A restriction in the quality and quantity of available qubits presents a substantial obstacle to application near-term early fault-tolerant quantum computers practical tasks. To confront this challenge, some techniques for effectively augmenting system size through classical processing have been proposed; one promising approach is circuit cutting. The main idea cutting decompose an original into smaller subcircuits combine outputs from these recover output. Although enables us simulate...

We propose a method to sequentially optimize arbitrary single-qubit gates in parametrized quantum circuits for simulating real- and imaginary-time evolution. The utilizes full degrees of freedom therefore can potentially obtain better performance. Specifically, it simultaneously optimizes both the axis angle gate, while known methods either with fixed, or vice versa. It generalizes sinusoidal cost functions by rotation. Furthermore, we demonstrate how be extended set two-qubit...

In quantum mechanics, measuring the expectation value of a general observable has an inherent statistical uncertainty that is quantified by variance or mean squared error measurement outcome. While can be reduced averaging several samples, number samples should minimized when each sample very costly. This especially case for fault-tolerant computing involves multiple observables nontrivial states in large systems exceed capabilities classical computers. this work, we provide adaptive...

Abstract In variational quantum algorithms, it is important to balance conflicting requirements of expressibility and trainability a parameterized circuit (PQC). However, appropriate PQC designs are not necessarily trivial. Here, we propose an algorithm for optimizing the structure, where single-qubit gates sequentially replaced by optimal ones via diagonalization matrix whose elements evaluated on slightly modified circuits. This replacement leads better approximation target states with...

Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various technologies; particular, it an essential subroutine computing algorithms. Notably, the theory identifies ultimate precision such estimator, which referred to as Cramér-Rao (QCR) lower bound or equivalently inverse Fisher information. Because directly determines those technological systems, highly demanded develop generic and...

The variational quantum eigensolver (VQE) is a hybrid algorithm to find the minimum eigenvalue/vector of given Hamiltonian by optimizing parameterized circuit (PQC) using classical computer. Sequential optimization methods, which are often used in tensor networks, popular for gates PQCs. In this paper, we focus on case where components be optimized single-qubit gates, analytic gate sequentially performed. analytical solution diagonalization matrix whose elements computed from expectation...

A restriction in the quality and quantity of available qubits presents a substantial obstacle to application near-term early fault-tolerant quantum computers practical tasks. To confront this challenge, some techniques for effectively augmenting system size through classical processing have been proposed; one promising approach is circuit cutting. The main idea cutting decompose an original into smaller sub-circuits combine outputs from these recover output. Although enables us simulate...

Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning, and quantum chemistry. Especially, many these can be reduced to finding minimum or maximum GEPs. One key handle GEPs is that memory usage computational complexity explode as size system interest grows. This paper aims at extending sequential optimizers for Sequential are a family algorithms iteratively solve analytical optimization single-qubit gates coordinate...

Quantum algorithms are still challenging to solve linear systems of equations on real devices. This challenge arises from the need for deep circuits and numerous ancilla qubits. We introduce quantum conjugate gradient (QCG) method using eigenvalue transformation (QET). The circuit depth this algorithm depends square root coefficient matrix's condition number $\kappa$, representing a improvement compared previous algorithms. qubits is constant, similar other QET-based Additionally, implement...

In quantum computation, amplitude estimation is a fundamental subroutine that utilized in various algorithms. A general important task of such problems to characterize the lower bound, which referred as Cram\'er-Rao bound (QCRB), and construct an optimal estimator achieves QCRB. This paper studies presence depolarizing noise with unknown intensity. The main difficulty this problem measurement depends on both state we aim estimate. To deal these issues, utilize variational circuits...

In variational algorithms, quantum circuits are conventionally parametrized with respect to single-qubit gates. this study, we parameterize a generalized controlled gate and propose an algorithm estimate the optimal parameters for locally minimizing cost value, where extend free quaternion selection method, optimization method gate. To benchmark performance, apply proposed various problems, including Variational Quantum Eigensolver (VQE) Ising molecular Hamiltonians, Algorithms (VQA)...

Simulating open quantum systems is an essential technique for understanding complex physical phenomena and advancing technologies. Some algorithms simulating Lindblad dynamics achieve logarithmically short circuit depth in terms of accuracy $\varepsilon$ by coherently encoding all possible jump processes with a large ancilla consumption. Minimizing the space complexity while achieving such logarithmic remains important challenge. In this work, we present algorithm general multiple operators...

Quantum-enhanced (i.e., less query complexity compared to any classical method) mean value estimation of observables is a fundamental task in various quantum technologies; particular, it an essential subroutine computing algorithms. Notably, the theory identifies ultimate precision such estimator, which referred as Cram\'{e}r-Rao (QCR) lower bound or equivalently inverse Fisher information. Because directly determines performance those technological systems, highly demanded develop generic...

Variational Quantum Eigensolver (VQE) is a hybrid algorithm for finding the minimum eigenvalue/vector of given Hamiltonian by optimizing parametrized quantum circuit (PQC) using classical computer. Sequential optimization methods, which are often used in tensor networks, popular gates PQCs. This paper focuses on case where components to be optimized single-qubit gates, analytic gate sequentially performed. The analytical solution diagonalization matrix whose elements computed from...

<title>Abstract</title> In variational quantum algorithms, it is important to balance conflicting requirements of expressibility and trainability a parameterized circuit (PQC). However, appropriate PQC designs are not necessarily trivial. Here, we propose an algorithm for optimizing the structure, where single-qubit gates sequentially replaced by optimal ones via diagonalization matrix whose elements evaluated on slightly modified circuits. This replacement leads better approximation target...

In this study, we present an investigation of shape optimisation analysis for a heat convection problem taking into account perimeter constraint condition. The incompressible Navier–Stokes equation using the Boussinesq approximation, continuity and energy are employed governing equations in field. mixed interpolation method is applied to solve flow field, quadratic linear triangular elements are, respectively, velocity pressure. element interpolate temperature. purpose study find optimal...