Abstract
Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without well-characterized gates. A recently proposed technique, known as randomized benchmarking tomography (RBT), sidesteps this self-consistency problem by designing experiments to be insensitive to preparation and measurement imperfections. We implement this proposal in a superconducting qubit system, using a number of experimental improvements including implementing each of the elements of the Clifford group in single ‘atomic’ pulses and custom control hardware to enable large overhead protocols. We show a robust reconstruction of several single-qubit quantum gates, including a unitary outside the Clifford group. We demonstrate that RBT yields physical gate reconstructions that are consistent with fidelities obtained by RB.
Highlights
All approaches to quantum tomography are forced to make trade-offs given the exponentially increasing resources necessary as the size of the system grows
An randomized benchmarking tomography (RBT) reconstruction requires at least 10 distinct decay experiments, where each observed decay rate pj is related to the trace overlap aj by Eq (4) [28]
We have empirically demonstrated the feasibility of RBT reconstructions of arbitrary single-qubit unitaries
Summary
All approaches to quantum tomography are forced to make trade-offs given the exponentially increasing resources necessary as the size of the system grows. Randomized benchmarking tomography (RBT) [7] is a recent proposal for near-complete process tomography that inherits the robustness of standard RB and its insensitivity to state preparation and measurement ignorance. Most notably, this technique allows for the estimation of the average fidelity of any applied gate relative to any unitary operation—in some cases, this estimation can even be done with a polynomial number of experiments. The additional run time leads to drift in parameters of the operation or in state-preparation and measurement errors This may break a fundamental assumption of most protocols that the parameters are fixed for all rounds of the experiment. A new method we use to achieve this re-introduces Z control to fixed-frequency qubits, creating single-pulse, or atomic, Clifford operations that minimize the average gate time by avoiding multi-pulse decompositions
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