Circuit quantization from first principles
Superconducting circuit quantization conventionally starts from classical Euler-Lagrange circuit equations of motion. Invoking the correspondence principle yields a canonically quantized description of circuit dynamics over a bosonic Hilbert space. This approach has been very successful for describi...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-08-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/dfrq-44vk |
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| author | Yun-Chih Liao Ben J. Powell Thomas M. Stace |
| author_facet | Yun-Chih Liao Ben J. Powell Thomas M. Stace |
| author_sort | Yun-Chih Liao |
| collection | DOAJ |
| description | Superconducting circuit quantization conventionally starts from classical Euler-Lagrange circuit equations of motion. Invoking the correspondence principle yields a canonically quantized description of circuit dynamics over a bosonic Hilbert space. This approach has been very successful for describing experiments, but implicitly starts from the classical Ginsberg-Landau mean-field theory for the circuit. Here, we employ a different approach that starts from a microscopic fermionic Hamiltonian for interacting electrons, whose ground space is described by the Bardeen-Cooper-Schrieffer (BCS) many-body wave function that underpins conventional superconductivity. We introduce the BCS ground space as a subspace of the full fermionic Hilbert space, and show that projecting the electronic Hamiltonian onto this subspace yields the standard Hamiltonian terms for Josephson junctions, capacitors, and inductors, from which standard quantized circuit models follow. This approach does not impose a spontaneously broken symmetry so that it consistently describes quantized circuits that support superpositions of phases, and the canonical commutation relations between phase and charge are derived from the underlying fermionic commutation properties, rather than imposed. By expanding the projective subspace, this approach can be extended to describe phenomena outside the BCS ground space, including quasiparticle excitations. |
| format | Article |
| id | doaj-art-0d60248476df402f809fb63b07fc7dfa |
| institution | DOAJ |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-0d60248476df402f809fb63b07fc7dfa2025-08-20T03:03:15ZengAmerican Physical SocietyPhysical Review Research2643-15642025-08-017303314410.1103/dfrq-44vkCircuit quantization from first principlesYun-Chih LiaoBen J. PowellThomas M. StaceSuperconducting circuit quantization conventionally starts from classical Euler-Lagrange circuit equations of motion. Invoking the correspondence principle yields a canonically quantized description of circuit dynamics over a bosonic Hilbert space. This approach has been very successful for describing experiments, but implicitly starts from the classical Ginsberg-Landau mean-field theory for the circuit. Here, we employ a different approach that starts from a microscopic fermionic Hamiltonian for interacting electrons, whose ground space is described by the Bardeen-Cooper-Schrieffer (BCS) many-body wave function that underpins conventional superconductivity. We introduce the BCS ground space as a subspace of the full fermionic Hilbert space, and show that projecting the electronic Hamiltonian onto this subspace yields the standard Hamiltonian terms for Josephson junctions, capacitors, and inductors, from which standard quantized circuit models follow. This approach does not impose a spontaneously broken symmetry so that it consistently describes quantized circuits that support superpositions of phases, and the canonical commutation relations between phase and charge are derived from the underlying fermionic commutation properties, rather than imposed. By expanding the projective subspace, this approach can be extended to describe phenomena outside the BCS ground space, including quasiparticle excitations.http://doi.org/10.1103/dfrq-44vk |
| spellingShingle | Yun-Chih Liao Ben J. Powell Thomas M. Stace Circuit quantization from first principles Physical Review Research |
| title | Circuit quantization from first principles |
| title_full | Circuit quantization from first principles |
| title_fullStr | Circuit quantization from first principles |
| title_full_unstemmed | Circuit quantization from first principles |
| title_short | Circuit quantization from first principles |
| title_sort | circuit quantization from first principles |
| url | http://doi.org/10.1103/dfrq-44vk |
| work_keys_str_mv | AT yunchihliao circuitquantizationfromfirstprinciples AT benjpowell circuitquantizationfromfirstprinciples AT thomasmstace circuitquantizationfromfirstprinciples |