Quantum state preparation via piecewise QSVT
arXiv:2409.07332 · doi:10.22331/q-2025-07-03-1786
Abstract
Efficient state preparation is essential for implementing efficient quantum algorithms. Whilst several techniques for low-cost state preparation exist, this work facilitates further classes of states, whose amplitudes are well approximated by piecewise polynomials. We show how such states can be efficiently prepared using a piecewise Quantum Singular Value Transformation along with a new piecewise linear diagonal block encoding. We illustrate this with the explicit examples of and . Further, our technique reduces the cost of window boosted Quantum Phase Estimation by efficiently preparing the B-spline window state. We demonstrate this window state requires 50 times fewer Toffolis to prepare than the state-of-the-art Kaiser window state, and we show that the B-spline window replicates the Kaiser window's exponential reduction in tail probability for QPE.
10 pages, comments welcome
References in corpus (30)
- Quantum computational chemistry
- Simulated Quantum Computation of Molecular Energies
- Quantum error correction below the surface code threshold
- Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
- Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
- Variational quantum algorithms for nonlinear problems
- Halving the cost of quantum addition
- Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications
- Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
- Efficient synthesis of universal Repeat-Until-Success circuits
- Efficient Quantum Circuits for Diagonal Unitaries Without Ancillas
- Black-box quantum state preparation without arithmetic
- A Threshold for Quantum Advantage in Derivative Pricing
- Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicator
- Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization
- Preparation of matrix product states with log-depth quantum circuits
- Quantum Simulation of Chemistry with Sublinear Scaling in Basis Size
- Trading T gates for dirty qubits in state preparation and unitary synthesis
- Block-encoding structured matrices for data input in quantum computing
- Analyzing Prospects for Quantum Advantage in Topological Data Analysis
- Efficient quantum amplitude encoding of polynomial functions
- Quantum algorithms for approximate function loading
- Quantum State Preparation of Normal Distributions using Matrix Product States
- Quantum Computation for Periodic Solids in Second Quantization
- Fast Black-Box Quantum State Preparation
- Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions
- The Problem with Grover-Rudolph State Preparation for Quantum Monte-Carlo
- Efficient Hamiltonian Simulation for Solving Option Price Dynamics
- End-to-end resource analysis for quantum interior point methods and portfolio optimization
- Rise of conditionally clean ancillae for efficient quantum circuit constructions