Abstract
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.
Highlights
Dynamical gate correction is an important topic in the field of quantum information technology because logical error-correction schemes require that the individual gate error be below a given threshold value [1]
We extend the geometric formalism to systems of multiple qubits subject to quasistatic noise
We show how to generalize the geometric formalism for producing dynamically corrected single-qubit gates to multiqubit systems
Summary
Dynamical gate correction is an important topic in the field of quantum information technology because logical error-correction schemes require that the individual gate error be below a given threshold value [1]. Conditions were given for canceling error at higher orders; for second order, the total signed area enclosed by the curve must equal zero This formalism was used to derive the fastest possible pulses implementing specific single-qubit gates given constraints on the magnitude of the driving field [30]. Pulses were represented as curves in three dimensions, with the strengths of the driving fields being related to the curvature and torsion of the curve This formalism effectively extends earlier techniques for reverse-engineering solutions to the Schrödinger equation to the realm of dynamically corrected gates [32,33]. [34] requires solving nonlocal and nonlinear constraints to obtain the desired waveforms, and it does not provide a way to cancel higher-order noise errors Despite these limitations, the method of Ref.
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