Variable-Time Adiabatic Quantum Search

These flashcards cover key concepts from the lecture on variable-time adiabatic quantum search, focusing on the optimal performance of quantum search algorithms and related mathematical foundations.

Grover’s Algorithm

A quantum algorithm that provides a quadratic speedup for unstructured search, finding a marked item among N candidates using O(√N) queries.

Tnaive

The worst-case time cost for a naive algorithm, represented as Tnaive = O(√N tmax), where tmax is the maximum time any input takes to check.

Toptimal

The optimal time for a search algorithm that takes into account the variable times of each query, represented as Toptimal = O(t1² + t2² + … + tN²).

Hamiltonian

A mathematical function used in quantum mechanics that describes the total energy of a system, utilized here to reflect both solution status and evaluation time.

Spectral Gap Condition

A condition ensuring that the evolution of the quantum system remains efficient during the optimization process.

Cost Distribution

An assumption that the costs of checking items are uneven, facilitating performance improvement in variable-time quantum searches.

Adiabatic Quantum Search

An approach to quantum searching that evolves from an initial state to a final state while maintaining certain constraints, preferable for variable-time query costs.

Probabilistic Approach

A method involving repeated tests at increasing time thresholds to simulate behaviors without prior knowledge of costs.

Bi-Level Cost Checking

Evaluating costs at two levels where most items are cheap and a few are expensive, affecting the efficiency of quantum algorithms.

Quantum Circuit

A model used for quantum computations, which consists of quantum gates and qubits, and can be utilized to simulate adiabatic evolutions.