Amplitude estimation without phase estimation
arXiv:1904.10246 · doi:10.1007/s11128-019-2565-2
Abstract
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.
13 pages. Almost the same as the journal published version
References in corpus (24)
- Quantum Computing in the NISQ era and beyond
- The theory of variational hybrid quantum-classical algorithms
- Quantum Amplitude Amplification and Estimation
- Quantum computers can search rapidly by using almost any transformation
- Quantum measurements and the Abelian Stabilizer Problem
- 10-qubit entanglement and parallel logic operations with a superconducting circuit
- Polynomial-time quantum algorithm for the simulation of chemical dynamics
- Observation of Entangled States of a Fully Controlled 20-Qubit System
- Quantum speedup of Monte Carlo methods
- Quantum Risk Analysis
- Quantum computational finance: Monte Carlo pricing of financial derivatives
- An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
- From transistor to trapped-ion computers for quantum chemistry
- Optimal Quantum Measurements of Expectation Values of Observables
- Efficient Bayesian Phase Estimation
- Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
- Quantum Approximate Counting, Simplified
- q-means: A quantum algorithm for unsupervised machine learning
- Quantum Perceptron Models
- Quantum Sub-Gaussian Mean Estimator
- Fast quantum algorithms for numerical integrals and stochastic processes
- Randomized gap and amplitude estimation
- Practical sampling schemes for quantum phase estimation
- Simpler Quantum Counting
Cited by in corpus (96)
- Quantum Computing for Finance: State of the Art and Future Prospects
- Quantum computing for finance
- Option Pricing using Quantum Computers
- Grover Adaptive Search for Constrained Polynomial Binary Optimization
- Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond
- Quantum Approximate Counting, Simplified
- A Threshold for Quantum Advantage in Derivative Pricing
- Minimizing estimation runtime on noisy quantum computers
- Low depth algorithms for quantum amplitude estimation
- Efficient State Preparation for Quantum Amplitude Estimation
- Quantum unary approach to option pricing
- A hybrid quantum-classical approach to mitigating measurement errors
- Faster Amplitude Estimation
- Prospects and challenges of quantum finance
- Variational quantum amplitude estimation
- Amplitude estimation via maximum likelihood on noisy quantum computer
- Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth
- Efficient quantum readout-error mitigation for sparse measurement outcomes of near-term quantum devices
- Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms
- Quantum algorithms for anomaly detection using amplitude estimation
- Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error
- Reduction of Qubits in Quantum Algorithm for Monte Carlo Simulation by Pseudo-random Number Generator
- Grover search revisited; application to image pattern matching
- A variational quantum algorithm for the Feynman-Kac formula
- Nonlinear dynamics as a ground-state solution on quantum computers
- Quantum Phase Processing and its Applications in Estimating Phase and Entropies
- Amplitude Estimation from Quantum Signal Processing
- The Problem with Grover-Rudolph State Preparation for Quantum Monte-Carlo
- Modified Grover operator for amplitude estimation
- Quantum algorithm for credit valuation adjustments
- Quantum Signal Processing for simulating cold plasma waves
- Quantum Monte Carlo for Economics: Stress Testing and Macroeconomic Deep Learning
- Derivative Pricing using Quantum Signal Processing
- Short Quantum Circuits in Reinforcement Learning Policies for the Vehicle Routing Problem
- Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors
- Efficient option pricing with unary-based photonic computing chip and generative adversarial learning
- Quantum Amplitude Amplification Operators
- Quantum-Enhanced Simulation-Based Optimization
- Noisy quantum amplitude estimation without noise estimation
- Exploring LLM-Driven Explanations for Quantum Algorithms
- Quantum simulation of colour in perturbative quantum chromodynamics
- Quantum Amplitude Estimation in the Presence of Noise
- Option pricing under stochastic volatility on a quantum computer
- Quantum Computation of Eigenvalues within Target Intervals
- Quantum Fourier Iterative Amplitude Estimation
- Agnostic Phase Estimation
- Quantum amplitude estimation algorithms on IBM quantum devices
- Solving Fractional Differential Equations on a Quantum Computer: A Variational Approach
- Towards practical Quantum Credit Risk Analysis
- Foundations for Bayesian inference with engineered likelihood functions for robust amplitude estimation
- Bayesian estimation for collisional thermometry
- Quantum self-learning Monte Carlo with quantum Fourier transform sampler
- End-to-end complexity for simulating the Schwinger model on quantum computers
- Noise-Aware Quantum Amplitude Estimation
- Linear Regression by Quantum Amplitude Estimation and its Extension to Convex Optimization
- Energy risk analysis with Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling
- Comparison of Amplitude Estimation Algorithms by Implementation
- Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers
- Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos
- Quantum Computation for Pricing the Collateralized Debt Obligations
- Modified Iterative Quantum Amplitude Estimation is Asymptotically Optimal
- Pricing multi-asset derivatives by finite difference method on a quantum computer
- Quantum Computing for Data Centric Engineering and Science
- Adaptive measurement strategy for noisy quantum amplitude estimation with variational quantum circuits
- Canonical Construction of Quantum Oracles
- Bayesian Quantum Amplitude Estimation
- Heisenberg-limited adaptive gradient estimation for multiple observables
- Quantum-enhanced mean value estimation via adaptive measurement
- Cosine series quantum sampling method with applications in signal and image processing
- The simulation of distributed quantum algorithms
- Simplifying a classical-quantum algorithm interpolation with quantum singular value transformations
- Noise tailoring for Robust Amplitude Estimation
- Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Quantum Data Loading
- Conditional Generative Models for Learning Stochastic Processes
- Quantum Realization of the Finite Element Method
- Quadratic speed-ups in quantum kernelized binary classification
- Quantum circuit to estimate pi using quantum amplitude estimation
- Dividing quantum circuits for time evolution of stochastic processes by orthogonal series density estimation
- Measurement Schemes for Quantum Linear Equation Solvers
- Quantum Approximate Counting with Nonadaptive Grover Iterations
- Efficient quantum algorithm for weighted partial sums and numerical integration
- A general approach to quantum integration of cross sections in high-energy physics
- Reducing runtime and error in VQE using deeper and noisier quantum circuits
- Practical numerical integration on NISQ devices
- Faster Quantum Algorithm for Multiple Observables Estimation in Fermionic Problems
- Quantum Machine Learning with SQUID
- Comprehensive Study on Heisenberg-limited Quantum Algorithms for Multiple Observables Estimation
- Quantum algorithm for solving McKean-Vlasov stochastic differential equations
- On the bias in iterative quantum amplitude estimation
- Detailed Account of Complexity for Implementation of Some Gate-Based Quantum Algorithms
- Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states
- Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators
- Quantum Algorithms for Unsupervised Machine Learning and Neural Networks
- Quantum Speedup of Monte Carlo Integration with respect to the Number of Dimensions and its Application to Finance
- Nonlinear path-following via the asymptotic numerical method on a quantum processor
- Sublinear quantum algorithms for estimating von Neumann entropy