Related papers: Quantum Computation of Prime Number Functions
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
Quantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any…
Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical…
We discuss how to build some partially entangled states of $n$ two-state quantum systems (qubits). The optimal partially entangled state with a high degree of symmetry is considered to be useful for overcoming a shot noise limit of Ramsey…
We present quantum-inspired algorithms for classification tasks inspired by the problem of quantum state discrimination. By construction, these algorithms can perform multiclass classification, prevent overfitting, and generate probability…
A binary string representation of prime occurrences is a sequence of bits, where $1$ entries encode positions of prime numbers. This is a convenient representation for analysis of prime distribution, since it allows for application of a…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
Multiplicative arithmetic functions satisfying the parallelogram functional equation on prime numbers are investigated. It is derived that the unique solution is a quadratic function by the Goldbach's conjecture.
We present a hybrid model of the unitary-evolution-based quantum computation model and the measurement-based quantum computation model. In the hybrid model part of a quantum circuit is simulated by unitary evolution and the rest by…
As one of the most intriguing intrinsic properties of quantum world, quantum superposition provokes great interests in its own generation. Oszmaniec [Phys. Rev. Lett. 116, 110403 (2016)] have proven that though a universal quantum machine…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
Quantum state discrimination is a fundamental information processing task that serves as a building block for numerous applications and provides implications at the foundational level. In this work, we consider minimum error discrimination…
The principle of teleportation can be used to perform a quantum computation even before its quantum input is defined. The basic idea is to perform the quantum computation at some earlier time with qubits which are part of an entangled…
We first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
We prove the STP=BQP conjecture of Freedman, Hastings and Shokrian-Zini [1], namely that the two-qubit singlet/triplet measurement is quantum computationally universal given only an initial ensemble of maximally mixed single qubits. This…
We introduce a model of computation based on quaternions, which is inspired on the quantum computing model. Pure states are vectors of a suitable linear space over the quaternions. Other aspects of the theory are the same as in quantum…
Estimating properties of a quantum state is an indispensable task in various applications of quantum information processing. To predict properties in the post-processing stage, it is inherent to first perceive the quantum state with a…
We examine two quantum operations, the Permutation Test and the Circle Test, which test the identity of n quantum states. These operations naturally extend the well-studied Swap Test on two quantum states. We first show the optimality of…