We experimentally demonstrate over 2 orders of magnitude increase in the room-temperature coherence time of nitrogen-vacancy centers in diamond by implementing decoupling techniques. We show that equal pulse spacing decoupling performs just as well as nonperiodic Uhrig decoupling and also allows us to take advantage of revivals in the echo to explore the longest coherence times. At short times, we can extend the coherence of particular quantum states out from T2*=2.7  μs out to an effective T2>340  μs. For preserving arbitrary states we show the experimental importance of using pulse sequences that compensate the imperfections of individual pulses for all input states through judicious choice of the phase of the pulses. We use these compensated sequences to enhance the echo revivals and show a coherence time of over 1.6 ms in ultrapure natural abundance 13C diamond.

We describe a scalable experimental protocol for estimating the average error of individual quantum computational gates. This protocol consists of interleaving random Clifford gates between the gate of interest and provides an estimate as well as theoretical bounds for the average error of the gate under test, so long as the average noise variation over all Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find a bounded average error of 0.003 [0,0.016] for the single-qubit gates X(π/2) and Y(π/2). These bounded values provide better estimates of the average error than those extracted via quantum process tomography.

Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states and measurement operators used to interrogate the system are generated by gates that have some systematic error, a situation all but unavoidable in any practical setting. These errors in tomography can not be fully corrected through oversampling or by performing a larger set of experiments. We present an alternative method for tomography to reconstruct an entire library of gates in a self-consistent manner. The essential ingredient is to define a likelihood function that assumes nothing about the gates used for preparation and measurement. In order to make the resulting optimization tractable we linearize about the target, a reasonable approximation when benchmarking a quantum computer as opposed to probing a black-box function.

verse order, as in this case, is the real essence of the Heisenberg uncertainty principle. Besides its fundamental importance, the experimental implementation of such a sequence of basic quantum operations is an essential tool for the full-scale engineering of a quantum light state optimized for a multitude of different tasks (15), including robust quantum communication. As any quantum operation, including non-Gaussian operations, is composed of photon additions and subtractions (i.e, it can be expressed as f ð% a; % a † Þ), our experimental results constitute a step toward the full quantum control of a field and the generation of highly entangled states (16).