Using Quantum Switches to Mitigate Noise in Grover's Search Algorithm
arXiv:2401.05866 · doi:10.1088/1751-8121/ad9efc
Abstract
Grover's quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a resource to mitigate the effects of noise. In this scenario, the noise is modeled by a depolarizing channel, which coherently acts on the entire quantum register. We show that a quantum switch can significantly reduce the error in Grover's search algorithm. We consider the success probability of finding the marked item as the sole quantifier of diminishing the effect of noise in the search space in the presence of quantum switch. We propose two frameworks for the application of quantum switches. In the first framework, we apply the superposition of channel's orders in the form of a switch and do a post-selection at every iteration of the applications of the Grover operator. In the second framework, we delay this measurement and post-selection until the very end. The number of post selections is minimal in the second scenario, and hence the noise reduction can be attributed more to the presence of quantum switch. We illustrate with an example of significant advantage in the success probability of Grover's algorithm using quantum switch.
17 pages (Main) + 11 pages (Appendix), 7 figures
References in corpus (27)
- Quantum Computing in the NISQ era and beyond
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum correlations with no causal order
- Quantum computations without definite causal structure
- Experimental Superposition of Orders of Quantum Gates
- Computational advantage from quantum-controlled ordering of gates
- Experimental Verification of an Indefinite Causal Order
- Enhanced communication with the assistance of indefinite causal order
- Perfect discrimination of no-signalling channels via quantum superposition of causal structures
- Indefinite Causal Order in a Quantum Switch
- Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
- Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
- Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
- Quantum Metrology with Indefinite Causal Order
- Indefinite causal order enables perfect quantum communication with zero capacity channels
- Quantum Switch for the Quantum Internet: Noiseless Communications through Noisy Channels
- Thermodynamic advancement in the causally inseparable occurrence of thermal maps
- Noise effect on Grover algorithm
- Asymptotically Improved Circuit for -ary Grover's Algorithm with Advanced Decomposition of -qudit Toffoli Gate
- Probing the qudit depolarizing channel
- Dynamic Grover Search: Applications in Recommendation systems and Optimization problems
- Grover's search with local and total depolarizing channel errors
- Quantum reading capacity: General definition and bounds
- Fault-ignorant Quantum Search
- Limit theorems and localization of three state quantum walks on a line defined by generalized Grover coins
- Indefinite causal order for quantum phase estimation with Pauli noise
- The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels