Related papers: Efficient quantum amplitude encoding of polynomial…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
We present a protocol for encoding $N$ real numbers stored in $N$ memory registers into the amplitudes of the quantum superposition that describes the state of $\log_2N$ qubits. This task is one of the main steps in quantum machine learning…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through block encodings, where additional ancilla qubits are introduced and later measured. While block…
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full…
We present a quantum algorithm for estimating the amplitude content of user-specified sequency bands in quantum-encoded signals. The method employs a sequency-ordered Quantum Walsh-Hadamard Transform (QWHT), a comparator-based oracle that…
For quantum algorithms for problems in which the task is to compute an entire field of values, like e.g. computational fluid dynamics (CFD), it is often proposed amplitude encoding w.r.t. multiple qubits; however, the efforts implied by it…
Implementing polynomial functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine…
Many quantum algorithms rely on the measurement of complex quantum amplitudes. Standard approaches to obtain the phase information, such as the Hadamard test, give rise to large overheads due to the need for global controlled-unitary…
We introduce the Hidden Polynomial Function Graph Problem as a natural generalization of an abelian Hidden Subgroup Problem (HSP) where the subgroups and their cosets correspond to graphs of linear functions over the finite field F_p. For…
Image-based data is a popular arena for testing quantum machine learning algorithms. A crucial factor in realizing quantum advantage for these applications is the ability to efficiently represent images as quantum states. Here we present a…
Amplitude filtering is concerned with identifying basis-states in a superposition whose amplitudes are greater than a specified threshold; probability filtering is defined analogously for probabilities. Given the scarcity of qubits, the…
Semidefinite programs are optimization methods with a wide array of applications, such as approximating difficult combinatorial problems. One such semidefinite program is the Goemans-Williamson algorithm, a popular integer relaxation…
This work investigates the expressive power of quantum circuits in approximating high-dimensional, real-valued functions. We focus on countably-parametric holomorphic maps $u:U\to \mathbb{R}$, where the parameter domain is…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
In this article, we compare the methods implementing the real-time evolution operator generated by a unitary diagonal matrix where its entries obey a known underlying real function. When the size of the unitary diagonal matrix is small, a…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Quantum computing has a potential to accelerate the data processing efficiency, especially in machine learning, by exploiting special features such as the quantum interference. The major challenge in this application is that, in general,…