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Falconry term for small stones which were fed to hawks to aid in digestion
In falconry, rangle is a term used for small stones which are fed to hawks to aid in digestion. These stones, which are generally slightly larger than
Rangle
Principle of quantum mechanics
{\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } : | Ψ ⟩ = c 0 | 0 ⟩ + c 1 | 1 ⟩ , {\displaystyle |\Psi \rangle =c_{0}|0\rangle +c_{1}|1\rangle ,} where
Quantum_superposition
Basic circuit in quantum computing
{1}{2}}|00\rangle +{\frac {1}{2}}|01\rangle +{\frac {1}{2}}|10\rangle +{\frac {1}{2}}|11\rangle ={\frac {|00\rangle +|01\rangle +|10\rangle +|11\rangle }{2}}}
Quantum_logic_gate
Foundational principle in quantum physics
x\rangle &\langle p\rangle \\\langle x\rangle &\langle x\star x\rangle &\langle x\star p\rangle \\\langle p\rangle &\langle p\star x\rangle &\langle
Uncertainty_principle
Vector space with generalized dot product
denoted with angle brackets such as in ⟨ a , b ⟩ {\displaystyle \langle a,b\rangle } . Inner products allow formal definitions of intuitive geometric notions
Inner_product_space
Computer hardware technology that uses quantum mechanics
{\displaystyle \alpha |0\rangle +\beta |1\rangle } , where | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } are the standard basis
Quantum_computing
Basic unit of quantum information
{|0\rangle }} and | 1 ⟩ {\displaystyle {|1\rangle }} : | ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ {\displaystyle {|\psi \rangle }=\alpha {|0\rangle }+\beta {|1\rangle }}
Qubit
Physics phenomenon
{\displaystyle |\Phi ^{\pm }\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle _{A}\otimes |0\rangle _{B}\pm |1\rangle _{A}\otimes |1\rangle _{B})} | Ψ ± ⟩ = 1 2 ( |
Quantum_entanglement
Physical phenomenon
{\displaystyle \{|0\rangle \otimes |0\rangle ,|0\rangle \otimes |1\rangle ,|1\rangle \otimes |0\rangle ,|1\rangle \otimes |1\rangle \}} with the quantum
Quantum_teleportation
Description of a quantum-mechanical system
m{\frac {d}{dt}}\langle x\rangle =\langle p\rangle ;\quad {\frac {d}{dt}}\langle p\rangle =-\left\langle V'(X)\right\rangle .} Although the first of these
Schrödinger_equation
1936 Australian film
Rangle River is a 1936 Australian Western film directed by Clarence G. Badger based on a story by Zane Grey. Marion Hastings returns to her father Dan's
Rangle_River
Mathematical inequality relating inner products and norms
inner product space where ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the inner product. Examples of inner products include the real and
Cauchy–Schwarz_inequality
Notation for quantum states
{\begin{aligned}|A\rangle &=|B\rangle +|C\rangle \\|C\rangle &=(-1+2i)|D\rangle \\|D\rangle &=\int _{-\infty }^{\infty }e^{-x^{2}}|x\rangle \,\mathrm {d} x\
Bra–ket_notation
Mathematical approach to quantum physics
Schrödinger equation: H ^ | Ψ ⟩ = E | Ψ ⟩ {\displaystyle {\hat {H}}|\Psi \rangle =E|\Psi \rangle } ) and add an additional "perturbing" Hamiltonian ( H ′ {\displaystyle
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Theorem about the dual of a Hilbert space
\rangle =\langle \,y,\cdot \,\rangle :H\to \mathbb {F} \quad {\text{ defined by }}\quad h\mapsto \langle \,h\mid y\,\rangle =\langle \,y,h\,\rangle .}
Riesz_representation_theorem
Quantum search algorithm
{\begin{cases}U_{f}|x\rangle |y\rangle =|x\rangle |\neg y\rangle &{\text{for }}x=\omega {\text{, that is, }}f(x)=1,\\U_{f}|x\rangle |y\rangle =|x\rangle |y\rangle &{\text{for
Grover's_algorithm
Mathematical description of quantum state
{\begin{aligned}|\Psi \rangle =I|\Psi \rangle &=\int |x\rangle \langle x|\Psi \rangle dx=\int \Psi (x)|x\rangle dx,\\|\Psi \rangle =I|\Psi \rangle &=\int |p\rangle \langle
Wave_function
Loss of quantum coherence
|{\text{before}}\rangle =\sum _{i}|i\rangle |\epsilon \rangle \langle i|\psi \rangle ,} where | i ⟩ | ϵ ⟩ {\displaystyle |i\rangle |\epsilon \rangle } is shorthand
Quantum_decoherence
Quantum mechanics principle
y ⟩ ) ) . {\displaystyle \langle \psi |{\Big (}(|x\rangle +|y\rangle )\otimes (|x\rangle +|y\rangle ){\Big )}.} This is zero, because the two particles
Pauli_exclusion_principle
Theorem in quantum mechanics
m{\frac {d}{dt}}\langle x\rangle =\langle p\rangle ,\;\;{\frac {d}{dt}}\langle p\rangle =-\left\langle V'(x)\right\rangle ~.} The Ehrenfest theorem is
Ehrenfest_theorem
Quantum mechanical model
{\begin{aligned}{\hat {a}}^{\dagger }|n\rangle &={\sqrt {n+1}}|n+1\rangle \\{\hat {a}}|n\rangle &={\sqrt {n}}|n-1\rangle .\end{aligned}}} From the relations
Quantum_harmonic_oscillator
Interaction of a quantum system with a classical observer
{2}}}(|0\rangle _{A}\otimes |0\rangle _{B}-|1\rangle _{A}\otimes |1\rangle _{B})\\|\Psi ^{+}\rangle &={\frac {1}{\sqrt {2}}}(|0\rangle _{A}\otimes |1\rangle _{B}+|1\rangle
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Mathematical entity to describe the probability of each possible measurement on a system
\left|\psi \right\rangle ={\frac {1}{\sqrt {2}}}{\bigl (}\left|\uparrow \downarrow \right\rangle -\left|\downarrow \uparrow \right\rangle {\bigr )},} which
Quantum_state
Quantum states of two qubits
{1}{2{\sqrt {2}}}}((|+\rangle _{A}+|-\rangle _{A})(|+\rangle _{B}+|-\rangle _{B})-(|+\rangle _{A}-|-\rangle _{A})(|+\rangle _{B}-|-\rangle _{B}))} = 1 2 2 (
Bell_state
Representation of a quantum mechanical system
|\psi \rangle =\cos \left(\theta /2\right)|0\rangle \,+\,e^{i\phi }\sin \left(\theta /2\right)|1\rangle =\cos \left(\theta /2\right)|0\rangle \,+\,(\cos
Bloch_sphere
Intrinsic quantum property of particles
y ⟩ , ⟨ S z ⟩ ] {\textstyle \langle S\rangle =[\langle S_{x}\rangle ,\langle S_{y}\rangle ,\langle S_{z}\rangle ]} . This vector then would describe the
Spin_(physics)
Conjugate transpose of an operator in infinite dimensions
{\displaystyle \langle Ax,y\rangle =\langle x,A^{*}y\rangle ,} where ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the inner product on the
Hermitian_adjoint
Mathematical structures that allow quantum mechanics to be explained
{\displaystyle |\psi _{k}\rangle \sim |\psi _{l}\rangle \;\;\Leftrightarrow \;\;|\psi _{k}\rangle =e^{i\alpha }|\psi _{l}\rangle ,\quad \ \alpha \in \mathbb
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Historical critique of quantum mechanics
\right\rangle ={\frac {1}{\sqrt {2}}}{\biggl (}\left|+z\right\rangle \otimes \left|-z\right\rangle -\left|-z\right\rangle \otimes \left|+z\right\rangle {\biggr
Einstein–Podolsky–Rosen paradox
Einstein–Podolsky–Rosen_paradox
Mathematical tool in quantum physics
|\psi \rangle =(|\psi _{1}\rangle +|\psi _{2}\rangle )/{\sqrt {2}},} with density matrix | ψ ⟩ ⟨ ψ | = 1 2 ( 1 1 1 1 ) . {\displaystyle |\psi \rangle \langle
Density_matrix
Number-state in quantum mechanics
n_{{\mathbf {k} }_{i}}...\rangle =n_{{\mathbf {k} }_{i}}|n_{{\mathbf {k} }_{1}},n_{{\mathbf {k} }_{2}},..n_{{\mathbf {k} }_{i}}...\rangle } Hence the Fock state
Fock_state
Theorem in quantum information science
B {\displaystyle U(|\phi \rangle _{A}\otimes |e\rangle _{B})=e^{i\alpha (\phi ,e)}|\phi \rangle _{A}\otimes |\phi \rangle _{B}} for some real number
No-cloning_theorem
Technique in quantum computation
{\displaystyle \mathrm {Re} \langle \psi |U|\psi \rangle } , where | ψ ⟩ {\displaystyle |\psi \rangle } is a quantum state and U {\displaystyle U} is a
Hadamard_test
Expected value of a quantum measurement
⟩ {\displaystyle \langle A\rangle =\langle \psi |A|\psi \rangle } in Dirac notation with | ψ ⟩ {\displaystyle |\psi \rangle } a normalized state vector
Expectation value (quantum mechanics)
Expectation_value_(quantum_mechanics)
Physics theorem
, {\displaystyle \langle T\rangle =-{\frac {1}{2}}\,\sum _{k=1}^{N}\langle \mathbf {F} _{k}\cdot \mathbf {r} _{k}\rangle ,} where T {\displaystyle T}
Virial_theorem
Description of physical properties at the atomic and subatomic scale
\sigma _{X}={\textstyle {\sqrt {\left\langle X^{2}\right\rangle -\left\langle X\right\rangle ^{2}}}},} and likewise for the momentum: σ P = ⟨ P 2 ⟩ −
Quantum_mechanics
Generalized measurement in quantum mechanics
|\gamma \rangle ={\frac {1}{\sqrt {2(1+|\langle \varphi |\psi \rangle |)}}}(|\psi \rangle +e^{i\arg(\langle \varphi |\psi \rangle )}|\varphi \rangle ).} Note
POVM
Quantum logic gate
|++\rangle =|+\rangle \otimes |+\rangle ={\frac {1}{2}}(|0\rangle +|1\rangle )\otimes (|0\rangle +|1\rangle )={\frac {1}{2}}(|00\rangle +|01\rangle +|10\rangle
Controlled_NOT_gate
Quantum computing technique
| g 1 ⟩ ) {\displaystyle {\frac {1}{\sqrt {2}}}(|0\rangle |g_{0}\rangle +|1\rangle |g_{1}\rangle )} where g 0 {\displaystyle g_{0}} and g 1 {\displaystyle
Uncomputation
Testable implication of local hidden-variable theories
rangle =\cos \theta \,|0\rangle +\sin \theta \,|1\rangle ,\qquad |a_{1}\rangle =-\sin \theta \,|0\rangle +\cos \theta \,|1\rangle ,\\&|b_{0}\rangle =\cos
CHSH_inequality
Type of quantum computer built out of Rydberg atoms
{\displaystyle H_{i}={\frac {1}{2}}((\Omega |1\rangle _{i}\langle r|+\Omega ^{*}|r\rangle _{i}\langle 1|)-\Delta |r\rangle _{i}\langle r|} is the Hamiltonian of
Neutral_atom_quantum_computer
Spectral line splitting in magnetic field
_{i}(g_{l}{\vec {l}}_{i}+g_{s}{\vec {s}}_{i}){\Big \rangle }={\big \langle }(g_{l}{\vec {L}}+g_{s}{\vec {S}}){\big \rangle },} where L → {\displaystyle {\vec {L}}}
Zeeman_effect
Specific quantum state of a quantum harmonic oscillator
{\displaystyle \left({X}-\langle {X}\rangle \right)\,|\alpha \rangle =-i\left({P}-\langle {P}\rangle \right)\,|\alpha \rangle {\text{,}}} or, equivalently, (
Coherent_state
Energy level of a quantum system
{H}}|\psi \rangle &={\hat {H}}(c_{1}|\psi _{1}\rangle +c_{2}|\psi _{2}\rangle )\\&=c_{1}{\hat {H}}|\psi _{1}\rangle +c_{2}{\hat {H}}|\psi _{2}\rangle \\&=E(c_{1}|\psi
Degenerate_energy_levels
Process in quantum computing
|0_{\rm {S}}\rangle ={\frac {1}{2{\sqrt {2}}}}(|000\rangle +|111\rangle )\otimes (|000\rangle +|111\rangle )\otimes (|000\rangle +|111\rangle )} | 1 S ⟩
Quantum_error_correction
American politician (1930–2025)
Charles Bernard Rangel (/ˈræŋɡəl/ RANG-gəl; June 11, 1930 – May 26, 2025) was an American politician who served as U.S. representative for districts in
Charles_Rangel
Coefficients in angular momentum eigenstates of quantum systems
m\rangle &=\hbar ^{2}j(j+1)|j\,m\rangle ,&j&\in \{0,{\tfrac {1}{2}},1,{\tfrac {3}{2}},\ldots \}\\\mathrm {j_{z}} |j\,m\rangle &=\hbar m|j\,m\rangle ,&m&\in
Clebsch–Gordan_coefficients
Type of vector space in math
{\displaystyle \|u+v\|^{2}=\langle u+v,u+v\rangle =\langle u,u\rangle +2\,\operatorname {Re} \langle u,v\rangle +\langle v,v\rangle =\|u\|^{2}+\|v\|^{2}\,.} By induction
Hilbert_space
Formulation of quantum mechanics
) ⟩ {\displaystyle |\psi (t_{0})\rangle } at time t0 to a state vector | ψ ( t ) ⟩ {\displaystyle |\psi (t)\rangle } at time t, the time-evolution operator
Schrödinger_picture
Concept in quantum mechanics
t ) | 1 ⟩ + c 2 ( t ) | 2 ⟩ . {\displaystyle |\Psi \rangle =c_{1}(t)|1\rangle +c_{2}(t)|2\rangle .} With the field absent, the energetic separation of
Adiabatic_theorem
Quantum algorithm for integer factorization
ψ ⟩ {\displaystyle |0\rangle |\psi \rangle } to output states close to | ϕ ⟩ | ψ ⟩ {\displaystyle |\phi \rangle |\psi \rangle } , where ϕ {\displaystyle
Shor's_algorithm
Abstract algebra concept
subset of a group G {\displaystyle G} , then ⟨ S ⟩ {\displaystyle \langle S\rangle } , the subgroup generated by S {\displaystyle S} , is the smallest subgroup
Generating_set_of_a_group
Type of quantum state
{\begin{cases}\langle x\rangle =\langle \langle z\rangle |X|\langle z\rangle \rangle \\\langle p\rangle =\langle \langle z\rangle |P|\langle z\rangle \rangle \\A=\langle
Squeezed_coherent_state
Mechanism in quantum computing
{\displaystyle |1\rangle |\psi \rangle \xrightarrow {{\text{Controlled}}-U} |1\rangle U|\psi \rangle =|1\rangle e^{i\phi }\cong |1\rangle |\psi \rangle } This shows
Phase_kickback
Quantum mechanical phenomenon
{\displaystyle |\psi (t)\rangle =c_{+}(t)|+\rangle +c_{-}(t)|-\rangle } in the stationary reference frame, where | + ⟩ {\displaystyle |+\rangle } and | − ⟩ {\displaystyle
Rabi_cycle
Matrix of inner products of vectors
j = ⟨ v i , v j ⟩ {\displaystyle G_{ij}=\left\langle v_{i},v_{j}\right\rangle } . If the vectors v 1 , … , v n {\displaystyle v_{1},\dots ,v_{n}} are
Gram_matrix
Orthonormalization of a set of vectors
{u} \rangle }{\langle \mathbf {u} ,\mathbf {u} \rangle }}\,\mathbf {u} ,} where ⟨ v , u ⟩ {\displaystyle \langle \mathbf {v} ,\mathbf {u} \rangle } denotes
Gram–Schmidt_process
Theorem in classical statistical mechanics
{pot} }}{\partial q}}\right\rangle =\langle q\cdot sCq^{s-1}\rangle =\langle sCq^{s}\rangle =s\langle H_{\mathrm {pot} }\rangle .} Thus, the average potential
Equipartition_theorem
{\displaystyle |x\rangle } - position eigenstate | α ⟩ , | β ⟩ , | γ ⟩ . . . {\displaystyle |\alpha \rangle ,|\beta \rangle ,|\gamma \rangle ...} - wave function
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
In functional analysis, a Hilbert space
{\displaystyle f\in H} , ⟨ f , K x ⟩ = f ( x ) . {\displaystyle \langle f,K_{x}\rangle =f(x).} The function K x {\displaystyle K_{x}} is then called the reproducing
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
Quantum operator for the sum of energies of a system
| a ⟩ ) = H ( U | a ⟩ ) . {\displaystyle UH|a\rangle =UE_{a}|a\rangle =E_{a}(U|a\rangle )=H\;(U|a\rangle ).} Since U {\displaystyle U} is nontrivial, at
Hamiltonian (quantum mechanics)
Hamiltonian_(quantum_mechanics)
Theorem used in quantum mechanics for angular momentum calculations
{\displaystyle \langle j\,m|T_{q}^{(k)}|j'\,m'\rangle =\langle j'\,m'\,k\,q|j\,m\rangle \langle j\|T^{(k)}\|j'\rangle ,} where T q ( k ) {\displaystyle T_{q}^{(k)}}
Wigner–Eckart_theorem
"Highly entangled" quantum state of 3 or more qubits
⟩ = | 000 ⟩ + | 111 ⟩ 2 {\displaystyle |\mathrm {GHZ} \rangle ={\frac {|000\rangle +|111\rangle }{\sqrt {2}}}} where the 0 or 1 values of the qubit correspond
Greenberger–Horne–Zeilinger state
Greenberger–Horne–Zeilinger_state
Quantum mechanical effect
(x_{1}-x_{2})^{2}\rangle _{\pm }=\langle x^{2}\rangle _{a}+\langle x^{2}\rangle _{b}-2\langle x\rangle _{a}\langle x\rangle _{b}\mp 2{\big |}\langle x\rangle _{ab}{\big
Exchange_interaction
{y}})\rangle }{\langle \rho ({\mathit {x}})\rangle \langle \rho ({\mathit {y}})\rangle }}-1={\frac {\langle \rho ({\mathit {x}})\rho ({\mathit {y}})\rangle
BGS_conjecture
Statistical physics theorem
⟩ 0 . {\displaystyle A(t)=\langle [x(t)-\langle x\rangle _{0}][x(0)-\langle x\rangle _{0}]\rangle _{0}.} Note that in the absence of a field the system
Fluctuation–dissipation theorem
Fluctuation–dissipation_theorem
System for describing optical polarization
|H\rangle } and | V ⟩ {\displaystyle |V\rangle } | D ⟩ {\displaystyle |D\rangle } and | A ⟩ {\displaystyle |A\rangle } | R ⟩ {\displaystyle |R\rangle }
Jones_calculus
Deterministic quantum algorithm
{1}{2}}(|0\rangle (|f(0)\oplus 0\rangle -|f(0)\oplus 1\rangle )+|1\rangle (|f(1)\oplus 0\rangle -|f(1)\oplus 1\rangle ))\\&={\frac {1}{2}}((-1)^{f(0)}|0\rangle (|0\rangle
Deutsch–Jozsa_algorithm
Quantum physics of light and matter in a cavity
{\displaystyle (\alpha |g\rangle +\beta |e\rangle )|0\rangle \leftrightarrow |g\rangle (\alpha |0\rangle +\beta |1\rangle )} , and can be repeated to
Cavity quantum electrodynamics
Cavity_quantum_electrodynamics
Calculation rule in quantum mechanics
measured in a system with normalized wave function | ψ ⟩ {\displaystyle |\psi \rangle } (see Bra–ket notation), corresponds to a self-adjoint operator A {\displaystyle
Born_rule
Operator in probability theory
y)=\int _{B}\langle x,z\rangle \langle y,z\rangle \,\mathrm {d} \mathbf {P} (z)} where ⟨ x , z ⟩ {\displaystyle \langle x,z\rangle } is now the value of
Covariance_operator
Objects that generalize functions
it is conventional to write ⟨ T , φ ⟩ {\displaystyle \langle T,\varphi \rangle } for the value of T acting on a test function φ {\displaystyle \varphi
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Specification of a mathematical group by generators and relations
a^{n}=1\rangle ,} where 1 is the group identity. This may be written equivalently as ⟨ a ∣ a n ⟩ , {\displaystyle \langle a\mid a^{n}\rangle ,} thanks
Presentation_of_a_group
Interpretation of quantum mechanics
}\rangle +\beta |{\downarrow }\rangle \right)\otimes |{\text{init}}\rangle &\rightarrow &\alpha |{\uparrow }\rangle \otimes |O_{\uparrow }\rangle +\beta
Relational_quantum_mechanics
Process by which a quantum system takes on a definitive state
= | ϕ i ⟩ . {\displaystyle |\psi \rangle =\sum _{i}c_{i}|\phi _{i}\rangle \mapsto |\psi '\rangle =|\phi _{i}\rangle .} where the arrow represents a measurement
Wave_function_collapse
Physical quantity conserved throughout a motion
\right\rangle +\left\langle \psi \right|{\frac {dQ}{dt}}\left|\psi \right\rangle +\left\langle \psi \right|Q\left({\frac {d}{dt}}\left|\psi \right\rangle
Constant_of_motion
Model in quantum optics
\left\{|g,0\rangle ;|e,0\rangle ,|g,1\rangle ;\cdots ;|e,n-1\rangle ,|g,n\rangle \right\}} where the states { | n ⟩ } {\displaystyle \left\{|n\rangle \right\}}
Jaynes–Cummings_model
Concept in linear algebra
\cdot \rangle } and unit vector u ∈ V {\displaystyle u\in V} as H u ( x ) := x − 2 ⟨ x , u ⟩ u . {\displaystyle H_{u}(x):=x-2\,\langle x,u\rangle \,u\,
Householder_transformation
Deviations from local realism
_{AB}\right\rangle ={\frac {1}{\sqrt {2}}}\left(\left|0\right\rangle _{A}\left|1\right\rangle _{B}-\left|1\right\rangle _{A}\left|0\right\rangle _{B}\right)={\frac
Quantum_nonlocality
Theorem in quantum mechanics
}\rangle } , i.e. H ^ λ | ψ λ ⟩ = E λ | ψ λ ⟩ . {\displaystyle {\hat {H}}_{\lambda }|\psi _{\lambda }\rangle =E_{\lambda }|\psi _{\lambda }\rangle .}
Hellmann–Feynman_theorem
Graphical language for quantum processes
{\displaystyle |0\rangle ,|1\rangle } and the Hadamard-transformed basis | + ⟩ = | 0 ⟩ + | 1 ⟩ 2 {\displaystyle |+\rangle ={\frac {|0\rangle +|1\rangle }{\sqrt
ZX-calculus
Matrix representing the effect of scattering on a physical system
0 ⟩ ≡ | 0 ⟩ . {\displaystyle |\mathrm {i} ,0\rangle =|\mathrm {f} ,0\rangle =|*,0\rangle \equiv |0\rangle .} The interaction is assumed adiabatically turned
S-matrix
Quantum computing implementation
{\displaystyle |g\rangle {\text{ and }}|e\rangle } (for ground and excited), or | 0 ⟩ and | 1 ⟩ {\displaystyle |0\rangle {\text{ and }}|1\rangle } . Superconducting
Superconducting quantum computing
Superconducting_quantum_computing
Binary operation, takes two matrices and returns a scalar
often denoted ⟨ A , B ⟩ F {\displaystyle \langle \mathbf {A} ,\mathbf {B} \rangle _{\mathrm {F} }} or A : B {\displaystyle {\rm {A:{\rm {B}}}}} . The operation
Frobenius_inner_product
Numerical calculations carrying along derivatives
u'\right\rangle +\left\langle v,v'\right\rangle &=\left\langle u+v,u'+v'\right\rangle \\[4px]\left\langle u,u'\right\rangle -\left\langle v,v'\right\rangle &=\left\langle
Automatic_differentiation
Transition rate formula
the initial state | i ⟩ {\displaystyle |i\rangle } to a set of final states | f ⟩ {\displaystyle |f\rangle } is essentially constant. It is given, to
Fermi's_golden_rule
Quantum state of multiple particles represented as complex matrices
|\Psi \rangle =\sum _{\{s\}}\operatorname {Tr} \left[A_{1}^{(s_{1})}A_{2}^{(s_{2})}\cdots A_{N}^{(s_{N})}\right]|s_{1}s_{2}\ldots s_{N}\rangle .} For
Matrix_product_state
Entangled 3-qubit quantum state
+ | 100 ⟩ ) {\displaystyle |\mathrm {W} \rangle ={\frac {1}{\sqrt {3}}}(|001\rangle +|010\rangle +|100\rangle )} and which is remarkable for representing
W_state
Technique for comparing quantum states
\psi \rangle +|1,\phi ,\psi \rangle +|0,\psi ,\phi \rangle -|1,\psi ,\phi \rangle )={\frac {1}{2}}|0\rangle (|\phi ,\psi \rangle +|\psi ,\phi \rangle )+{\frac
Swap_test
Formulation of classical mechanics in terms of Hilbert spaces
{\displaystyle m{\frac {d}{dt}}\langle x\rangle =\langle p\rangle ,\qquad {\frac {d}{dt}}\langle p\rangle =\langle -U'(x)\rangle ,} aka, Newton's laws of motion
Koopman–von Neumann classical mechanics
Koopman–von_Neumann_classical_mechanics
Quantization giving rise to photons
{k} ,\mu \rangle &=h\nu |\mathbf {k} ,\mu \rangle &&{\hbox{with}}\quad \nu =c|\mathbf {k} |\\P_{\textrm {EM}}|\mathbf {k} ,\mu \rangle &=\hbar \mathbf
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Family of quantum error correcting codes
{\displaystyle |D_{2}^{4}\rangle ={\frac {|0011\rangle +|0101\rangle +|1001\rangle +|0110\rangle +|1010\rangle +|1100\rangle }{\sqrt {6}}}} The real parameter
Gnu_code
Operators useful in quantum mechanics
{\begin{aligned}a\left|n\right\rangle &=(n)\left|n{-}1\right\rangle \\[1ex]a^{\dagger }\left|n\right\rangle &=\left|n{+}1\right\rangle \end{aligned}}} note that
Creation and annihilation operators
Creation_and_annihilation_operators
Rule system for formal languages
{\text{Stmt}}\rangle \to \langle {\text{Id}}\rangle =\langle {\text{Expr}}\rangle ;} replaces ⟨ Stmt ⟩ {\displaystyle \langle {\text{Stmt}}\rangle } with ⟨
Context-free_grammar
{n}})^{2}\right\rangle -\langle {\hat {n}}\rangle }{\langle {\hat {n}}\rangle }}={\frac {\langle {\hat {n}}^{2}\rangle -\langle {\hat {n}}\rangle ^{2}}{\langle
Mandel_Q_parameter
Algorithm
a 2 , x ⟩ = b 2 } , … {\textstyle \{x:\langle a_{1},x\rangle =b_{1}\},\{x:\langle a_{2},x\rangle =b_{2}\},\dots } . There are versions of the method that
Kaczmarz_method
Magnetic property of ordinary materials
x^{2}\right\rangle \;=\;\left\langle y^{2}\right\rangle \;=\;\left\langle z^{2}\right\rangle \;=\;{\frac {1}{3}}\left\langle r^{2}\right\rangle } , where
Diamagnetism
Type of error correction in quantum computing
{L}}\rangle ={\frac {1}{4}}[&|00000\rangle +|10010\rangle +|01001\rangle +|10100\rangle +|01010\rangle -|11011\rangle -|00110\rangle -|11000\rangle \\-&|11101\rangle
Five-qubit error correcting code
Five-qubit_error_correcting_code
Quantum-mechanical many-body entangled state
{\displaystyle |{\text{NOON}}\rangle ={\frac {|N\rangle _{a}|0\rangle _{b}+e^{iN\theta }|{0}\rangle _{a}|{N}\rangle _{b}}{\sqrt {2}}},\,} which represents
NOON_state
In mathematics, a linear operator acting on inner product space
y\rangle =|\lambda |^{2}\langle Ax,x\rangle +\lambda ^{*}\mu \langle Ax,y\rangle +\lambda \mu ^{*}\langle Ay,x\rangle +|\mu |^{2}\langle Ay,y\rangle \\[1mm]=|\lambda
Positive_operator
RANGLE
RANGLE
RANGLE
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
One with Shining
Surname or Lastname
English
English : probably a respelling of Lownsbrough, a habitational name from Londesborough in the East Riding of Yorkshire, which is named with the Old Norse personal name Lothinn + Old English burh ‘stronghold’.
Boy/Male
German Hungarian Swedish
Powerful ruler.
Girl/Female
English
and Kayla, meaning: keeper of the keys; pure.
Boy/Male
Hindu
One possessing fame, Lord of fame
Boy/Male
Muslim
Mercy
Boy/Male
Australian, Dutch, German, Greek
Manly; Warrior
Boy/Male
Hindu
To decorate
Girl/Female
Indian, Telugu
Goddess of Wealth
Girl/Female
Bengali, Hindu, Indian, Marathi, Sanskrit, Traditional
Flag
RANGLE
RANGLE
RANGLE
RANGLE
RANGLE
v. i.
To range about in an irregular manner.