Approximate Quantum Fourier Transform and Decoherence

Abstract

We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive approximations can be made before the accuracy of AQFT (as compared with regular quantum Fourier transform) is compromised. We show that for some computations an approximation may imply a better performance.

14 pages, 10 fig. (8 *.eps files). More information on http://eve.physics.ox.ac.uk/QChome.html http://www.physics.helsinki.fi/~kasuomin http://www.physics.helsinki.fi/~kira/group.html

References in corpus (6)

• Conditional Quantum Dynamics and Logic Gates
• Quantum Computers and Dissipation
• Semiclassical Fourier Transform for Quantum Computation
• Universality in Quantum Computation
• A Universal Two--Bit Gate for Quantum Computation
• Realistic lower bounds for the factorization time of large numbers on a quantum computer

Cited by in corpus (62)

• Quantum Computing
• Quantum algorithms for algebraic problems
• Practical characterization of quantum devices without tomography
• Synthesis of Quantum Circuits for Linear Nearest Neighbor Architectures
• Addition on a Quantum Computer
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• CutQC: Using Small Quantum Computers for Large Quantum Circuit Evaluations
• Simulating chemistry efficiently on fault-tolerant quantum computers
• Quantum algorithm for distributed clock synchronization
• Decoherence limits to quantum computation using trapped ions
• Quantum Computation
• Approximate Quantum Fourier Transform with $O(n\log (n))$ T gates
• Linear-Depth Quantum Circuits for n-qubit Toffoli gates with no Ancilla
• Demonstration of Shor's factoring algorithm for N=21 on IBM quantum processors
• Efficient classical simulation of the approximate quantum Fourier transform
• Quantum Fourier Transform using Dynamic Circuits
• General-Purpose Parallel Simulator for Quantum Computing
• Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform
• Quantum fast Fourier transform using multilevel atoms
• Quantum arithmetic operations based on quantum Fourier transform on signed integers
• Quantum Computation Beyond the Circuit Model
• Large-Scale Simulation of Shor's Quantum Factoring Algorithm
• Quantum learning by measurement and feedback
• Decoherence on Grover's quantum algorithm: perturbative approach
• Scaling laws for Shor's algorithm with a banded quantum Fourier transform
• Quantum error correction of dephasing in 3 qubits
• Efficient implementations of the Quantum Fourier Transform: an experimental perspective
• Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition
• Quantum synthesis of arbitrary unitary operators
• Exploiting dynamic quantum circuits in a quantum algorithm with superconducting qubits
• Quantum computation from a quantum logical perspective
• A Hardware-Aware Gate Cutting Framework for Practical Quantum Circuit Knitting
• Design of quantum Fourier transforms and quantum algorithms by using circulant Hamiltonians
• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage
• Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks
• Higher order perturbation theory for decoherence in Grover's algorithm
• Measured Quantum Fourier Transform of 1024 Qubits on Fiber Optics
• Implementation of Quantum Fourier Transform and Quantum Hashing for a Quantum Device with Arbitrary Qubits Connection Graphs
• Quantum locally linear embedding for nonlinear dimensionality reduction
• Heisenberg-limited Bayesian phase estimation with low-depth digital quantum circuits
• Quantum Circuit Distillation and Compression
• Quantum circuits for partial differential equations in Fourier space
• An Improvement in Quantum Fourier Transform
• Polynomial T-depth Quantum Solvability of Noisy Binary Linear Problem: From Quantum-Sample Preparation to Main Computation
• Quadratic speed-ups in quantum kernelized binary classification
• QRCC: Evaluating Large Quantum Circuits on Small Quantum Computers through Integrated Qubit Reuse and Circuit Cutting
• Performance Evaluations of Signed and Unsigned Noisy Approximate Quantum Fourier Arithmetic
• Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering
• Approximation Errors
• Quantum Circuit Pruning: Improving Fidelity via Compilation-Aware Circuit Approximation
• Tradeoff between noise and banding in a quantum adder with qudits
• Leggett-Garg inequalities with deformed Pegg-Barnett phase observables
• Quantum Phase Estimation with Arbitrary Constant-precision Phase Shift Operators
• Quantum Algorithms for Discrete Log Require Precise Rotations
• Exploring the Impact of Affine Loop Transformations in Qubit Allocation
• Quantum Fourier Transform in Oscillating Modes
• Ptychographic estimation of pure multiqubit states in a quantum device
• Improved Bounds for the Approximate QFT
• The limits of quantum circuit simulation with low precision arithmetic
• Simulation of Quantum Circuits via Stabilizer Frames
• Scaling and better approximating quantum Fourier transform by higher radices
• Operator Imprecision and Scaling of Shor's Algorithm