Glossary
Adjoint: Transpose complex conjugate of an operator.
Basis
Bath system:
Bell's theorem
Bit flip error
Bloch sphere
Bra-ket notation:
Classical bit: A classical bit is represented by two different states of a classical system, which are represented by 1 and 0. (1.3)
Closed system
Commutator: The commutator of A and B, signified by [A,B], is AB-BA. Its value may be found by implementing the operators of A and B on a test function. If something has a commutator of zero, it is said to commute.
Complex conjugate:
Complex number: A complex number has a real and imaginary part. A complex number can be represented in the form a+bi or Ce^(i\theta).
Controlled not (CNOT gate)
Controlled operation: An operation on a state or set of states that is conditioned on another state or set of states.
Definite matrix (see matrix properties)
Density matrix
Density operator
Depolarizing error
Determinant: When rows or columns of a matrix are taken as vectors, the determinant is the volume enclosed by those vectors and corresponding parallel vectors creating parallelograms. Determinants only exist for square matrices.
Dirac delta function
DiVincenzo's requirements for quantum computing
Dot product: The scalar that results when two vectors have their corresponding components multiplied, and each of these products summed.
Eigenfunction
Eigenvalue
Eigenvector
Entangled state
Environment system (see Bath system)
EPR paradox
Euler's law
Expectation value:
Exponentiating a matrix (see matrix exponential)
Gate (see Quantum gate)
Gram-Schmidt decomposition (see Schmidt decomposition)
Grover's algorithm
H bar: Planck's constant divided by 2\pi
Hadamard gate
Hamiltonian: The operator for all conservative (able to be transformed) energy in the system. In quantum mechanics most energy is conservative.
Heisenberg uncertainty principle (see uncertainty principle)
Hermitian: An operator whose transpose equals its complex conjugate.
Hidden variable theory (see also local hidden variable theory):
Hilbert-Schmidt inner product (2.4)
i: square root of negative one
Identity matrix:
Isolated system (see Closed system)
Ket: See bra-ket notation
Kraus representation (or Kraus decomposition) (see SMR representation)
Linear map: A transformation from one vector to another using one operator once.
Local actions
Local hidden variable theory (see also hidden variable theory):
Matrix exponential
Matrix properties
Matrix transformation
Measurement
No cloning theorem: No operator can duplicate an arbitrary quantum state.
Noise
Normalization: A process of scaling some set of numbers or functions in order that an operation including them returns a desired value. For instance the set of all possible probabilities is usually scaled or normalized so they sum to one.
Open system
Operator-sum representation (see SMR representation)
Ordered basis
Orthogonal
Outer product
P gate:
Partial trace
Pauli matrices: The X,Y,Z gates.
Phase flip error
Phase gate: See Z gate or P gate
Planck's constant:
Polarization
Positive definite and semidefinite matrix (see matrix properties)
Probability for existing in a state:
Projector: A transformation such that P^2=P.
Projection postulate
Pure state
QKD: See quantum key distribution
Quantum bit: See Qubit
Quantum cryptography
Quantum dense coding
Quantum gate: A unitary transformation applied to one or more qubits.
Quantum key distribution:
Quantum NOT gate: see X gate
Qubit: A Qubit is represented by two states of a quantum mechanical system. (1.3)
Rank
Reduced density operator
RSA encryption
Schmidt decomposition
Schrodinger's Equation
set
Shor's algorithm
SMR representation
Spin
Spooky action at a distance
Superposition: A qubit state in superposition, \phi may be written as |\phi>=\alpha|0>+\beta|1> where \alpha and \beta are complex numbers.
Taylor expansion
Teleportation
Tensor product
Trace
Transpose
Turing machine
Uncertainty principle
Unitary transformation: A transformation which leaves the magnitude of any object it transforms the same.
Universal quantum computing
Universal set of gates (universality) (2.6)
X gate (2.3.2)
Vector space
Y gate
Z gate, or phase-flip gate (2.3.2)
