The control of qubit states is often impeded by systematic control errors. Compensating pulse sequences have emerged as a resource efficient method for quantum error reduction. In this review, we discuss compensating composite pulse methods, and introduce a unifying control-theoretic framework using a dynamic interaction picture. This admits a novel geometric picture where sequences are interpreted as vector paths on the dynamical Lie algebra. Sequences for single-qubit and multi-qubit operations are described with this method.

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The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantum computers based on the XY interaction, single-qubit composite pulse sequences naturally correct systematic errors. For quantum computers based on the Heisenberg or exchange interaction, the composite pulse sequences reduce the logical single-qubit gate errors but increase the errors for logical two-qubit gates.

We demonstrate universal quantum control over chains of ions in a surface-electrode ion trap, including all the fundamental operations necessary to perform algorithms in a one-dimensional, nearest-neighbor quantum computing architecture. We realize both single-qubit operations and nearest-neighbor entangling gates with Raman laser beams, and we interleave the two gate types. We report average single-qubit gate fidelities as high as 0.970(1) for two-, three-, and four-ion chains, characterized with randomized benchmarking. We generate Bell states between the nearest-neighbor pairs of a three-ion chain, with fidelity up to 0.84(2). We combine one-and two-qubit gates to perform quantum process tomography of a CNOTgate in a two-ion chain, and we report an overall fidelity of 0.76(3). System overviewThe experimental system is shown schematically in figure 1(a). We trap chains of 171 Yb + ions 60 μm above the surface-electrode ion trap described in [19]. This trap features through-chip vias instead of wirebonds. The