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Diamond quantum processors consisting of a nitrogen-vacancy centre and surrounding nuclear spins have been the key to significant advancements in room-temperature quantum computing, quantum sensing and microscopy. The optimisation of these processors is crucial for the development of large-scale diamond quantum computers and the next generation of enhanced quantum sensors and microscopes. Here, we present a full model of multi-qubit diamond quantum processors and develop a semi-analytical method for designing gate pulses. This method optimises gate speed and fidelity in the presence of random control errors and is readily compatible with feedback optimisation routines. We theoretically demonstrate infidelities approaching ∼10−5 for single-qubit gates and established evidence that this can also be achieved for a two-qubit CZ gate. Consequently, our method reduces the effects of control errors below the errors introduced by hyperfine field misalignment and the unavoidable decoherence that is intrinsic to the processors. Having developed this optimal control, we simulated the performance of a diamond quantum processor by computing quantum Fourier transforms. We find that the simulated diamond quantum processor is able to achieve fast operations with low error probability. [ABSTRACT FROM AUTHOR]

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver. [ABSTRACT FROM AUTHOR]

Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40Ca+ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm. [ABSTRACT FROM AUTHOR]

We consider quantum learning machines-quantum computers that modify themselves in order to improve their performance in some way-that are trained to perform certain classical task, i.e. to execute a function that takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machines in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the kth root of NOT (NOT = logical negation), with k = 2m and mϵℕ. The reason for this speed-up is that the classical machine requires memory of size log k = m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k. [ABSTRACT FROM AUTHOR]