Emulating Quantum Circuits With Generalized Ising Machines
The primary objective of this paper is to present an exact and general procedure for mapping any sequence of quantum gates onto a network of probabilistic p-bits which can take on one of two values 0 and 1. The first <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2023-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10278418/ |
| _version_ | 1797648681119252480 |
|---|---|
| author | Shuvro Chowdhury Kerem Y. Camsari Supriyo Datta |
| author_facet | Shuvro Chowdhury Kerem Y. Camsari Supriyo Datta |
| author_sort | Shuvro Chowdhury |
| collection | DOAJ |
| description | The primary objective of this paper is to present an exact and general procedure for mapping any sequence of quantum gates onto a network of probabilistic p-bits which can take on one of two values 0 and 1. The first <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> p-bits represent the input qubits, while the other p-bits represent the qubits after the application of successive gating operations. We can view this structure as a Boltzmann machine whose states each represent a Feynman path leading from an initial configuration of qubits to a final configuration. Each such path has a complex amplitude <inline-formula> <tex-math notation="LaTeX">$\psi $ </tex-math></inline-formula> which can be associated with a complex energy. The real part of this energy can be used to generate samples of Feynman paths in the usual way, while the imaginary part is accounted for by treating the samples as complex entities, unlike ordinary Boltzmann machines where samples are positive. Quantum gates often have purely imaginary energy functions for which all configurations have the same probability and one cannot take advantage of sampling techniques. Typically this would require us to collect <inline-formula> <tex-math notation="LaTeX">$2^{nd}$ </tex-math></inline-formula> samples which would severely limit its utility. However, if we can use suitable transformations to introduce a real part in the energy function then powerful sampling algorithms like Gibbs sampling can be harnessed to get acceptable results with far fewer samples and perhaps even escape the exponential scaling with <inline-formula> <tex-math notation="LaTeX">$nd$ </tex-math></inline-formula>. This algorithmic acceleration can then be supplemented with special-purpose hardware accelerators like Ising Machines which can obtain a very large number of samples per second through a combination of massive parallelism, pipelining, and clockless mixed-signal operation made possible by codesigning circuits and architectures to match the algorithm. Our results for mapping an arbitrary quantum circuit to a Boltzmann machine with a complex energy function should help push the boundaries of the simulability of quantum circuits with probabilistic resources and compare them with NISQ-era quantum computers. |
| first_indexed | 2024-03-11T15:35:28Z |
| format | Article |
| id | doaj.art-ca986b9a49ec446a9d1746bb22ec6723 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-11T15:35:28Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-ca986b9a49ec446a9d1746bb22ec67232023-10-26T23:01:07ZengIEEEIEEE Access2169-35362023-01-011111694411695510.1109/ACCESS.2023.332384710278418Emulating Quantum Circuits With Generalized Ising MachinesShuvro Chowdhury0https://orcid.org/0000-0002-6325-0790Kerem Y. Camsari1https://orcid.org/0000-0002-6876-8812Supriyo Datta2https://orcid.org/0000-0001-8577-984XDepartment of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USADepartment of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USAElmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USAThe primary objective of this paper is to present an exact and general procedure for mapping any sequence of quantum gates onto a network of probabilistic p-bits which can take on one of two values 0 and 1. The first <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> p-bits represent the input qubits, while the other p-bits represent the qubits after the application of successive gating operations. We can view this structure as a Boltzmann machine whose states each represent a Feynman path leading from an initial configuration of qubits to a final configuration. Each such path has a complex amplitude <inline-formula> <tex-math notation="LaTeX">$\psi $ </tex-math></inline-formula> which can be associated with a complex energy. The real part of this energy can be used to generate samples of Feynman paths in the usual way, while the imaginary part is accounted for by treating the samples as complex entities, unlike ordinary Boltzmann machines where samples are positive. Quantum gates often have purely imaginary energy functions for which all configurations have the same probability and one cannot take advantage of sampling techniques. Typically this would require us to collect <inline-formula> <tex-math notation="LaTeX">$2^{nd}$ </tex-math></inline-formula> samples which would severely limit its utility. However, if we can use suitable transformations to introduce a real part in the energy function then powerful sampling algorithms like Gibbs sampling can be harnessed to get acceptable results with far fewer samples and perhaps even escape the exponential scaling with <inline-formula> <tex-math notation="LaTeX">$nd$ </tex-math></inline-formula>. This algorithmic acceleration can then be supplemented with special-purpose hardware accelerators like Ising Machines which can obtain a very large number of samples per second through a combination of massive parallelism, pipelining, and clockless mixed-signal operation made possible by codesigning circuits and architectures to match the algorithm. Our results for mapping an arbitrary quantum circuit to a Boltzmann machine with a complex energy function should help push the boundaries of the simulability of quantum circuits with probabilistic resources and compare them with NISQ-era quantum computers.https://ieeexplore.ieee.org/document/10278418/Hardware acceleratorsIsing machinesmassive parallelismp-bitsquantum circuitsFeynman path |
| spellingShingle | Shuvro Chowdhury Kerem Y. Camsari Supriyo Datta Emulating Quantum Circuits With Generalized Ising Machines IEEE Access Hardware accelerators Ising machines massive parallelism p-bits quantum circuits Feynman path |
| title | Emulating Quantum Circuits With Generalized Ising Machines |
| title_full | Emulating Quantum Circuits With Generalized Ising Machines |
| title_fullStr | Emulating Quantum Circuits With Generalized Ising Machines |
| title_full_unstemmed | Emulating Quantum Circuits With Generalized Ising Machines |
| title_short | Emulating Quantum Circuits With Generalized Ising Machines |
| title_sort | emulating quantum circuits with generalized ising machines |
| topic | Hardware accelerators Ising machines massive parallelism p-bits quantum circuits Feynman path |
| url | https://ieeexplore.ieee.org/document/10278418/ |
| work_keys_str_mv | AT shuvrochowdhury emulatingquantumcircuitswithgeneralizedisingmachines AT keremycamsari emulatingquantumcircuitswithgeneralizedisingmachines AT supriyodatta emulatingquantumcircuitswithgeneralizedisingmachines |