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.

See quop_mpi.Ansatz.set_initial_state().

final state

The system state after the action of the ansatz unitary.

See quop_mpi.Ansatz.get_final_state().

ansatz unitary

The sequence of unitaries that constitute one ansatz iteration.

See quop_mpi.Ansatz.set_unitaries().

unitary

A unitary operator parameterised by an 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.Unitary and quop_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.Unitary and quop_mpi.propagator.

operator parameter

Variational parameter that parameterise the structure of an operator.

See quop_mpi.Unitary and quop_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.

See quop_mpi.propagator.diagonal.

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 iterations) of the ansatz unitary.

See quop_mpi.Ansatz.set_depth().

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 variational parameters grows linearly with the ansatz depth.

See quop_mpi.param for predefined parameter initialisation functions.

observables

A real vector of scalar quality values associated with each simulated basis state (lower is better). Defines the diagonal observables operator \(\hat{O}\).

See quop_mpi.Ansatz.set_observables().

objective function

The expectation value of the observables operator, minimised by the classical optimiser.

\[\langle \theta | \hat{O} | \theta \rangle\]

See quop_mpi.Ansatz.objective_function().

free parameters

The subset of variational parameters to be tuned via classical optimisation of the objective function. When using a parameter map, the free parameters are mapped to the full variational parameter vector.

See quop_mpi.Ansatz.set_parameter_map().

optimiser

The classical optimiser responsible for minimisation of the objective function via variation of the free variational parameters.

See quop_mpi.Ansatz.set_optimiser().