From 0df68e04fd12688c79304e1a7293d7f90767bddc Mon Sep 17 00:00:00 2001 From: kwyip Date: Mon, 19 Aug 2019 15:49:37 -0700 Subject: [PATCH 1/4] Add files via upload --- Book_about_Quadratization.bbl | 11 ++++++++++- Book_about_Quadratization.pdf | Bin 531632 -> 532146 bytes Book_about_Quadratization.tex | 4 ++-- k-local-quadratization.bib | 9 +++++++++ 4 files changed, 21 insertions(+), 3 deletions(-) diff --git a/Book_about_Quadratization.bbl b/Book_about_Quadratization.bbl index e46ad07..dd8ffd4 100644 --- a/Book_about_Quadratization.bbl +++ b/Book_about_Quadratization.bbl @@ -6,7 +6,7 @@ %Control: page (1) range %Control: year (0) verbatim %Control: production of eprint (0) enabled -\begin{thebibliography}{58}% +\begin{thebibliography}{59}% \makeatletter \providecommand \@ifxundefined [1]{% \@ifx{#1\undefined} @@ -275,6 +275,15 @@ {journal} {Quantum Information Processing}\ }\textbf {\bibinfo {volume} {7}},\ \bibinfo {pages} {193--209} (\bibinfo {year} {2008})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Kumar}(2008)}]{k08}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {T.~K.~Satish}\ + \bibnamefont {Kumar}},\ }\bibfield {title} {\enquote {\bibinfo {title} {A + framework for hybrid tractability results in {Boolean} weighted constraint + satisfaction problems},}\ }in\ \href {\doibase 10.1007/978-3-540-85958-1\_19} + {\emph {\bibinfo {booktitle} {the International Conference on Principles and + Practice of Constraint Programming}}}\ (\bibinfo {year} {2008})\ pp.\ + \bibinfo {pages} {282--297}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Chancellor}\ \emph {et~al.}(2016{\natexlab{a}})\citenamefont {Chancellor}, \citenamefont {Zohren},\ and\ \citenamefont {Warburton}}]{Chancellor2016b}% diff --git a/Book_about_Quadratization.pdf b/Book_about_Quadratization.pdf index ee9c1b129c6ed1173289d1ef3f85c4b27f66100e..224c1d5e491f28f169af09cc2226d03ba3ee7044 100644 GIT binary patch delta 58843 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{NoStop}% \bibitem [{\citenamefont {Yip}\ \emph {et~al.}(2019)\citenamefont {Yip}, - \citenamefont {Xu}, \citenamefont {Kumar},\ and\ \citenamefont - {Koenig}}]{yxkk19}% + \citenamefont {Xu}, \citenamefont {Koenig},\ and\ \citenamefont + {Kumar}}]{yxkk19}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {Ka~Wa}\ \bibnamefont {Yip}}, \bibinfo {author} {\bibfnamefont {Hong}\ \bibnamefont {Xu}}, \bibinfo - {author} {\bibfnamefont {T.~K.~Satish}\ \bibnamefont {Kumar}}, \ and\ - \bibinfo {author} {\bibfnamefont {Sven}\ \bibnamefont {Koenig}},\ }\bibfield + {author} {\bibfnamefont {Sven}\ \bibnamefont {Koenig}}, \ and\ \bibinfo + {author} {\bibfnamefont {T.~K.~Satish}\ \bibnamefont {Kumar}},\ }\bibfield {title} {\enquote {\bibinfo {title} {Quadratic reformulation of nonlinear pseudo-boolean functions via the constraint composite graph},}\ }in\ \href {\doibase 10.1007/978-3-030-19212-9\_43} {\emph {\bibinfo {booktitle} {the - International Conference on Integration of Artificial Intelligence and - Operations Research Techniques in Constraint Programming}}}\ (\bibinfo {year} - {2019})\ pp.\ \bibinfo {pages} {643--660}\BibitemShut {NoStop}% + International Conference on Integration of Constraint Programming, Artificial + Intelligence, and Operations Research}}}\ (\bibinfo {year} {2019})\ pp.\ + \bibinfo {pages} {643--660}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Choi}(2008)}]{vchoi08}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {Vicky}\ \bibnamefont {Choi}},\ }\bibfield {title} {\enquote {\bibinfo {title} {Minor-embedding in - adiabatic quantum computation: {I}. the parameter setting problem},}\ }\href - {\doibase 10.1007/s11128-008-0082-9} {\bibfield {journal} {\bibinfo + adiabatic quantum computation: {I}. {T}he parameter setting problem},}\ + }\href {\doibase 10.1007/s11128-008-0082-9} {\bibfield {journal} {\bibinfo {journal} {Quantum Information Processing}\ }\textbf {\bibinfo {volume} {7}},\ \bibinfo {pages} 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zNBmq?oGz1llKCv^%36AZcvEADm>19LGG1%mC#2T2Sh$tHck-(Hn7ja{`_-m|Ufv`A zSv1;8Z4u~HYf6ld(UUIhRMib+z@l>nr;Iku a > 0$. $x_a$ and $x_L$ are the two auxiliary variables introduced for positive monomial and $x_{a'}$ is the auxiliary variable introduced for negative monomial. +where $J \geq L > a > 0$. $b_a$ and $b_L$ are the two auxiliary variables introduced for a positive monomial and $b_{a'}$ is the auxiliary variable introduced for a negative monomial. \refsec \begin{itemize} -\item Original paper: \cite{yxkk19}. Derivation (Theorem 1), inspired by 2008, (Theorem 3): \cite{vchoi08}. -\item Background on CCG (Constraint composite graph): \cite{k08}. +\item Original paper:~\cite{yxkk19}. Derivation (Theorem 1) is inspired by (Theorem 3) in~\cite{vchoi08}. +\item Background on CCG:~\cite{k08}. \end{itemize} diff --git a/k-local-quadratization.bib b/k-local-quadratization.bib index 38fd3fa..03286d1 100644 --- a/k-local-quadratization.bib +++ b/k-local-quadratization.bib @@ -1006,17 +1006,17 @@ @inproceedings{Boros2018boundsPaper } @inproceedings{yxkk19, - author = "Yip, Ka Wa and Xu, Hong and Kumar, T. K. Satish and Koenig, Sven", + author = "Yip, Ka Wa and Xu, Hong and Koenig, Sven and Kumar, T.~K.~Satish", year = "2019", title = "Quadratic Reformulation of Nonlinear Pseudo-Boolean Functions via the Constraint Composite Graph", - booktitle = "the International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming", + booktitle = "the International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research", pages = {643--660}, doi = {10.1007/978-3-030-19212-9\_43} } @article{vchoi08, author="Choi, Vicky", -title="Minor-embedding in adiabatic quantum computation: {I}. The parameter setting problem", +title="Minor-embedding in adiabatic quantum computation: {I}. {T}he parameter setting problem", journal="Quantum Information Processing", year=2008, volume=7, @@ -1029,7 +1029,7 @@ @inproceedings{k08 year={2008}, booktitle={the International Conference on Principles and Practice of Constraint Programming}, title={A Framework for Hybrid Tractability Results in {Boolean} Weighted Constraint Satisfaction Problems}, -author={Kumar, T. K. Satish}, +author={Kumar, T.~K.~Satish}, pages={282--297}, doi = {10.1007/978-3-540-85958-1\_19} } \ No newline at end of file From fc0d79ca15f6ee139a9e1a064f55e4c238507b93 Mon Sep 17 00:00:00 2001 From: kwyip Date: Thu, 25 Jun 2020 19:11:19 -0700 Subject: [PATCH 3/4] Add files via upload --- problem_transmon_4_levels_vinay 2.jl | 131 +++++++++++++++++++++++++++ 1 file changed, 131 insertions(+) create mode 100644 problem_transmon_4_levels_vinay 2.jl diff --git a/problem_transmon_4_levels_vinay 2.jl b/problem_transmon_4_levels_vinay 2.jl new file mode 100644 index 0000000..bde38e7 --- /dev/null +++ b/problem_transmon_4_levels_vinay 2.jl @@ -0,0 +1,131 @@ +using LinearAlgebra +using QuantumAnnealingTools, OrdinaryDiffEq + + +const PHI_0 = 2.067833831e-15 +const H_PLANCK = 6.62607015e-34; +const E_CHARGE = 1.602176634e-19; + + +################# Fucntions ############################# +function transmon_H(e_j, e_c, n_max, ϕx, d) + n2 = Diagonal([(i)^2 for i = -n_max:n_max]) + tot_n = 2 * n_max + 1 + ϕ0 = atan(d * tan(ϕx / 2)) + + d1 = Bidiagonal(zeros(Int64, tot_n), [1 for i = 1:tot_n-1], :L) + cosphi = 1 / 2 * (exp(1im * ϕ0) * d1 + exp(-1im * ϕ0) * Transpose(d1)) + + H = ( + 4 * e_c * n2 - + e_j * cos(ϕx / 2) * sqrt(1 + d^2 * tan(ϕx / 2)^2) * cosphi + ) #### here I am taking ng = 0 i.e. we are always at the sweet spot + return H ## in GHz +end + + +function A_current(e_j_eff, d, phi_x, n_max) + tot_n = 2 * n_max + 1 + d1 = Bidiagonal(zeros(Int64, tot_n), [1 for i = 1:tot_n-1], :L) + cosphi = 1 / 2 * (d1 + Transpose(d1)) + sinphi = 1 / 2im * (d1 - Transpose(d1)) + + + A = + H_PLANCK * + 1e9 * + ( + e_j_eff * pi / PHI_0 * + (sin(phi_x / 2) * cosphi - d * cos(phi_x / 2) * sinphi) + ) + return A +end + + +function make_drive_H(n_max, ωq, η) + ## This function returns the H_drive matrix already in the diagonal basis of H_sys + tot_n = 2 * n_max + 1 + a_dagger = Bidiagonal( + zeros(Float64, tot_n), + [sqrt(i) * (1 - (i - 1) / 2 * η / ωq) for i = 1:tot_n-1], + :L, + ) + a = Transpose(a_dagger) + H_x = (a + a_dagger) ./ 2 + H_y = 1im * (-a + a_dagger) ./ 2 + N_hat = Diagonal([i - 1 for i = 1:tot_n]) + return H_x, H_y, N_hat#,a_dagger*a +end +######################################################## + +function build_hamiltonian_and_coupling( + E_J, + E_C, + n, + phi_x_value, + d_value; + n_trunc = 4, +) + H_trans = transmon_H(E_J, E_C, n, phi_x_value, d_value) + e_list = eigvals(H_trans) + e_list_new = e_list - e_list[1] * ones(2 * n + 1) + ω10 = e_list_new[2] - e_list_new[1] + ω21 = e_list_new[3] - e_list_new[2] + η_1 = -ω21 + ω10 + A = A_current(E_J, d_value, phi_x_value, n) + + U_eigen = eigvecs(H_trans) + H_trans_diag = U_eigen' * H_trans * U_eigen + A_eigen = U_eigen' * A * U_eigen + H_drive_x, H_drive_y, num_op = make_drive_H(n, ω10, η_1) + + H_trans_trunc = H_trans_diag[1:n_trunc, 1:n_trunc] + A_eigen_trunc = A_eigen[1:n_trunc, 1:n_trunc] + Ay = A_eigen_trunc .- Diagonal(diag(A_eigen_trunc)) + Az = zeros(4, 4) .+ Diagonal(diag(A_eigen_trunc)) + + H_trans_trunc = + H_trans_trunc - H_trans_trunc[1, 1] * Diagonal([1 for i = 1:n_trunc]) + + H_trans_trunc, A_eigen_trunc, Ay, Az +end + +## setting the parameters +### We want for qubit 2, wq = 5.23817555736479 GHz and Anharmoicity = 331.9 MHz +E_J = 13.4## in GHz +E_C = 0.287 ## in GHz +n = 20 ## number of levels +d_value = 0.03 +phi_x_value = 0.04 * pi + +const num_op_trunc = Diagonal([i - 1 for i = 1:4]) +const Hm, Am, Ay, Az = + build_hamiltonian_and_coupling(E_J, E_C, n, phi_x_value, d_value) +const ωd = real(Hm[2, 2] - Hm[1, 1] + 0.004) +const H_rotated = Hm - ωd * num_op_trunc + +build_unitary(tf) = (s) -> exp(-2im * π * s * tf * Diagonal(H_rotated)) + +calc_unitary(s, tf) = Diagonal(exp.(-1im * ωd * s * tf * 2 * π * (0:3))) + +function build_rotate_coupling(tf, mat) + coupling = function (s) + U = calc_unitary(s, tf) + 2 * π * g * PHI_0 / H_PLANCK * 1e-9 * U' * mat * U + end + CustomCouplings([coupling]) +end + +const v0 = [1.0, 0im, 0, 0] +const v1 = [0im, 1.0, 0, 0] +const vp = (v0 + v1) / sqrt(2) +const v2 = [0.0, 0, 1.0, 0] +const v3 = [0.0, 0, 1.0, 0] +const vm = (v0 - v1) / sqrt(2) +const vip = (v0 + 1im * v1) / sqrt(2) +const vim = (v0 - 1im * v1) / sqrt(2) + +## parameters for both the bath +const η = 1e-4 +const T = 20 +const g = 0.03 From 84f1a1e7b562b1e4e49cf28089f28a458eacd57e Mon Sep 17 00:00:00 2001 From: kwyip Date: Thu, 25 Jun 2020 19:12:00 -0700 Subject: [PATCH 4/4] Delete problem_transmon_4_levels_vinay 2.jl --- problem_transmon_4_levels_vinay 2.jl | 131 --------------------------- 1 file changed, 131 deletions(-) delete mode 100644 problem_transmon_4_levels_vinay 2.jl diff --git a/problem_transmon_4_levels_vinay 2.jl b/problem_transmon_4_levels_vinay 2.jl deleted file mode 100644 index bde38e7..0000000 --- a/problem_transmon_4_levels_vinay 2.jl +++ /dev/null @@ -1,131 +0,0 @@ -using LinearAlgebra -using QuantumAnnealingTools, OrdinaryDiffEq - - -const PHI_0 = 2.067833831e-15 -const H_PLANCK = 6.62607015e-34; -const E_CHARGE = 1.602176634e-19; - - -################# Fucntions ############################# -function transmon_H(e_j, e_c, n_max, ϕx, d) - n2 = Diagonal([(i)^2 for i = -n_max:n_max]) - tot_n = 2 * n_max + 1 - ϕ0 = atan(d * tan(ϕx / 2)) - - d1 = Bidiagonal(zeros(Int64, tot_n), [1 for i = 1:tot_n-1], :L) - cosphi = 1 / 2 * (exp(1im * ϕ0) * d1 + exp(-1im * ϕ0) * Transpose(d1)) - - H = ( - 4 * e_c * n2 - - e_j * cos(ϕx / 2) * sqrt(1 + d^2 * tan(ϕx / 2)^2) * cosphi - ) #### here I am taking ng = 0 i.e. we are always at the sweet spot - return H ## in GHz -end - - -function A_current(e_j_eff, d, phi_x, n_max) - tot_n = 2 * n_max + 1 - d1 = Bidiagonal(zeros(Int64, tot_n), [1 for i = 1:tot_n-1], :L) - cosphi = 1 / 2 * (d1 + Transpose(d1)) - sinphi = 1 / 2im * (d1 - Transpose(d1)) - - - A = - H_PLANCK * - 1e9 * - ( - e_j_eff * pi / PHI_0 * - (sin(phi_x / 2) * cosphi - d * cos(phi_x / 2) * sinphi) - ) - return A -end - - -function make_drive_H(n_max, ωq, η) - ## This function returns the H_drive matrix already in the diagonal basis of H_sys - tot_n = 2 * n_max + 1 - a_dagger = Bidiagonal( - zeros(Float64, tot_n), - [sqrt(i) * (1 - (i - 1) / 2 * η / ωq) for i = 1:tot_n-1], - :L, - ) - a = Transpose(a_dagger) - H_x = (a + a_dagger) ./ 2 - H_y = 1im * (-a + a_dagger) ./ 2 - N_hat = Diagonal([i - 1 for i = 1:tot_n]) - return H_x, H_y, N_hat#,a_dagger*a -end -######################################################## - -function build_hamiltonian_and_coupling( - E_J, - E_C, - n, - phi_x_value, - d_value; - n_trunc = 4, -) - H_trans = transmon_H(E_J, E_C, n, phi_x_value, d_value) - e_list = eigvals(H_trans) - e_list_new = e_list - e_list[1] * ones(2 * n + 1) - ω10 = e_list_new[2] - e_list_new[1] - ω21 = e_list_new[3] - e_list_new[2] - η_1 = -ω21 + ω10 - A = A_current(E_J, d_value, phi_x_value, n) - - U_eigen = eigvecs(H_trans) - H_trans_diag = U_eigen' * H_trans * U_eigen - A_eigen = U_eigen' * A * U_eigen - H_drive_x, H_drive_y, num_op = make_drive_H(n, ω10, η_1) - - H_trans_trunc = H_trans_diag[1:n_trunc, 1:n_trunc] - A_eigen_trunc = A_eigen[1:n_trunc, 1:n_trunc] - Ay = A_eigen_trunc .- Diagonal(diag(A_eigen_trunc)) - Az = zeros(4, 4) .+ Diagonal(diag(A_eigen_trunc)) - - H_trans_trunc = - H_trans_trunc - H_trans_trunc[1, 1] * Diagonal([1 for i = 1:n_trunc]) - - H_trans_trunc, A_eigen_trunc, Ay, Az -end - -## setting the parameters -### We want for qubit 2, wq = 5.23817555736479 GHz and Anharmoicity = 331.9 MHz -E_J = 13.4## in GHz -E_C = 0.287 ## in GHz -n = 20 ## number of levels -d_value = 0.03 -phi_x_value = 0.04 * pi - -const num_op_trunc = Diagonal([i - 1 for i = 1:4]) -const Hm, Am, Ay, Az = - build_hamiltonian_and_coupling(E_J, E_C, n, phi_x_value, d_value) -const ωd = real(Hm[2, 2] - Hm[1, 1] + 0.004) -const H_rotated = Hm - ωd * num_op_trunc - -build_unitary(tf) = (s) -> exp(-2im * π * s * tf * Diagonal(H_rotated)) - -calc_unitary(s, tf) = Diagonal(exp.(-1im * ωd * s * tf * 2 * π * (0:3))) - -function build_rotate_coupling(tf, mat) - coupling = function (s) - U = calc_unitary(s, tf) - 2 * π * g * PHI_0 / H_PLANCK * 1e-9 * U' * mat * U - end - CustomCouplings([coupling]) -end - -const v0 = [1.0, 0im, 0, 0] -const v1 = [0im, 1.0, 0, 0] -const vp = (v0 + v1) / sqrt(2) -const v2 = [0.0, 0, 1.0, 0] -const v3 = [0.0, 0, 1.0, 0] -const vm = (v0 - v1) / sqrt(2) -const vip = (v0 + 1im * v1) / sqrt(2) -const vim = (v0 - 1im * v1) / sqrt(2) - -## parameters for both the bath -const η = 1e-4 -const T = 20 -const g = 0.03