Related papers: Quantum Arithmetic on Galois Fields
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
Galois field (GF) arithmetic circuits find numerous applications in communications, signal processing, and security engineering. Formal verification techniques of GF circuits are scarce and limited to circuits with known bit positions of…
A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
We study the problem of compilation of quantum algorithms into optimized physical-level circuits executable in a quantum information processing (QIP) experiment based on trapped atomic ions. We report a complete strategy: starting with an…
In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the…
A viable approach for building large-scale quantum computers is to interlink small-scale quantum computers with a quantum network to create a larger distributed quantum computer. When designing quantum algorithms for such a distributed…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
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…
Any quantum program on a realistic quantum device must be compiled into an executable form while taking into account the underlying hardware constraints. Stringent restrictions on architecture and control imposed by physical platforms make…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…
We describe a general-purpose framework to design quantum algorithms relying upon an efficient handling of arrays. The corner-stone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding the need to…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a…
We show how the quantum fast Fourier transform (QFFT) can be made exact for arbitrary orders (first for large primes). For most quantum algorithms only the quantum Fourier transform of order $2^n$ is needed, and this can be done exactly.…
Continuous improvements in quantum computing hardware are exposing the need for simultaneous advances in software. Large-scale implementation of quantum algorithms requires rapid and automated compilation routines such as circuit synthesis…