A Speed Boost for Quantum Factoring

In the past 30 years, computer scientists have streamlined Shor’s algorithm in preparation. For the day that quantum technology matures enough to run it. But a new variant. From the New York University computer scientist Oded Regev. Is faster in a fundamentally new sense. It’s the first to improve the relationship between the size of the number being factored and the number of quantum operations required to factor it. “It’s really remarkable that somebody has apparently been able to improve the complexity of this result many, many years later,” said Ashley Montanaro, a quantum computing researcher at the University of Bristol. “This is really exciting.

Finding Factors

Quantum computers derive their Phone Number List power from the peculiar way they process information. Classical computers use bits, each of which must always be in one of two states. Labeled 0 and Quantum bits, or “qubits,” can additionally be in combinations of their 0 and 1 states — a phenomenon called superposition. It’s also possible to coax multiple qubits into a collective superposition state. A two-qubit superposition has four components that can perform different computations simultaneously. And the number of such components grows exponentially as the number of qubits increases. That allows quantum computers to effectively perform exponentially many different computations in parallel. But there’s a catch: Reading the result of a computation performed in superposition only reveals the answer to the part computed by one random component.

Lost in the Trees

Regev began his academic career CH Leads in the late 1990s. When cryptographers were searching for a new form of public-key cryptography. That wasn’t vulnerable to Shor’s algorithm. The most promising approach, called lattice-based cryptography. Relies on the apparent difficulty of computational problems involving high-dimensional arrays of points, or lattices. One such problem is akin to the task of locating the tree closest to a random point in a forest. Oded Regev in a white shirt in front of a green background Oded Regev developed a multidimensional version of Shor’s algorithm that runs even faster. Courtesy of Oded Regev “If it’s a hundred-dimensional forest, then that’s much more complicated than if it’s a two-dimensional forest.

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