This glossary contains the words people can use to study variational quantum algorithms.
Area law
collocation
A law according to which entropy of a subsystem scales with system boundary size
Example: Such area laws have been proven for all gapped spin models
en: Закон границ
Converge
verb
Approach a limit
Example: In this work, we analytically study the convergence properties of hybrid variational optimizations.
en: Сходиться
Deteriorate
verb
Get worse
Example: We show that the convergence speed is typically unaffected by the presence of a small amount of noise, while the accuracy of the solution typically deteriorates as the noise strength increases.
en: Ухудшаться
Detrimental
adjective
Negative, destructive
Example: Different authors have studied the effect of noise in protocols designed for the noiseless case and found that noise is usually detrimental
en: Вредоносный, разрушительный
Discernible
adjective
Measurable, distinguishable
Example: The variational approach employed here found an experimentally discernible improvement of 5.77% and 3.95% for three and four qubits, respectively
en: Различимый, измеримый
Embody
verb
Represent, include somehting itself
Example: The task is that of solving some combinatorial problem, with ˆH an Ising-like Hamiltonian whose ground state embodies the solution of the problem.
en: Включать, представлять собой
Gapped hamiltonian
collocation
A hamiltonian with a finite energy difference between ground and exited states
Example: One might wonder whether an exponentially dimensional subspace of strong area law states can be constructed while imposing decaying two-point correlations for distant observables, a property known to occur in ground states of local gapped Hamiltonians
en: Гамильтониан с щелью
Ground state
collocation
Quantum state with the lowest eigenvalue(energy)
Example: Yet, it has become clear in recent years that ground states—and a number of other natural states—usually occupy only a tiny fraction of this Hilbert space
en: Основное состояние
Hilbert space
collocation
Vector space of all possible quantum states of the considered system
Example: However, naive numerical descriptions of such quantum systems require prohibitive resources, for the simple reason that the dimension of the underlying Hilbert space grows exponentially in the system size.
en: Гильбертово пространство
Local hamiltonian
collocation
Hamiltonian which includes only the local terms (connecting neighboring sites)
Example: Moreover, not all states satisfying area laws are eigenstates of local Hamiltonians.
en: Локальный гамильтониан
Objective function
collocation
A function that should be optimized to prepare the target state
Example: The objective function will depend on the problem to be solved.
en: Целевая функция/функция стоимости
Problem Hamiltonian
collocation
The hamiltonian which is minimized with the considered algorithm
Example: In our algorithm, mixing and problem (oracle) Hamiltonians are applied to the system in a sequence that is periodic in time.
en: Целевой Гамильтониан
Quantum advantage
collocation
An advantage that quantum systems can provide over the classical ones
Example: It remains an open question whether QAOA circuits provide a quantum advantage for approximate optimization.
en: Квантовое превосходство
Robustness
noun
An ability to resist, stay unaffected
Example: Using this bound, we study the convergence property of the quantum approximate optimization algorithm under realistic noise models, showing the robustness of the algorithm against different noise strengths.
en: Устойчивость, сопротивляемость
Spin-coherent states
collocation
States obtained by the action of exponentiated mixer on the zero state
Example: We also introduce a tool, a representation based on spin-coherent states, for the design and analysis of the QAOA-type circuits
en: Спин-когерентные состояния
Transverse field
collocation
A field applied in orthogonal direction. In hamiltonian form it corresponds to orthogonal non-comuting terms
Example: In our algorithm, the problem Hamiltonian (oracle) and a transverse field are applied alternately to the system in a periodic manner
en: Поперечное поле
Unstructured quantum search
collocation
A search in unstructured database using some quantum algorithm
Example: A natural question is whether it is possible to implement unstructured quantum search in the circuit model using the transverse field instead of Grover’s diffusion operator.
en: Квантовый поиск в неупорядоченной базе данных
Variational angles
collocation
Circuit parameters that are iteratively adjusted to optimize the objective function
Example: When considering variational angles for the diffusion operator but not for the oracle operator, there is still the same advantage as in the case of the variational algorithm with only one angle shared between the oracle and the diffusion operator.
en: Вариационные параметры/углы
Variational ansatz
collocation
A chosen structure of variational quantum circuit.
Example: To compare these variational algorithms with Grover’s algorithm, consider the variational ansatz case for p = 1.
en: Вариационный анзац
Variational quantum eigensolver
collocation
An algorithm that variationally finds the minimum of the problem hamiltonian
Example: Here we take inspiration from algorithms such as the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA).