相关论文: Efficient factorization with a single pure qubit a…

Quantum computing algorithms using the quantum Fourier transform require repeated use of a phase shift gate. In the case of qubits using optical photons for operation, this gate can be implemented using single-photon beams focused close to…

We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin…

We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…

The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…

We show that the quantum Fisher information about any phase parameter encoded in a family of pure quantum states can be faithfully compressed into a single qubit, accompanied by a logarithmic amount of classical bits. When the phase is…

Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…

We discuss the implementation of quantum logic in a system of strongly interacting particles. The implementation is qubitless since ``logical qubits'' don't correspond to any physical two-state subsystems. As an illustration, we present the…

We discuss two qualities of quantum systems: various correlations existing between their subsystems and the distingushability of different quantum states. This is then applied to analysing quantum information processing. While quantum…

Quantum signal processing (QSP) and the quantum singular value transformation (QSVT) are pivotal tools for simplifying the development of quantum algorithms. These techniques leverage polynomial transformations on the eigenvalues or…

A scheme of implementing the Grover search algorithm based on Josephson charge qubits has been proposed, which would be a key step to scale more complex quantum algorithms and very important for constructing a real quantum computer via…

The quantum algorithms of Deutsch, Simon and Shor are described in a way which highlights their dependence on the Fourier transform. The general construction of the Fourier transform on an Abelian group is outlined and this provides a…

Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…

We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \log^{2 +…

We propose new quantum algorithms to solve the regulator and the principal ideal problem in a real-quadratic number field. We improve the algorithms proposed by Hallgren by using two different techniques. The first improvement is the usage…

Quantum algorithms face significant challenges due to qubit susceptibility to environmental noise, and quantum error correction typically requires prohibitive resource overhead. This paper proposes that quantum algorithms may possess…

This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No…

Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…

For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer…

Withdrawn by the author due to irreparable errors. We present a quantum algorithm that in the black-box model performs a search in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a success probability of at least…

In this paper, we study the nature of entanglement in quantum Grover's and Shor's algorithms. So far, the authors who have been interested in this problem have approached the question quantitatively by introducing entanglement measures…