Glossary
- QVA
A Quantum Variational Algorithm. For a quantum system with system size basis states (i.e. a complex vector of length system size), QuOp_MPI simulates QVAs of the form,
\[|\theta \rangle=\left( \prod_{i = 1}^{D}\hat{U}(\theta_i) \right) | \Psi_0 \rangle\]where \(| \theta \rangle\) is the final state of the quantum system, \(D\) is the ansatz depth, \(\hat{U}\) is the ansatz unitary, \(\theta = \theta_i\) are real variational parameters and \(|\Psi_0\rangle\) is the initial state of the quantum system.
See
quop_mpi.Ansatz.- system state
The quantum system prior to or after the action of the ansatz unitary (the initial state or final state).
- system size
The number of basis states (size) of the simulated quantum system.
See
quop_mpi.Ansatz.- initial state
The starting system state, by default an equal superposition of all states.
- final state
The system state after the action of the ansatz unitary.
- ansatz unitary
The sequence of unitaries that constitute one ansatz iteration.
- unitary
A unitary operator parameterised by and arbitrary number of variational parameters,
\[\hat{U}_i(\phi) = \exp(-\text{i} (\phi_0 \hat{M}(\phi_1,...,\phi_m))\]where \(\phi = (\phi_0,...,\phi_m)\) are a sequential subsection of the variational parameters and \(\hat{M}\) is a matrix operator. The \(\phi_0\) is a unitary parameter and \((\phi_1,...,\phi_m)\) are operator parameters.
See
quop_mpi.Unitaryandquop_mpi.propagator.- operator
The matrix exponent of a unitary, parameterised by arbitrary number (none or more) of variational parameters.
- unitary parameter
A variational parameter that scales the elements of an operator via multiplication.
See
quop_mpi.Unitaryandquop_mpi.propagator.- operator parameter
Variational parameter that parametertise the structure of an operator.
See
quop_mpi.Unitaryandquop_mpi.propagator.- Phase-Shift Unitary
A unitary with a diagonal operator. Typically used to phase-encode the solution quality values of a particular optimisation problem.
- Mixing Unitary
A unitary whose operator has off-diagonal elements. Drives the transfer of probability amplitude between quantum basis states.
See,
- ansatz depth
The number of repeats (or s) of the ansatz unitary.
- variational parameters
Classically tunable parameters of an ansatz unitary. Each ansatz iteration is associated with its own subset of parameters, such that the total number of varitional parameters grows linearly with the ansatz depth.
- observables
A real vector of scalar quality values associated with each simulated basis state (lower is better). Defines the diagonal observables operator \(\hat{O}\).
- objective function
The expectation value of the observables operator, minimised by the classical optimiser.
\[\langle \theta | \hat{O} | \theta \rangle\]quop_mpi.Ansatz.objective_function().- free parameters
The subset of variational parameters to be tuned via classical optimisation of the objective function. See
quop_mpi.Ansatz.set_free_params().- optimiser
The classical optimiser responsible for minimisation of the objective function via variation of the free variational parameters.