Abstract
Near term quantum computers suffer from the presence of different noise sources. In order to mitigate for this effect and acquire results with significantly better accuracy, there is the urge of designing efficient error correction or error mitigation schemes. The cost of such techniques is usually high in terms of resource requirements, either in hardware or at the algorithmic level. In this work, we follow a pragmatic approach and we use repetition codes as scalable schemes with the potential to provide more accurate solutions to problems of interest in quantum chemistry and physics. We investigate different repetition code layouts and we propose a circular repetition scheme with connectivity requirements that are native on IBM Quantum hardware. We showcase our approach in multiple IBM Quantum devices and validate our results using a simplified theoretical noise model. We highlight the effect of using the proposed scheme in an electronic structure variational quantum eigensolver calculation and in the simulation of time evolution for a quantum Ising model.
Highlights
Quantum computers are composed of fragile quantum systems that cannot be fully isolated from external noise, and whose manipulations imply a level of uncertainty
Circular Repetition Code To further improve the performances of repetition encodings, we propose a circular variant, directly inspired by the heavy hexagonal topology of IBM Quantum processors and explicitly designed to protect against bit flip errors induced by the implementation of Uencoding itself
State (b)18 17 16 15 no encoding 2+1 chain 4+1 chain 6+1 chain ibmq_manhattan 2+1 split 4+1 split 6+1 split 8+1 split we report the average readout errors obtained on the IBM Quantum superconducting processor ibmq boeblingen for using {2, 4} + 1-qubit chain and split repetition codes, as well as the 4 + 1 + 1-qubit circular encoding
Summary
Quantum computers are composed of fragile quantum systems that cannot be fully isolated from external noise, and whose manipulations imply a level of uncertainty (unless error correction protocols are applied). The exact nature of these inaccuracies depends on the different qubit technologies employed, the presence of errors is inherent to all qubit architectures [1] These limitations of state-of-the-art quantum computers stands at odds with the need for accuracy in the calculations (e.g., chemical accuracy in electronic structure calculations). For the particular case of mitigating measurement errors there are certain schemes proposed for the increased accuracy in the estimation of mean values of observables [23,24,25] These schemes extend the computational reach of current quantum processors, they just constitute an intermediate step towards fully error corrected (fault tolerant) quantum computation. IV with some important remarks related to the nearterm applicability and the scalability of our approach for future quantum simulations
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