s stringlengths 1 39 | o stringclasses 996
values | p stringlengths 7 77 | confidence float64 0.4 1 | predicate_class stringclasses 2
values | community int64 0 14 ⌀ | equation_name stringlengths 14 73 ⌀ | equation_latex stringlengths 5 217 ⌀ | equation_sympy stringclasses 617
values | equation_form stringclasses 472
values | variables stringlengths 2 85 ⌀ | domain stringclasses 119
values | scm_name stringclasses 165
values | source stringlengths 9 50 ⌀ | extraction_method stringclasses 8
values |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
t | t | urn:hailstone:chemistry_physics:structural_equation[f957d78c22a1] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.08259v1.eq_1921 | Ψ_{\textit{Mult}} \equiv Ψ= N - \underset{1 \leq i \leq N}{\prod} \mathrm{exp} \big[ - q_i x_i \big] | arxiv_extracted | ["t", "i", "e", "x"] | arxiv | arxiv | arxiv:quant-ph:2605.08259v1 | cross_domain_amplification | |
n | c | urn:hailstone:chemistry_physics:structural_equation[03ab52da0956] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.06414v1.eq_1922 | -\nabla\cdot(a(x)\nabla u(x))=f(x), | arxiv_extracted | ["a", "n", "b", "c", "l"] | arxiv | arxiv | arxiv:quant-ph:2605.06414v1 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[60329d0bd4d6] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.05633v1.eq_1923 | \varphi = 0 | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:quant-ph:2605.05633v1 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[6b162c21a3cf] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.05633v1.eq_1924 | \varphi = π | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:quant-ph:2605.05633v1 | cross_domain_amplification | |
p | r | urn:hailstone:chemistry_physics:structural_equation[4c4e7c26ac53] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.05369v1.eq_1925 | p_{\mathrm{th}}=0.70 | arxiv_extracted | ["a", "t", "m", "h", "p", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.05369v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[6fcf8055a41d] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.05036v1.eq_1926 | \mathrm{rt}_B(H, s, g) = Θ(d_C \log N_L) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.05036v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[1accc94f2249] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.05036v1.eq_1927 | \mathrm{rt}_B = Ω(d_C \log N_L) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.05036v1 | cross_domain_amplification | |
C_{l_1} | n | urn:hailstone:chemistry_physics:structural_equation[7a1ab0167e0c] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.04429v2.eq_1928 | C_{l_1}(ρ(t)) = \sin^2(φ/2) | arxiv_extracted | ["t", "i", "s", "n", "C_{l_1}"] | arxiv | arxiv | arxiv:quant-ph:2605.04429v2 | cross_domain_amplification | |
t | k | urn:hailstone:chemistry_physics:structural_equation[6c2f3038a5dd] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.04429v2.eq_1929 | (α+ 1)t = π/4 + kπ/2 | arxiv_extracted | ["t", "k"] | arxiv | arxiv | arxiv:quant-ph:2605.04429v2 | cross_domain_amplification | |
T_c | r | urn:hailstone:chemistry_physics:structural_equation[c9efaf011bf3] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.04047v1.eq_1930 | T_c^{\mathrm{ext}}/τ= 25 | arxiv_extracted | ["a", "t", "m", "h", "r", "T_c"] | arxiv | arxiv | arxiv:quant-ph:2605.04047v1 | cross_domain_amplification | |
T_c | r | urn:hailstone:chemistry_physics:structural_equation[bc5edc9ab15a] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.04047v1.eq_1931 | T_c^{\mathrm{ext}}/τ= 50 | arxiv_extracted | ["a", "t", "m", "h", "r", "T_c"] | arxiv | arxiv | arxiv:quant-ph:2605.04047v1 | cross_domain_amplification | |
g | f | urn:hailstone:chemistry_physics:structural_equation[78f84962a7a9] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.04042v2.eq_1932 | g_{\rm eff} = g\sqrt{N}) | arxiv_extracted | ["e", "f", "g", "m", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.04042v2 | cross_domain_amplification | |
g | O | urn:hailstone:chemistry_physics:structural_equation[e7bc364b76ae] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.03910v1.eq_1933 | g_\text{OM} / (2 π) = 800 | arxiv_extracted | ["e", "g", "t", "O", "x"] | arxiv | arxiv | arxiv:quant-ph:2605.03910v1 | cross_domain_amplification | |
t | M | urn:hailstone:chemistry_physics:structural_equation[33d96587f346] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.03910v1.eq_1934 | Γ_\text{OM}/(2 π)= 1.1 | arxiv_extracted | ["e", "t", "M", "O", "x"] | arxiv | arxiv | arxiv:quant-ph:2605.03910v1 | cross_domain_amplification | |
s | p_i | urn:hailstone:chemistry_physics:structural_equation[afd9b3f1e42e] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.03685v1.eq_1935 | \sum_{i=1}^n f(p_i) | arxiv_extracted | ["f", "m_{i", "p_i", "u", "s", "n"] | arxiv | arxiv | arxiv:quant-ph:2605.03685v1 | cross_domain_amplification | |
p_i | n | urn:hailstone:chemistry_physics:structural_equation[d7f4b7a28c99] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.03685v1.eq_1936 | (p_i)_{i=1}^n | arxiv_extracted | ["n", "p_i", "i"] | arxiv | arxiv | arxiv:quant-ph:2605.03685v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[c875c8d521c9] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.03366v1.eq_1937 | \mathcal{F}_μ=(\mathcal{F}_t(x),0,0,0) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:quant-ph:2605.03366v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[e463946d8909] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.03366v1.eq_1938 | \mathcal{F}_t(x)=Ω\, r(x) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:quant-ph:2605.03366v1 | cross_domain_amplification | |
N | a | urn:hailstone:chemistry_physics:structural_equation[4e6d5349bccf] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.03056v1.eq_1939 | N_{\rm real}=2000 | arxiv_extracted | ["e", "a", "m", "r", "N"] | arxiv | arxiv | arxiv:quant-ph:2605.03056v1 | cross_domain_amplification | |
I | h | urn:hailstone:chemistry_physics:structural_equation[fc118c823ba8] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.02876v1.eq_1940 | I(\hat{x},\hat{y})=0 | arxiv_extracted | ["a", "t", "h", "I", "x"] | arxiv | arxiv | arxiv:quant-ph:2605.02876v1 | cross_domain_amplification | |
m | c | urn:hailstone:chemistry_physics:structural_equation[daf5ef8cde7c] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.02876v1.eq_1941 | \max_{\vec{n}_1,\vec{n}_2}| I_{W}|=35/27\approx 1.296 | arxiv_extracted | ["e", "a", "m", "c", "v", "x"] | arxiv | arxiv | arxiv:quant-ph:2605.02876v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[dca1c0be8af6] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.02498v2.eq_1942 | \mathrm{rt}(H) = Θ(\log N) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.02498v2 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[ad09d944ba0c] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.02498v2.eq_1943 | \mathrm(H_L) = O(\log N) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.02498v2 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[a48497988a9f] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.02406v1.eq_1944 | \mathrm{mod}\,σ_\mathrm{y} = 2 \times 10^{-16} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.02406v1 | cross_domain_amplification | |
P | y | urn:hailstone:chemistry_physics:structural_equation[0ce771ae3bd2] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.02332v1.eq_1945 | P(x,y)=0 | arxiv_extracted | ["y", "P", "x"] | arxiv | arxiv | arxiv:quant-ph:2605.02332v1 | cross_domain_amplification | |
s | L | urn:hailstone:chemistry_physics:structural_equation[963f72e4c408] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.02211v1.eq_1946 | \sum_{i \in L} w(i) \langle ψ| H_i | ψ\rangle \in (1 \pm ε) \sum_{i = 1}^m \langle ψ| H_i | ψ\rangle | arxiv_extracted | ["m_{i", "i", "u", "L", "s", "n"] | arxiv | arxiv | arxiv:quant-ph:2605.02211v1 | cross_domain_amplification | |
p | a | urn:hailstone:chemistry_physics:structural_equation[aaad51da4afd] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.08148v1.eq_1947 | \partial_μA^μ= 0 | arxiv_extracted | ["a", "t", "i", "p", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.08148v1 | cross_domain_amplification | |
B | r | urn:hailstone:chemistry_physics:structural_equation[815014d14022] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.01319v1.eq_1948 | B_{\mathrm{eff},k}=R_k\sqrt{N_{\mathrm{eff},k}} | arxiv_extracted | ["a", "B", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.01319v1 | cross_domain_amplification | |
s | s | urn:hailstone:chemistry_physics:structural_equation[b0803d151c4e] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.01233v1.eq_1949 | \sqrt{s} = 7 | arxiv_extracted | ["s", "t", "q", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.01233v1 | cross_domain_amplification | |
l | e | urn:hailstone:chemistry_physics:structural_equation[c33f544ac9b5] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00952v1.eq_1950 | \langle E_i|\hat{J}_z|E_i\rangle=0 | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:quant-ph:2605.00952v1 | cross_domain_amplification | |
r | m | urn:hailstone:chemistry_physics:structural_equation[f648ace53455] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00952v1.eq_1951 | η_{\rm MF}=(Nm_*)^2/(2G_{01})\approx2.42 | arxiv_extracted | ["F", "M", "m", "r", "N"] | arxiv | arxiv | arxiv:quant-ph:2605.00952v1 | cross_domain_amplification | |
G_{01} | l | urn:hailstone:chemistry_physics:structural_equation[ef0fac0be5a0] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00952v1.eq_1952 | G_{01}=\frac{1}{2}(\langle E_0|\hat{J}_z^2|E_0\rangle+\langle E_1|\hat{J}_z^2|E_1\rangle) | arxiv_extracted | ["f", "a", "G_{01}", "r", "c", "l"] | arxiv | arxiv | arxiv:quant-ph:2605.00952v1 | cross_domain_amplification | |
r | c | urn:hailstone:chemistry_physics:structural_equation[fc9b26d0aa51] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00952v1.eq_1953 | η_{\rm exact}=(G_{01}+J_{01}^2)/G_{01}\approx1.86 | arxiv_extracted | ["e", "a", "m", "r", "c", "x"] | arxiv | arxiv | arxiv:quant-ph:2605.00952v1 | cross_domain_amplification | |
J_{01} | l | urn:hailstone:chemistry_physics:structural_equation[aca1e9067f2b] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00952v1.eq_1954 | J_{01}=\langle E_0|\hat{J}_z|E_1\rangle | arxiv_extracted | ["J_{01}", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:quant-ph:2605.00952v1 | cross_domain_amplification | |
N | P_N | urn:hailstone:chemistry_physics:structural_equation[59995ca5481b] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.28127v2.eq_1955 | ψ_N(x,y)=e^{-αr^2/2}P_N(x,y) | arxiv_extracted | ["e", "y", "P_N", "r", "N", "x"] | arxiv | arxiv | arxiv:quant-ph:2604.28127v2 | cross_domain_amplification | |
s | s | urn:hailstone:chemistry_physics:structural_equation[318cef1834c9] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.27886v1.eq_1956 | {\sf EXP}={\sf NEXP} | arxiv_extracted | ["f", "P", "X", "s", "E"] | arxiv | arxiv | arxiv:quant-ph:2604.27886v1 | cross_domain_amplification | |
s | q | urn:hailstone:chemistry_physics:structural_equation[b9d67b22c823] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.27886v1.eq_1957 | {\sf StoqMA}(k) = {\sf StoqMA}(2) | arxiv_extracted | ["f", "q", "t", "S", "o", "s"] | arxiv | arxiv | arxiv:quant-ph:2604.27886v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[1db05711fc0f] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00075v1.eq_1958 | \mathcal{A}(O')' = \bigcap_{W \supset O}\mathcal{A}(W) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:quant-ph:2605.00075v1 | cross_domain_amplification | |
g_{am} | a | urn:hailstone:chemistry_physics:structural_equation[da5ac6422b13] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.27608v1.eq_1959 | g_{am}=\sqrt{κ_aκ_m}/2 | arxiv_extracted | ["g_{am}", "q", "a", "t", "r", "s"] | arxiv | arxiv | arxiv:quant-ph:2604.27608v1 | cross_domain_amplification | |
P_M | i | urn:hailstone:chemistry_physics:structural_equation[597dd2b496dc] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.27339v1.eq_1960 | P_M([e_i])=δ_i | arxiv_extracted | ["e_i", "P_M", "i"] | arxiv | arxiv | arxiv:quant-ph:2604.27339v1 | cross_domain_amplification | |
h | T | urn:hailstone:chemistry_physics:structural_equation[b1eaffdda1dc] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00053v2.eq_1961 | \hbar ω= k_B T \ln 3 | arxiv_extracted | ["a", "T", "h", "r", "b", "k_B"] | arxiv | arxiv | arxiv:quant-ph:2605.00053v2 | cross_domain_amplification | |
s | t | urn:hailstone:chemistry_physics:structural_equation[fbdc97950786] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00053v2.eq_1962 | \sqrt{S_h} = 2.1 \times 10^{-22}/\sqrt{\rm Hz} | arxiv_extracted | ["q", "t", "S_h}", "r", "s"] | arxiv | arxiv | arxiv:quant-ph:2605.00053v2 | cross_domain_amplification | |
l | r | urn:hailstone:chemistry_physics:structural_equation[f5480e1cad81] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.26927v1.eq_1963 | \left\{\frac{1}{N},ρ_i^{\otimes k}\right\}_{i=1}^N | arxiv_extracted | ["e", "f", "t", "r", "l"] | arxiv | arxiv | arxiv:quant-ph:2604.26927v1 | cross_domain_amplification | |
F | r | urn:hailstone:chemistry_physics:structural_equation[20d3d0b93b90] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.26663v1.eq_1964 | F_{\mathrm{hw}}=0.987 | arxiv_extracted | ["F", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.26663v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[145836b1b059] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.26625v2.eq_1965 | \mathcal{H}=L^2(0,T;\mathbb{R}) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:quant-ph:2604.26625v2 | cross_domain_amplification | |
s | l | urn:hailstone:chemistry_physics:structural_equation[955eff064c5d] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.26625v2.eq_1966 | Γ(s)_{\ell\ell'}=\int_0^T S(t)\,c_\ell(s,t)\,c_{\ell'}(s,t)\,\mathrm{d}t | arxiv_extracted | ["s", "l", "e"] | arxiv | arxiv | arxiv:quant-ph:2604.26625v2 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[cd329e4c4ed2] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.26625v2.eq_1967 | Γ_{\varepsilon}:=Γ+\varepsilon^{2}I | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:quant-ph:2604.26625v2 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[5321af135ca0] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.26625v2.eq_1968 | κ(Γ_{\varepsilon})=(σ_{\max}^{2}+\varepsilon^{2})/(σ_{\min}^{2}+\varepsilon^{2}) | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:quant-ph:2604.26625v2 | cross_domain_amplification | |
h_{m} | h | urn:hailstone:chemistry_physics:structural_equation[716d52eea860] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.26625v2.eq_1969 | |h_{m}-C_{m}|=\mathcal{O}(\varepsilon^{2}) | arxiv_extracted | ["a", "t", "m", "C_{m}", "h", "h_{m}"] | arxiv | arxiv | arxiv:quant-ph:2604.26625v2 | cross_domain_amplification | |
s | n | urn:hailstone:chemistry_physics:structural_equation[a7ae16094b66] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.25708v2.eq_1970 | \shots = 16\nqubits^2 | arxiv_extracted | ["t", "h", "o", "s", "n"] | arxiv | arxiv | arxiv:quant-ph:2604.25708v2 | cross_domain_amplification | |
d | r | urn:hailstone:chemistry_physics:structural_equation[1ade682692cd] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.25631v1.eq_1971 | d_{\mathrm{eff}} = N(p+1)χ^2 | arxiv_extracted | ["a", "t", "m", "h", "r", "d"] | arxiv | arxiv | arxiv:quant-ph:2604.25631v1 | cross_domain_amplification | |
U | f | urn:hailstone:chemistry_physics:structural_equation[ea36ba313692] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.25503v2.eq_1972 | \Utwof = 0.250000 | arxiv_extracted | ["f", "w", "t", "o", "U"] | arxiv | arxiv | arxiv:quant-ph:2604.25503v2 | cross_domain_amplification | |
m_r | m_r | urn:hailstone:chemistry_physics:structural_equation[6d2bad5fda6f] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.25429v1.eq_1973 | δm_r'=λ_r\,δm_r | arxiv_extracted | ["r", "m_r"] | arxiv | arxiv | arxiv:quant-ph:2604.25429v1 | cross_domain_amplification | |
m | r | urn:hailstone:chemistry_physics:structural_equation[04dffa4020f6] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.25429v1.eq_1974 | m^{\mathrm{eq}}=Mf^{\mathrm{eq}} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.25429v1 | cross_domain_amplification | |
p | r | urn:hailstone:chemistry_physics:structural_equation[f0b1205f7fec] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.24423v1.eq_1975 | p_{\mathrm{crit}}=2/3 | arxiv_extracted | ["a", "t", "m", "h", "p", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.24423v1 | cross_domain_amplification | |
s | i | urn:hailstone:chemistry_physics:structural_equation[90511f68932e] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.24289v1.eq_1976 | \sum_{k=0}^d\binom{n}{k} | arxiv_extracted | ["i", "m_{k", "u", "s", "b", "d"] | arxiv | arxiv | arxiv:quant-ph:2604.24289v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[f6f0ce4402df] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.24133v1.eq_1977 | \mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.24133v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[fc03ab93e0b7] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23991v1.eq_1978 | \mathcal S=\operatorname{span} \{ \lvert 0\rangle, \lvert 1\rangle \} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:quant-ph:2604.23991v1 | cross_domain_amplification | |
l | r | urn:hailstone:chemistry_physics:structural_equation[54643c9d2abf] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23991v1.eq_1979 | \lvert ψ\rangle = ω_1\lvert 0\rangle + ω_2\lvert 1\rangle | arxiv_extracted | ["e", "t", "r", "l", "v"] | arxiv | arxiv | arxiv:quant-ph:2604.23991v1 | cross_domain_amplification | |
T | t | urn:hailstone:chemistry_physics:structural_equation[a19bc378c6cc] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23898v2.eq_1980 | \Tcal_{ij} = d^{-1}\tr[(\hat P_i \hat Q_j)^2] | arxiv_extracted | ["a", "t", "d", "c", "l_{ij}", "T"] | arxiv | arxiv | arxiv:quant-ph:2604.23898v2 | cross_domain_amplification | |
c | x_{i | urn:hailstone:chemistry_physics:structural_equation[802885ca3e81] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23898v2.eq_1981 | c_\MU = \max_{i,j}|\langle a_i,b_i | c_j,b_j\rangle| | arxiv_extracted | ["a", "M", "m", "x_{i", "U", "c"] | arxiv | arxiv | arxiv:quant-ph:2604.23898v2 | cross_domain_amplification | |
S_2 | s | urn:hailstone:chemistry_physics:structural_equation[6dfcfed06b9f] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23898v2.eq_1982 | S_2(\Gcal) = \sum_αS_2(\Gcal_α) | arxiv_extracted | ["a", "G", "S_2", "s", "c", "l"] | arxiv | arxiv | arxiv:quant-ph:2604.23898v2 | cross_domain_amplification | |
c | U | urn:hailstone:chemistry_physics:structural_equation[43ce4fb6561e] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23898v2.eq_1983 | c_\MU = 1 | arxiv_extracted | ["U", "M", "c"] | arxiv | arxiv | arxiv:quant-ph:2604.23898v2 | cross_domain_amplification | |
F_1 | F_2 | urn:hailstone:chemistry_physics:structural_equation[9692939b5d38] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23672v1.eq_1984 | |F_1|=2|F_2| | arxiv_extracted | ["F_2", "F_1"] | arxiv | arxiv | arxiv:quant-ph:2604.23672v1 | cross_domain_amplification | |
s | f | urn:hailstone:chemistry_physics:structural_equation[6c4bcd2dcb8b] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23544v2.eq_1985 | \sum_{n=1}^{\infty}n^α | arxiv_extracted | ["f", "m_{n", "i", "u", "s", "n"] | arxiv | arxiv | arxiv:quant-ph:2604.23544v2 | cross_domain_amplification | |
s | f | urn:hailstone:chemistry_physics:structural_equation[e0de8e37a4da] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23544v2.eq_1986 | \sum_{n=1}^{\infty}n^m | arxiv_extracted | ["f", "m_{n", "i", "u", "s", "n"] | arxiv | arxiv | arxiv:quant-ph:2604.23544v2 | cross_domain_amplification | |
s | f | urn:hailstone:chemistry_physics:structural_equation[86768d5d9ae9] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23544v2.eq_1987 | \sum_{n=1}^{\infty} n^m = (2πi)^{-1}\oint_C L^m K_L(z) z^{-1}\mathrm{d}z | arxiv_extracted | ["f", "m_{n", "i", "u", "s", "n"] | arxiv | arxiv | arxiv:quant-ph:2604.23544v2 | cross_domain_amplification | |
s | f | urn:hailstone:chemistry_physics:structural_equation[77418a740a4e] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.23544v2.eq_1988 | \sum_{n=1}^{\infty}n^α=(2πi)^{-1}\int_{\tilde{C}} L^α K_L(z) z^{-1}\mathrm{d}z | arxiv_extracted | ["f", "m_{n", "i", "u", "s", "n"] | arxiv | arxiv | arxiv:quant-ph:2604.23544v2 | cross_domain_amplification | |
r | l | urn:hailstone:chemistry_physics:structural_equation[4e8b5897f70f] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.22521v2.eq_1989 | {\rm TEN} = 2 \ln 2 | arxiv_extracted | ["T", "m", "r", "E", "l", "N"] | arxiv | arxiv | arxiv:quant-ph:2604.22521v2 | cross_domain_amplification | |
r | l | urn:hailstone:chemistry_physics:structural_equation[d7f09d1a8233] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.22521v2.eq_1990 | {\rm TEN} = \ln 2 | arxiv_extracted | ["T", "m", "r", "E", "l", "N"] | arxiv | arxiv | arxiv:quant-ph:2604.22521v2 | cross_domain_amplification | |
x | l | urn:hailstone:chemistry_physics:structural_equation[96524f10e246] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.22463v1.eq_1991 | |x\rangle=\vec{x}/\lVert\vec{x}\rVert | arxiv_extracted | ["g", "a", "r", "n", "l", "x"] | arxiv | arxiv | arxiv:quant-ph:2604.22463v1 | cross_domain_amplification | |
e | r | urn:hailstone:chemistry_physics:structural_equation[ff98c0cfbb73] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.22463v1.eq_1992 | |e^{\vec{x}} \rangle= e^{\vec{x}}/\lVert e^{\vec{x}}\rVert | arxiv_extracted | ["e", "r", "c", "v", "x"] | arxiv | arxiv | arxiv:quant-ph:2604.22463v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[7e256f859c25] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.21929v2.eq_1993 | \mathcal{S}(S) = σ(H_S) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:quant-ph:2604.21929v2 | cross_domain_amplification | |
M_2 | g | urn:hailstone:chemistry_physics:structural_equation[4f2393d97e35] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.21955v1.eq_1994 | (M_2/n,\langle H\rangle)=(0,4.00) | arxiv_extracted | ["g", "a", "M_2", "n", "l"] | arxiv | arxiv | arxiv:quant-ph:2604.21955v1 | cross_domain_amplification | |
t | a | urn:hailstone:chemistry_physics:structural_equation[51907bc807d7] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.21955v1.eq_1995 | Φ_\text{max}=4.10 | arxiv_extracted | ["e", "a", "t", "m", "x"] | arxiv | arxiv | arxiv:quant-ph:2604.21955v1 | cross_domain_amplification | |
T | b | urn:hailstone:chemistry_physics:structural_equation[f94e109b93c1] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.21373v1.eq_1996 | T^*{\mathbb R}^{2}={\mathbb C}^2 | arxiv_extracted | ["a", "t", "m", "h", "b", "T"] | arxiv | arxiv | arxiv:quant-ph:2604.21373v1 | cross_domain_amplification | |
H | r | urn:hailstone:chemistry_physics:structural_equation[4351597f2190] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.21210v1.eq_1997 | H_{\mathrm{meas}} = r A / τ | arxiv_extracted | ["a", "t", "m", "H", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.21210v1 | cross_domain_amplification | |
l | A | urn:hailstone:chemistry_physics:structural_equation[50e4fc1a6744] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.21210v1.eq_1998 | δ\log P_F / δρ= r A / τ= H_{\mathrm{meas}} | arxiv_extracted | ["g", "P_F", "o", "A", "r", "l"] | arxiv | arxiv | arxiv:quant-ph:2604.21210v1 | cross_domain_amplification | |
t | e | urn:hailstone:chemistry_physics:structural_equation[417b5ae98458] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.20776v1.eq_1999 | \tildeμ= 0 | arxiv_extracted | ["e", "t", "i", "d", "l"] | arxiv | arxiv | arxiv:quant-ph:2604.20776v1 | cross_domain_amplification | |
v | r | urn:hailstone:chemistry_physics:structural_equation[c974d9f708cc] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.20482v1.eq_2000 | v_{\mathrm{avg}} = 20~\mathrm{m\,s^{-1}} | arxiv_extracted | ["a", "t", "m", "h", "r", "v"] | arxiv | arxiv | arxiv:quant-ph:2604.20482v1 | cross_domain_amplification | |
F | x | urn:hailstone:chemistry_physics:structural_equation[06e200379629] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00026v2.eq_2001 | ΔF_{\rm max}\!=\!+0.303 | arxiv_extracted | ["F", "a", "m", "r", "x"] | arxiv | arxiv | arxiv:quant-ph:2605.00026v2 | cross_domain_amplification | |
I | M | urn:hailstone:chemistry_physics:structural_equation[7ba194ad5b5c] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.19848v1.eq_2002 | |Δω_I| = 1/(2M) | arxiv_extracted | ["M", "I"] | arxiv | arxiv | arxiv:quant-ph:2604.19848v1 | cross_domain_amplification | |
S | B | urn:hailstone:chemistry_physics:structural_equation[9aaffd8b55b3] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.19848v1.eq_2003 | δS_{\text{BH}} = 4πr_+/(r_+ - r_-) | arxiv_extracted | ["e", "B", "t", "S", "x"] | arxiv | arxiv | arxiv:quant-ph:2604.19848v1 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[87625af16e06] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.18837v1.eq_2004 | \varepsilon^2 = 0.73 | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:quant-ph:2604.18837v1 | cross_domain_amplification | |
S | t | urn:hailstone:chemistry_physics:structural_equation[f8da2042524a] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.18662v1.eq_2005 | S(T) = \sqrt{\langleσ_x\rangle_c^2 + \langleσ_y\rangle_c^2} | arxiv_extracted | ["q", "t", "S", "r", "s", "T"] | arxiv | arxiv | arxiv:quant-ph:2604.18662v1 | cross_domain_amplification | |
i | e | urn:hailstone:chemistry_physics:structural_equation[24c5281a1b57] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.17917v1.eq_2006 | induces the Koopman unitary U on L2(M) and the crossed-product finite von Neumann algebra Mu\,:= L | arxiv_extracted | ["e", "i", "u", "c", "n", "d"] | arxiv | arxiv | arxiv:quant-ph:2604.17917v1 | cross_domain_amplification | |
p | r | urn:hailstone:chemistry_physics:structural_equation[85e404e73e3c] | 1 | structural_equation | 2 | arxiv.quant-ph.2605.00021v2.eq_2007 | p\mathrm{O}_2 = 0 | arxiv_extracted | ["a", "t", "m", "h", "p", "r"] | arxiv | arxiv | arxiv:quant-ph:2605.00021v2 | cross_domain_amplification | |
P | P | urn:hailstone:chemistry_physics:structural_equation[a42ff42bd6b2] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.16779v3.eq_2008 | Δξ_P = (P^\top P)^{-1}P^\top Q\,\hatξ_Q | arxiv_extracted | ["t", "p", "P", "o"] | arxiv | arxiv | arxiv:quant-ph:2604.16779v3 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[8a19e28e838f] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.16179v1.eq_2009 | \mathrm{Ra} = 10^{10} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.16179v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[987436e84dd5] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.16179v1.eq_2010 | \mathrm{Ra} = 10^{11} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.16179v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[8a19e28e838f] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.16179v1.eq_2011 | \mathrm{Ra} = 10^{10} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.16179v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[2d163e67d699] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.16179v1.eq_2012 | \mathrm{Ra} = 10^{9} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:quant-ph:2604.16179v1 | cross_domain_amplification | |
d | c | urn:hailstone:chemistry_physics:structural_equation[1c68d038c572] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.15445v1.eq_2013 | d_{\mathcal{U}} = 7/4 | arxiv_extracted | ["a", "t", "m", "h", "c", "d"] | arxiv | arxiv | arxiv:quant-ph:2604.15445v1 | cross_domain_amplification | |
d | c | urn:hailstone:chemistry_physics:structural_equation[19bd74362d82] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.15445v1.eq_2014 | d_{\mathcal{U}} = 5/2 | arxiv_extracted | ["a", "t", "m", "h", "c", "d"] | arxiv | arxiv | arxiv:quant-ph:2604.15445v1 | cross_domain_amplification | |
Z_k | l | urn:hailstone:chemistry_physics:structural_equation[97f538151546] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.15436v1.eq_2015 | |Z_k\rangle = Z^{1/2^{k}}|{+}\rangle | arxiv_extracted | ["g", "a", "Z_k", "r", "n", "l"] | arxiv | arxiv | arxiv:quant-ph:2604.15436v1 | cross_domain_amplification | |
Q | j | urn:hailstone:chemistry_physics:structural_equation[e423da7be9ff] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.15248v1.eq_2016 | Q(x) = \sum_{i < j} x_ix_j | arxiv_extracted | ["Q", "m_{i", "j", "u", "s", "x"] | arxiv | arxiv | arxiv:quant-ph:2604.15248v1 | cross_domain_amplification | |
s | k | urn:hailstone:chemistry_physics:structural_equation[0d744fff3da4] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.15214v2.eq_2017 | \sum_{i=1}^N α_i k(x,x_i) | arxiv_extracted | ["m_{i", "i", "u", "s", "k", "N"] | arxiv | arxiv | arxiv:quant-ph:2604.15214v2 | cross_domain_amplification | |
v | h | urn:hailstone:chemistry_physics:structural_equation[e8d3ef0571aa] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.15110v1.eq_2018 | \{ \vec{A} = [k_1(\hat{r}\times\vecΓ) + k_2\vecΓ + k_3(\vecΓ\cdot\hat{r})\hat{r}]/r, \varphi = f_1(r)\,(\vecΓ\cdot\hat{r}) + f_2(r)\} | arxiv_extracted | ["e", "k_1", "h", "A", "c", "v"] | arxiv | arxiv | arxiv:quant-ph:2604.15110v1 | cross_domain_amplification | |
C | k | urn:hailstone:chemistry_physics:structural_equation[73502c762b76] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.15051v1.eq_2019 | CPS_K(k=3) = 0.08788 | arxiv_extracted | ["S_K", "k", "P", "C"] | arxiv | arxiv | arxiv:quant-ph:2604.15051v1 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[c7f1ba8838ec] | 1 | structural_equation | 2 | arxiv.quant-ph.2604.15025v2.eq_2020 | \varepsilon = \max_k \varepsilon_k | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:quant-ph:2604.15025v2 | cross_domain_amplification |
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