Calculating Unknown Eigenvalues with a Quantum Algorithm
arXiv:1110.4276 · doi:10.1038/nphoton.2012.360
Abstract
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct the algorithm. We have implemented the complete quantum phase estimation algorithm for a single qubit unitary in which the answer is calculated by the algorithm. We use a new approach to implementing the controlled-unitary operations that lie at the heart of the majority of quantum algorithms that is more efficient and does not require the eigenvalues of the unitary to be known. These results point the way to efficient quantum simulations and quantum metrology applications in the near term, and to factoring large numbers in the longer term. This approach is architecture independent and thus can be used in other physical implementations.
References in corpus (11)
- Silica-on-Silicon Waveguide Quantum Circuits
- Entanglement-free Heisenberg-limited phase estimation
- Universal digital quantum simulation with trapped ions
- Shor's quantum factoring algorithm on a photonic chip
- Manipulating multi-photon entanglement in waveguide quantum circuits
- Experimental demonstration of Shor's algorithm with quantum entanglement
- Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit
- Efficient Toffoli Gates Using Qudits
- Demonstration of Shor's quantum factoring algorithm using photonic qubits
- Quantum simulation of the Klein paradox with trapped ions
- Adding control to arbitrary unknown quantum operations
Cited by in corpus (27)
- Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
- Computational advantage from quantum-controlled ordering of gates
- Entanglement-Based Machine Learning on a Quantum Computer
- Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
- Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
- Quantum circuits cannot control unknown operations
- Solving systems of linear equations on a quantum computer
- Robust architecture for programmable universal unitaries
- Recent advances for quantum classifiers
- Communication through coherent control of quantum channels
- Hybrid quantum linear equation algorithm and its experimental test on IBM Quantum Experience
- Quantum Phase Estimation with Time-Frequency Qudits in a Single Photon
- Optimal design of error-tolerant reprogrammable multiport interferometers
- Design and Construction of a Brain-Like Computer: A New Class of Frequency-Fractal Computing Using Wireless Communication in a Supramolecular Organic, Inorganic System
- Highly Efficient Processing Multi-photon States
- Quantum processing by remote quantum control
- Quantum conditional operations
- Quantum algorithm for universal implementation of projective measurement of energy
- Nonlocal quantum gate on quantum continuous variables with minimum resources
- Linear optical demonstration of quantum speed-up with a single qudit
- Reassessing the computational advantage of quantum-controlled ordering of gates
- Universal control of quantum processes using sector-preserving channels
- Hybrid algorithms to solve linear systems of equations with limited qubit resources
- Multiple multi-control unitary operations: implementation and applications
- Quantum Phase Estimation Algorithm for Finding Polynomial Roots
- Quantum control of entangled photon-pair generation in electron-atom collisions driven by laser-synthesized free-electron wave packets
- Precision magnetometry exploiting excited state quantum phase transitions