Convex optimization using quantum oracles

  • Can quantum computers solve optimization problems?

    Quantum computing is a future-oriented topic that has been gaining popularity in recent years.
    While full general-purpose quantum computing is not generally available right now (January 2023), certain specialized machines can be used already to solve optimization problems extremely fast..

  • How does a quantum Oracle work?

    A quantum oracle O is a "black box" operation that is used as input to another algorithm.
    Often, such operations are defined using a classical function f: {0, 1} n → {0, 1} m which takes n-bit binary input and produces an m-bit binary output..

  • What is a quantum Oracle?

    Photo by Joel Filipe on Unsplash.
    Quantum Oracle is a black box used extensively in quantum algorithms for the estimation of functions using qubits..

  • What is quantum computing used for optimization problems?

    It can perform operations on a combination of all possible solutions.
    It divides the intractable complexity into bits to calculate simple solutions.
    Explanation: Quantum computing (QC) is the next frontier in computation and has piqued the scientific community's interest in recent years..

  • What is quantum Oracle?

    The quantum oracle is nothing but a placeholder for a transformation gate.
    While it changes the state of the system, it does not tell the future or answer any question.
    It is up to you to identify how the different gates it may stand for, affect the quantum state differently..

  • An example of an unconstrained convex optimization problem is linear regression, where the goal is to find the best-fit line that minimizes the sum of squared errors between the predicted and actual values.
We study to what extent quantum algorithms can speed up solving convex optimization problems. Following the classical literature we assume access to a convex set via various oracles, and we examine the efficiency of reductions between the different oracles.

How can a separation oracle be implemented using quantum queries?

In particular, we show how a separation oracle can be implemented using quantum queries to a membership oracle, which is an exponential quantum speed-up over the membership queries that are needed classically

We show that a quantum computer can very efficiently compute an approximate subgradient of a convex Lipschitz function


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