2/tg and the axial trap frequency is νz = 1.95 MHz. The Raman beams propagate at 45◦ to the trap z-axis, such that their wave-vector difference is along z. We cool both axial modes of the ions close to the ground state of motion by Raman sideband cooling; the centre-of-mass mode, rather than the stretch mode, is used to implement the gate to avoid coupling to the (uncooled) radial modes of the trap [3].

Hybrid quantum logic and a test of Bell’s inequality using two different atomic isotopes

Entanglement is one of the most fundamental properties of quantum mechanics, and is the key resource for quantum information processing (QIP). Bipartite entangled states of identical particles have been generated and studied in several experiments, and post-selected or heralded entangled states involving pairs of photons, single photons and single atoms, or different nuclei in the solid state, have also been produced. Here we use a deterministic quantum logic gate to generate a ‘hybrid’ entangled state of two trapped-ion qubits held in different isotopes of calcium, perform full tomography of the state produced, and make a test of Bell’s inequality with non-identical atoms. We use a laser-driven two-qubit gate, whose mechanism is insensitive to the qubits’ energy splittings, to produce a maximally entangled state of one 40Ca+ qubit and one 43Ca+ qubit, held 3.5 micrometres apart in the same ion trap, with 99.8 ± 0.6 per cent fidelity. We test the CHSH (Clauser–Horne–Shimony–Holt) version of Bell’s inequality for this novel entangled state and find that it is violated by 15 standard deviations; in this test, we close the detection loophole but not the locality loophole. Mixed-species quantum logic is a powerful technique for the construction of a quantum computer based on trapped ions, as it allows protection of memory qubits while other qubits undergo logic operations or are used as photonic interfaces to other processing units. The entangling gate mechanism used here can also be applied to qubits stored in different atomic elements; this would allow both memory and logic gate errors caused by photon scattering to be reduced below the levels required for fault-tolerant quantum error correction, which is an essential prerequisite for general-purpose quantum computing.

Microwave control electrodes for scalable, parallel, single-qubit operations in a surface-electrode ion trap

We propose a surface ion trap design incorporating microwave control electrodes for near-field single-qubit control. The electrodes are arranged so as to provide arbitrary frequency, amplitude and polarization control of the microwave field in one trap zone, whilst a similar set of electrodes is used to null the residual microwave field in a neighbouring zone. The geometry is chosen to reduce the residual field to the 0.5 % level without nulling fields; with nulling, the crosstalk may be kept close to the 0.01 % level for realistic microwave amplitude and phase drift. Using standard photolithography and electroplating techniques, we have fabricated a proof-of-principle electrode array with two trapping zones. We discuss requirements for the microwave drive system and prospects for scalability to a large 2-D trap array.