A vocabulary for the journey
Concise starting definitions, with the distinctions that matter. Follow each term back to the full lesson for equations, assumptions, and source context.
52 terms, linked to their lesson context.
A
- Active space
- The selected orbitals and electrons treated explicitly in a correlated calculation.
Reducing this space is a model approximation, not merely a smaller file or a guaranteed accuracy improvement.
- Amplitude
- A real or complex coefficient of a quantum state in a specified basis. Its absolute square contributes an outcome probability.
Relative signs and phases carry information that probabilities alone do not.
- Amplitude amplification
- A coherent reflection-based procedure that increases the weight in a specifically marked subspace.
The oracle defines what is “good.” Its implementation and repeated cost matter.
B
- Basis set
- A finite collection of functions used to expand one-electron orbital shapes.
Basis error is distinct from error in solving the model in that basis.
- Bitstring
- A sequence of zeros and ones representing an indexed register value or measurement outcome.
Bit order and its relation to orbital or qubit indices are conventions, not universal facts.
- Block encoding
- A construction placing a scaled operator in an ancilla-selected block of a larger unitary.
Normalization and the chosen unitary’s spectral map are needed to interpret an estimated phase.
C
- CASCI
- Complete active-space configuration interaction: solve the full determinant problem within chosen active orbitals, with those orbitals fixed.
It is complete within the selected space, not automatically exact for the full molecular problem.
- CASSCF
- Complete active-space self-consistent field: optimize active-space configuration coefficients together with orbitals.
Orbital optimization does not automatically recover all correlation outside the active space.
- Chemical accuracy
- An application-dependent error target used when deciding whether an approximate result is useful for chemistry.
State the actual target and property; an energy tolerance is not a device failure probability.
- Cholesky factorization
- A structured factor representation that can exploit the Coulomb tensor’s pair-index properties.
Thresholds, reconstruction cost, and approximation error must travel with the representation.
- Code distance
- A property of an error-correcting code related to the minimum size of an undetectable logical error.
Physical overhead and logical reliability depend on a full code and noise model, not distance alone.
- Configuration interaction
- A method that expresses a many-electron state as a linear combination of determinants and solves for the coefficients.
Which determinants are retained defines the CI problem; full, active-space, and selected CI are distinct.
- Correlation
- Many-electron behavior that cannot be captured adequately by an independent-particle description alone.
The relevant meaning is the structure of the joint state, not just a statistical association between two columns.
- Coupled cluster
- A correlated-state method using an exponential excitation-operator parameterization around a reference.
Cluster amplitudes and left-state information are not simply a normalized vector of CI coefficients.
D
- Density functional theory
- An electronic-structure approach organized around the density and an approximate energy functional.
Kohn-Sham DFT shares SCF machinery with HF but uses a different energy model.
- Density matrix
- An operator describing a quantum state or a reduced part of it, including expectation-value information.
A one-electron reduced density is not the full many-electron amplitude vector.
- Determinant
- An antisymmetrized product of occupied spin orbitals, used as a many-electron basis state.
Antisymmetry supplies the sign behavior required for indistinguishable fermions.
- DIIS
- Direct inversion in the iterative subspace, a method that uses prior residuals to accelerate iterative solutions.
Convergence acceleration is not a proof that the final solution is stable or scientifically sufficient.
E
- Effective core potential
- An effective interaction replacing an explicit treatment of some core-electron effects.
It changes the modeled Hamiltonian and is distinct from freezing occupations or selecting a basis.
- Eigenstate
- A state that an operator maps to itself multiplied by a scalar eigenvalue.
For a Hamiltonian, that eigenvalue is an energy; a trial superposition need not have one definite energy.
F
H
- Hamiltonian
- The energy operator specifying the interactions and dynamics of the selected physical model.
The Hamiltonian and the state are different objects. Their basis, ordering, units, and constants must agree.
- Hartree-Fock
- A mean-field approximation that optimizes a single-determinant description through its orbitals.
A converged HF state is not necessarily stable, globally optimal, or accurate enough for strong correlation.
- Hubbard model
- A lattice model combining hopping with local interaction terms, commonly used to study correlated occupation.
It is a parameterized model, not automatically a first-principles description of a particular material.
J
- Jordan-Wigner mapping
- A fermion-to-qubit mapping using parity strings to preserve fermionic signs.
Mode ordering and encoded-state construction must match the mapped Hamiltonian.
L
M
- Magic-state factory
- A fault-tolerant resource used to prepare special states needed for certain non-Clifford operations.
Factories can materially affect physical qubits and runtime; the toy patch calculator deliberately excludes them.
- Measurement shot
- One repetition that prepares, executes, and measures the specified experiment.
More shots can reduce sampling uncertainty without correcting systematic bias.
N
O
P
- Pauli operator
- One of the single-qubit operators I, X, Y, and Z, or a tensor product of them over a register.
Mapped Hamiltonians often become weighted sums of these products.
- Phase estimation
- A family of algorithms for resolving eigenphases of a specified unitary.
Energy decoding needs a convention, scale, and alias/branch choice; a phase is not an automatically unique ground energy.
- Physical qubit
- A device-level quantum information carrier.
Turning physical qubits into reliable logical operations requires a specified error-correction and hardware model.
- Product formula
- An approximation that composes evolutions of individual Hamiltonian pieces to approximate evolution under their sum.
Noncommutation, formula order, time, and step count determine the approximation behavior.
Q
- Qubit-wise commutation
- Compatibility in which each position’s nonidentity Pauli factors commute.
It is stricter than global commutation and supports a shared product measurement basis.
R
- Reduced density matrix
- A partial description retaining information for observables involving a limited number of particles or modes.
Availability and cost are capabilities of the state/solver, not automatic properties of every container.
S
- Self-consistent field
- An iterative procedure seeking agreement between a density and the effective operator whose solution produces it.
Stopping criteria and stability checks are different diagnostics.
- Spin orbital
- A spatial orbital paired with a spin function, defining one one-electron mode.
Each spin orbital can be occupied at most once; a spatial orbital can host two opposite-spin electrons.
T
- Tapering
- A reduction of a qubit representation using known symmetry-sector information.
The state and observables must be transformed consistently, and the chosen sector must contain the intended physics.
U
V
W
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