Constructing Smaller Pauli Twirling Sets for Arbitrary Error Channels

Twirling is a technique widely used for converting arbitrary noise channels into Pauli channels in error threshold estimations of quantum error correction codes. It is vitally useful both in real experiments and in classical quantum simulations. Minimising the size of the twirling gate set increases the efficiency of simulations and in experiments it might reduce both the number of runs required and the circuit depth (and hence the error burden). Conventional twirling uses the full set of Pauli gates as the set of twirling gates. This article provides a theoretical background for Pauli twirling and a way to construct a twirling gate set with a number of members comparable to the size of the Pauli basis of the given error channel, which is usually much smaller than the full set of Pauli gates. We also show that twirling is equivalent to stabiliser measurements with discarded measurement results, which enables us to further reduce the size of the twirling gate set.Comment: Fixed typos, added another example and improve presentation

A Practical Framework for Quantum Error Mitigation

Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent framework that can highlight their underlying connections while providing guidance for their practical performance. In this article, we construct a general framework named linear quantum error mitigation that includes most of the state-of-the-art quantum error mitigation schemes. Within the framework, quantum error mitigation can be effectively viewed as extracting the error-mitigated state out of the noisy state. The fraction of error-mitigated state that is successfully extracted, called extraction rate, will indicate the cost-effectiveness of the given mitigation scheme. Using the framework, we can derive and compare the fidelity boost, sampling overhead and extraction rate across various mitigation schemes under practical assumptions. The structure, insights and intuitions provided by the framework can serve as a basis for further developments of new schemes

Psychophysical Responses Comparison in Spatial Visual, Audiovisual, and Auditory BCI-Spelling Paradigms

The paper presents a pilot study conducted with spatial visual, audiovisual and auditory brain-computer-interface (BCI) based speller paradigms. The psychophysical experiments are conducted with healthy subjects in order to evaluate a difficulty and a possible response accuracy variability. We also present preliminary EEG results in offline BCI mode. The obtained results validate a thesis, that spatial auditory only paradigm performs as good as the traditional visual and audiovisual speller BCI tasks.Comment: The 6th International Conference on Soft Computing and Intelligent Systems and The 13th International Symposium on Advanced Intelligent Systems, 201

Mitigating Coherent Noise Using Pauli Conjugation

Coherent noise can be much more damaging than incoherent (probabilistic) noise in the context of quantum error correction. One solution is to use twirling to turn coherent noise into incoherent Pauli channels. In this Article, we show that some of the coherence of the noise channel can actually be used to improve its logical fidelity by simply sandwiching the noise with a chosen pair of Pauli gates, which we call Pauli conjugation. Using the optimal Pauli conjugation, we can achieve a higher logical fidelity than using twirling and doing nothing. We devise a way to search for the optimal Pauli conjugation scheme and apply it to Steane code, 9-qubit Shor code and distance-3 surface code under global coherent $Z$ noise. The optimal conjugation schemes show improvement in logical fidelity over twirling while the weights of the conjugation gates we need to apply are lower than the average weight of the twirling gates. In our example noise and codes, the concatenated threshold obtained using conjugation is consistently higher than the twirling threshold and can be up to 1.5 times higher than the original threshold where no mitigation is applied. Our simulations show that Pauli conjugation can be robust against gate errors. With the help of logical twirling, the undesirable coherence in the noise channel can be removed and the advantages of conjugation over twirling can persist as we go to multiple rounds of quantum error correction.Comment: Added explanations about the mechanism of conjugation

A Silicon Surface Code Architecture Resilient Against Leakage Errors

Spin qubits in silicon quantum dots are one of the most promising building blocks for large scale quantum computers thanks to their high qubit density and compatibility with the existing semiconductor technologies. High fidelity single-qubit gates exceeding the threshold of error correction codes like the surface code have been demonstrated, while two-qubit gates have reached 98\% fidelity and are improving rapidly. However, there are other types of error --- such as charge leakage and propagation --- that may occur in quantum dot arrays and which cannot be corrected by quantum error correction codes, making them potentially damaging even when their probability is small. We propose a surface code architecture for silicon quantum dot spin qubits that is robust against leakage errors by incorporating multi-electron mediator dots. Charge leakage in the qubit dots is transferred to the mediator dots via charge relaxation processes and then removed using charge reservoirs attached to the mediators. A stabiliser-check cycle, optimised for our hardware, then removes the correlations between the residual physical errors. Through simulations we obtain the surface code threshold for the charge leakage errors and show that in our architecture the damage due to charge leakage errors is reduced to a similar level to that of the usual depolarising gate noise. Spin leakage errors in our architecture are constrained to only ancilla qubits and can be removed during quantum error correction via reinitialisations of ancillae, which ensure the robustness of our architecture against spin leakage as well. Our use of an elongated mediator dots creates spaces throughout the quantum dot array for charge reservoirs, measuring devices and control gates, providing the scalability in the design