Related papers: Quantum Circuit Implementation of Two Matrix Produ…
Quantum machine learning models are designed for performing learning tasks. Some quantum classifier models are proposed to assign classes of inputs based on fidelity measurements. Quantum Hadamard test is a well-known quantum algorithm for…
To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the…
A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using…
We propose a novel quantum approach to signal processing, including a quantum algorithm for low-pass and high-pass filtering, based on the sequency-ordered Walsh-Hadamard transform. We present quantum circuits for performing the…
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…
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…
Matrix-product unitaries (MPUs) are many-body unitary operators that, as a consequence of their tensor-network structure, preserve the entanglement area law in 1D systems. However, it is unknown how to implement an MPU as a quantum circuit…
Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any…
Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
We show that an n-th root of the Walsh-Hadamard transform (obtained from the Hadamard gate and a cyclic permutation of the qubits), together with two diagonal matrices, namely a local qubit-flip (for a fixed but arbitrary qubit) and a…
We consider the quantum implementations of the two classical iterative solvers for a system of linear equations, including the Kaczmarz method which uses a row of coefficient matrix in each iteration step, and the coordinate descent method…
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…
A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of…
Utility-scale quantum programs contain operations on the order of $>10^{15}$ which must be prepared and piped from a classical co-processor to the control unit of the quantum device. The latency of this process significantly increases with…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
Optical computing harnesses the speed of light to perform vector-matrix operations efficiently. It leverages interference, a cornerstone of quantum computing algorithms, to enable parallel computations. In this work, we interweave quantum…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…