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