Related papers: Generalization of the Deutsch algorithm using two …

Linear optics is a promising alternative for the realization of quantum computation protocols due to the recent advancements in integrated photonic technology. In this context usually qubit based quantum circuits are considered, however,…

The Gottesman-Knill theorem established that stabilizer states and operations can be efficiently simulated classically. For qudits with dimension three and greater, stabilizer states and Clifford operations have been found to correspond to…

We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…

We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm…

A new scheme of quantum coding is presented. The scheme concerns the quantum states to which Schumacher's compression does not apply. It is shown that two qubits can be encoded in a single qutrit in such a way that one can faithfully…

In this paper, we present a generalisation of the Phase Kick-Back technique, which is central to some of the classical algorithms in quantum computing, such as the Deutsch--Jozsa algorithm, Simon's algorithm or Grover's algorithm. We will…

When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…

We study the bit complexity of two methods, related to the Euclidean algorithm, for computing cubic and quartic analogs of the Jacobi symbol. The main bottleneck in such procedures is computation of a quotient for long division. We give…

We consider a family of unstructured problems, for which we propose a method for constructing analog, continuous-time quantum algorithms that are more efficient than their classical counterparts. In this family of problems, which we refer…

In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such…

We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability (2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is similar to that of a…

Classical branching programs are studied to understand the space complexity of computational problems. Prior to this work, Nakanishi and Ablayev had separately defined two different quantum versions of branching programs that we refer to as…

We present a zero-crossings counting problem that is a generalization of the Bernstein-Vazirani problem. The goal of this problem is to count the number of zero-crossings (or sign changes) in a special type of sequence S, whose definition…

We show that thresholds for fault-tolerant quantum computation are solely determined by the quality of single-system operations if one allows for d-dimensional systems with $8 \leq d \leq 32$. Each system serves to store one logical qubit…

The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…

A classical analogue of Deutsch and Jozsa's algorithm is given and its implications on quantum computing is discussed

Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…

A relation is established in the present paper between Dicke states in a d-dimensional space and vectors in the representation space of a generalized Weyl-Heisenberg algebra of finite dimension d. This provides a natural way to deal with…

Using trapped ion quantum bits in a scalable microfabricated surface trap, we perform the Bernstein-Vazirani algorithm. Our architecture relies upon ion transport and can readily be expanded to larger systems. The algorithm is demonstrated…

Optimization problems are prevalent in various fields, and the gradient-based gradient descent algorithm is a widely adopted optimization method. However, in classical computing, computing the numerical gradient for a function with $d$…