Error statistics and scalability of quantum error mitigation formulas

• URL: http://arxiv.org/abs/2112.06255v2
• Date: Fri, 14 Apr 2023 07:38:58 GMT
• Title: Error statistics and scalability of quantum error mitigation formulas
• Authors: Dayue Qin, Yanzhu Chen, Ying Li
• Abstract summary: We apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly $O(epsilon N)$ with the gate number $N$ before mitigation and sub-linearly $O(epsilon' Ngamma)$ after mitigation. The $sqrtN$ scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits.
• Score: 4.762232147934851
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources . While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly $O(\epsilon N)$ with the gate number $N$ before mitigation and sub-linearly $O(\epsilon' N^\gamma)$ after mitigation, where $\gamma \approx 0.5$, $\epsilon$ is the error rate of a quantum gate, and $\epsilon'$ is a protocol-dependent factor. The $\sqrt{N}$ scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.

Related papers

• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits [84.60542868688235]
  leakage out of the computational subspace arising from the multi-level structure of qubit implementations. We present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion.
  arXiv  Detail & Related papers  (2023-09-13T16:21:32Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Quantum error mitigation via matrix product operators [27.426057220671336]
  Quantum error mitigation (QEM) can suppress errors in measurement results via repeated experiments and post decomposition of data. MPO representation increases the accuracy of modeling noise without consuming more experimental resources. Our method is hopeful of being applied to circuits in higher dimensions with more qubits and deeper depth.
  arXiv  Detail & Related papers  (2022-01-03T16:57:43Z)
• $i$-QER: An Intelligent Approach towards Quantum Error Reduction [5.055934439032756]
  We introduce $i$-QER, a scalable machine learning-based approach to evaluate errors in a quantum circuit. The $i$-QER predicts possible errors in a given quantum circuit using supervised learning models. It cuts the large quantum circuit into two smaller sub-circuits using an error-influenced fragmentation strategy.
  arXiv  Detail & Related papers  (2021-10-12T20:45:03Z)
• Towards Demonstrating Fault Tolerance in Small Circuits Using Bacon-Shor Codes [5.352699766206807]
  We study a next step - fault-tolerantly implementing quantum circuits. We compute pseudo-thresholds for the Pauli error rate $p$ in a depolarizing noise model. We see that multiple rounds of stabilizer measurements give an improvement over performing a single round at the end.
  arXiv  Detail & Related papers  (2021-08-04T14:24:14Z)
• Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version) [6.349076549152475]
  We present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the $(hatrho,delta)$-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits.
  arXiv  Detail & Related papers  (2021-04-13T16:45:57Z)
• Exponential suppression of bit or phase flip errors with repetitive error correction [56.362599585843085]
  State-of-the-art quantum platforms typically have physical error rates near $10-3$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits. We implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors.
  arXiv  Detail & Related papers  (2021-02-11T17:11:20Z)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)
• Describing quantum metrology with erasure errors using weight distributions of classical codes [9.391375268580806]
  We consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field.
  arXiv  Detail & Related papers  (2020-07-06T16:22:40Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.