Noise-induced barren plateaus in variational quantum algorithms
Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the n...
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| Vydáno v: | Nature communications Ročník 12; číslo 1; s. 6961 - 11 |
|---|---|
| Hlavní autoři: | , , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
London
Nature Publishing Group UK
29.11.2021
Nature Publishing Group Nature Portfolio |
| Témata: | |
| ISSN: | 2041-1723, 2041-1723 |
| On-line přístup: | Získat plný text |
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| Abstract | Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits
n
if the depth of the ansatz grows linearly with
n
. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.
Variational quantum algorithms (VQAs) are a leading candidate for useful applications of near-term quantum computing, but limitations due to unavoidable noise have not been clearly characterized. Here, the authors prove that local Pauli noise can cause vanishing gradients rendering VQAs untrainable. |
|---|---|
| AbstractList | Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits
n
if the depth of the ansatz grows linearly with
n
. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model. Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model. Variational quantum algorithms (VQAs) are a leading candidate for useful applications of near-term quantum computing, but limitations due to unavoidable noise have not been clearly characterized. Here, the authors prove that local Pauli noise can cause vanishing gradients rendering VQAs untrainable. Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n . These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model. Variational quantum algorithms (VQAs) are a leading candidate for useful applications of near-term quantum computing, but limitations due to unavoidable noise have not been clearly characterized. Here, the authors prove that local Pauli noise can cause vanishing gradients rendering VQAs untrainable. Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model. Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model. Variational quantum algorithms (VQAs) are a leading candidate for useful applications of near-term quantum computing, but limitations due to unavoidable noise have not been clearly characterized. Here, the authors prove that local Pauli noise can cause vanishing gradients rendering VQAs untrainable. |
| ArticleNumber | 6961 |
| Author | Cincio, Lukasz Fontana, Enrico Coles, Patrick J. Sone, Akira Cerezo, M. Sharma, Kunal Wang, Samson |
| Author_xml | – sequence: 1 givenname: Samson orcidid: 0000-0003-2344-0634 surname: Wang fullname: Wang, Samson email: samsonwang@outlook.com organization: Theoretical Division, Los Alamos National Laboratory, Imperial College London – sequence: 2 givenname: Enrico surname: Fontana fullname: Fontana, Enrico organization: Theoretical Division, Los Alamos National Laboratory, University of Strathclyde, National Physical Laboratory – sequence: 3 givenname: M. orcidid: 0000-0002-2757-3170 surname: Cerezo fullname: Cerezo, M. email: cerezo@lanl.gov organization: Theoretical Division, Los Alamos National Laboratory, Center for Nonlinear Studies, Los Alamos National Laboratory – sequence: 4 givenname: Kunal surname: Sharma fullname: Sharma, Kunal organization: Theoretical Division, Los Alamos National Laboratory, Hearne Institute for Theoretical Physics and Department of Physics and Astronomy, Louisiana State University, Joint Center for Quantum Information and Computer Science, University of Maryland – sequence: 5 givenname: Akira orcidid: 0000-0003-3539-6140 surname: Sone fullname: Sone, Akira organization: Theoretical Division, Los Alamos National Laboratory, Center for Nonlinear Studies, Los Alamos National Laboratory, Aliro Technologies, Inc – sequence: 6 givenname: Lukasz surname: Cincio fullname: Cincio, Lukasz organization: Theoretical Division, Los Alamos National Laboratory – sequence: 7 givenname: Patrick J. orcidid: 0000-0001-9879-8425 surname: Coles fullname: Coles, Patrick J. email: pcoles@lanl.gov organization: Theoretical Division, Los Alamos National Laboratory |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/34845216$$D View this record in MEDLINE/PubMed https://www.osti.gov/biblio/1832931$$D View this record in Osti.gov |
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| Snippet | Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether... Variational quantum algorithms (VQAs) are a leading candidate for useful applications of near-term quantum computing, but limitations due to unavoidable noise... |
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| SubjectTerms | 639/766/259 639/766/483/481 Algorithms CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Computers Humanities and Social Sciences information theory and computation multidisciplinary Noise Plateaus Quantum computing quantum information Qubits (quantum computing) Science Science (multidisciplinary) |
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| Title | Noise-induced barren plateaus in variational quantum algorithms |
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