Black-Box Quantum State Preparation with Inverse Coefficients

Abstract

Black-box quantum state preparation is a fundamental building block for many higher-level quantum algorithms, which is applied to transduce the data from computational basis into amplitude. Here we present a new algorithm for performing black-box state preparation with inverse coefficients based on the technique of inequality test. This algorithm can be used as a subroutine to perform the controlled rotation stage of the Harrow-Hassidim-Lloyd (HHL) algorithm and the associated matrix inversion algorithms with exceedingly low cost. Furthermore, we extend this approach to address the general black-box state preparation problem where the transduced coefficient is a general non-linear function. The present algorithm greatly relieves the need to do arithmetic and the error is only resulted from the truncated error of binary string. It is expected that our algorithm will find wide usage both in the NISQ and fault-tolerant quantum algorithms.

arXiv comment11 pages, 3 figures

References in corpus (19)

• Quantum Machine Learning
• Quantum algorithm for solving linear systems of equations
• Quantum support vector machine for big data classification
• Quantum machine learning in feature Hilbert spaces
• Quantum random access memory
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Quantum Data Fitting
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• Halving the cost of quantum addition
• Efficient quantum algorithm for dissipative nonlinear differential equations
• Fixed-point quantum search with an optimal number of queries
• Quantum algorithm and circuit design solving the Poisson equation
• Circuit-Based Quantum Random Access Memory for Classical Data
• Black-box quantum state preparation without arithmetic
• Quantum Analog-Digital Conversion
• Scalable quantum memory in the ultrastrong coupling regime
• Quantum Circuits for Toom-Cook Multiplication
• Quantum circuits design for evaluating transcendental functions based on a function-value binary expansion method
• Fast Black-Box Quantum State Preparation Based on Linear Combination of Unitaries

Cited by in corpus (6)

• Quantum computing for finance
• Efficient quantum amplitude encoding of polynomial functions
• Option pricing under stochastic volatility on a quantum computer
• Quantum mean estimation for lattice field theory
• Energy risk analysis with Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling
• Time series generation for option pricing on quantum computers using tensor network