Mitigating Readout Noise in [[4,2,2]]-Encoded VQE Using Repetition Codes

Quantum computing holds the promise of exponential speedup and high computational accuracy in quantum chemistry simulations. Yet, the presence of quantum noise in current hardware poses a significant barrier to achieving this promise, necessitating robust error mitigation and correction techniques. Here, we investigate the use of the [n,k] repetition code for readout error mitigation and assess its impact on the accuracy of energy estimates from unencoded and [[4,2,2]]-encoded VQE ansatz for simulating the ground state of hydrogen on the realistic emulator of a noisy quantum computer.  The [2,1] repetition code improves energy estimates for both encoded and unencoded ansatz, while the [3,1] code markedly improves the estimate from the encoded ansatz but deteriorates that of the unencoded simulation.  For the [[4,2,2]]-encoded ansatz, the [3,1] encoding with post-selection effectively eliminates readout noise, evidenced by close agreement with results from numerical simulations under depolarizing noise alone. Despite a threefold increase in qubit and two-qubit gate overhead, the method improves the energy accuracy by nearly 6 mHa, based on 188000 shots and a discard rate after post-selection of only 2%. These findings demonstrate that simple repetition codes can substantially enhance measurement reliability and offer valuable insights into the trade-offs between redundancy and resource overhead in near-term quantum error mitigation.