Quantum conjugate gradient method using the positive-side quantum eigenvalue transformation
read the original abstract
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 the quantum conjugate gradient (QCG) method using the quantum eigenvalue transformation (QET). The circuit depth of this algorithm depends on the square root of the coefficient matrix's condition number $\kappa$, representing a square root improvement compared to the previous quantum algorithms, while the total query complexity worsens. The number of ancilla qubits is constant, similar to other QET-based algorithms. Additionally, to implement the QCG method efficiently, we devise a QET-based technique that uses only the positive side of the polynomial (denoted by $P(x)$ for $x\in[0,1]$). We conduct numerical experiments by applying our algorithm to the one-dimensional Poisson equation and successfully solve it. Based on the numerical results, our algorithm significantly improves circuit depth, outperforming another QET-based algorithm by three to four orders of magnitude.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Constrained Optimal Polynomials for Quantum Linear System Solvers
Constrained Uniform Polynomial (CUP) and Constrained Adaptive Polynomial (CAP) solvers achieve lower error than standard QSVT and Chebyshev methods in noise-limited regimes by optimizing accuracy versus block-encoding...
-
Nonisothermal global-pressure exactness in fractured multiphase flow with aperture feedback
A new mixed saturation-temperature compatibility condition is derived for exact global-pressure equivalence in nonisothermal multiphase fractured flow, with numerical benchmarks confirming regimes where exactness hold...
-
Generalized quantum singular value transformation with application in quantum conjugate gradient least squares algorithm
Introduces GQSVT for non-unitary matrices by extending GQSP and applies it to a hybrid quantum CGLS solver.
-
Nonisothermal global-pressure exactness in fractured multiphase flow with aperture feedback
Constrained optimal polynomials (CUP and CAP) reduce quantum linear system solver errors under noise by jointly optimizing approximation accuracy and block-encoding normalization, outperforming standard QSVT and Cheby...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.