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The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made difficult by the intractability of the time-dependent Schrodinger equation, especially in multiqubit systems. Here, we show that this issue can be sidestepped by using a formalism in which the cumulative error during a gate is represented geometrically as a curve in a multi-dimensional Euclidean space. Cancellation of noise errors to leading order corresponds to closure of the curve, a condition that can be satisfied without solving the Schrodinger equation. We develop and uncover general properties of this geometric formalism, and derive a recursion relation that maps control fields to curvatures for Hamiltonians of arbitrary dimension. We demonstrate examples by using the geometric method to design dynamically corrected gates for a class of two-qubit Hamiltonians that is relevant for both superconducting transmon qubits and semiconductor spin qubits. We propose this geometric formalism as a general technique for pulse-induced error suppression in quantum computing gate operations.
Quantum information technologies demand highly accurate control over quantum systems. Achieving this requires control techniques that perform well despite the presence of decohering noise and other adverse effects. Here, we review a general technique
Precise control of an open quantum system is critical to quantum information processing, but is challenging due to inevitable interactions between the quantum system and the environment. We demonstrated experimentally at room temperature a type of dy
Previous schemes of nonadiabatic holonomic quantum computation were focused mainly on realizing a universal set of elementary gates. Multiqubit controlled gates could be built by decomposing them into a series of the universal gates. In this article,
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are needed to pro
To solve classically hard problems, quantum computers need to be resilient to the influence of noise and decoherence. In such a fault-tolerant quantum computer, noise-induced errors must be detected and corrected in real-time to prevent them from pro