Entangling operations are among the most important primitive gates employed in quantum computing and it is crucial to ensure high-fidelity implementations as systems are scaled up. We experimentally realize and characterize a simple scheme to minimize errors in entangling operations related to the residual excitation of mediating bosonic oscillator modes that both improves gate-robustness and provides scaling benefits in larger systems. The technique employs discrete phase shifts in the control field driving the gate operation, determined either analytically or numerically, to ensure all modes are de-excited at arbitrary user-defined times. We demonstrate an average gate fidelity of 99.4(2)% across a wide range of parameters in a system of 171 Yb + trapped ion qubits, and observe a reduction of gate error in the presence of common experimental error sources. Our approach provides a unified framework to achieve robustness against both static and time-varying laser amplitude and frequency detuning errors. We verify these capabilities through systemidentification experiments revealing improvements in error-susceptibility achieved in phase-modulated gates.The ability to perform robust, high fidelity entangling gates in multi-qubit systems is a key requirement for realizing scalable quantum information processing 1 . In several hardware architectures, qubits are entangled through shared bosonic oscillator modes via an interaction that is moderated by an external driving field. The Mølmer-Sørensen (MS) gate in trapped ions 2-4 and the resonator-induced phase gate in superconducting circuits 5-7 are both of this type. In addition, interactions simultaneously employing multiple bosonic modes have been explored to improve gate fidelities 8 and probe novel types of interactions 9 in superconducting circuits.A major source of error for oscillator-mediated gates is residual qubit-oscillator entanglement at the end of the operation 10 . This detrimental effect can arise due to the presence of quasi-static or time-varying noise on the driving field, slow drifts in experimental parameters such as the qubit and oscillator frequencies, or the presence of spectator modes that are not properly accounted for in the gate construction. In trapped ion systems, various schemes have been demonstrated that minimize this residual coupling 11-15 , with some also incorporating the ability to simultaneously decouple from multiple modes 16-21 . Their common feature is a temporal modulation of the driving field, modifying the trajectories of the joint qubit-oscillator states in each oscillator's phase space.In this work, we experimentally demonstrate a new class of phase-modulated (ΦM) entangling gates using trapped ions in the presence of multi-mode motional spectra. Specifically, we implement an MS-type interaca) These three authors contributed equally to this work. b) Current address: Fachrichtung Physik, Universität des Saarlandes, tion and employ discrete phase shifts of the driving field to suppress dominant gate errors. Using both an ana...

Reaching high-speed, high-fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. We directly optimize the amplitude and phase of each sample point of the digitized control pulse. We thereby fully exploit the capabilities of the pulse generation electronics and create a 4.16 ns single-qubit pulse with 99.76 % fidelity and 0.044 % leakage. This is a sevenfold reduction of the leakage rate and a threefold reduction in standard errors of the best DRAG pulse we have calibrated at such short durations on the same system.

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Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171 Yb + ion-qubit and inject engineered noise /σ z ð Þto probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlatedσ z errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlatedσ x orσ y errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.

Quantum algorithms often benefit from the ability to execute multi-qubit (>2) gates. To date, such multi-qubit gates are typically decomposed into single- and two-qubit gates, particularly in superconducting qubit architectures. The ability to perform multi-qubit operations in a single step could vastly improve the fidelity and execution time of many algorithms. Here, we propose a single shot method for executing an i-Toffoli gate, a three-qubit gate with two control and one target qubit, using currently existing superconducting hardware. We show numerical evidence for a process fidelity over 99.5% and a gate time of 450 ns for superconducting qubits interacting via tunable couplers. Our method can straight forwardly be extended to implement gates with more than two control qubits at similar fidelities.

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