Implementing Quantum Finite Automata Algorithms on Noisy Devices

• URL: http://arxiv.org/abs/2105.06184v1
• Date: Thu, 13 May 2021 10:51:28 GMT
• Title: Implementing Quantum Finite Automata Algorithms on Noisy Devices
• Authors: Utku Birkan, \"Ozlem Salehi, Viktor Olejar, Cem Nurlu, and Abuzer Yakary{\i}lmaz
• Abstract summary: We present improved circuit based implementations for QFA algorithms recognizing the $ MOD_p $ problem using the Qiskit framework. We run the circuits on real IBM quantum devices but due to the limitation of the real quantum devices in the NISQ era, the results are heavily affected by the noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum finite automata (QFAs) literature offers an alternative mathematical model for studying quantum systems with finite memory. As a superiority of quantum computing, QFAs have been shown exponentially more succinct on certain problems such as recognizing the language $ MOD_p = \{a^j \mid j \equiv 0 \mod p\} $ with bounded error, where $p$ is a prime number. In this paper we present improved circuit based implementations for QFA algorithms recognizing the $ MOD_p $ problem using the Qiskit framework. We focus on the case $p=11$ and provide a 3 qubit implementation for the $MOD_{11}$ problem reducing the total number of required gates using alternative approaches. We run the circuits on real IBM quantum devices but due to the limitation of the real quantum devices in the NISQ era, the results are heavily affected by the noise. This limitation reveals once again the need for algorithms using less amount of resources. Consequently, we consider an alternative 3 qubit implementation which works better in practice and obtain promising results even for the problem $ MOD_{31} $.

Related papers

• On the practicality of quantum sieving algorithms for the shortest vector problem [42.70026220176376]
  lattice-based cryptography is one of the main candidates of post-quantum cryptography. cryptographic security against quantum attackers is based on lattice problems like the shortest vector problem (SVP) Asymptotic quantum speedups for solving SVP are known and rely on Grover's search.
  arXiv  Detail & Related papers  (2024-10-17T16:54:41Z)
• Quantum hashing algorithm implementation [0.0]
  We implement a quantum hashing algorithm which is based on a fingerprinting technique presented by Ambainis and Frievalds, 1988, on gate-based quantum computers. We consider 16-qubit and 27-qubit IBMQ computers with the special graphs of qubits representing nearest neighbor architecture that is not Linear Nearest Neighbor (LNN) one.
  arXiv  Detail & Related papers  (2024-07-14T09:41:16Z)
• A two-circuit approach to reducing quantum resources for the quantum lattice Boltzmann method [41.66129197681683]
  Current quantum algorithms for solving CFD problems use a single quantum circuit and, in some cases, lattice-based methods. We introduce the a novel multiple circuits algorithm that makes use of a quantum lattice Boltzmann method (QLBM) The problem is cast as a stream function--vorticity formulation of the 2D Navier-Stokes equations and verified and tested on a 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• Non-Linear Transformations of Quantum Amplitudes: Exponential Improvement, Generalization, and Applications [0.0]
  Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. We present a framework for applying a general class of non-linear functions to the amplitudes of quantum states. Our work provides an important and efficient building block with potentially numerous applications in areas such as optimization, state preparation, quantum chemistry, and machine learning.
  arXiv  Detail & Related papers  (2023-09-18T14:57:21Z)
• Iterative Qubits Management for Quantum Index Searching in a Hybrid System [56.39703478198019]
  IQuCS aims at index searching and counting in a quantum-classical hybrid system. We implement IQuCS with Qiskit and conduct intensive experiments. Results demonstrate that it reduces qubits consumption by up to 66.2%.
  arXiv  Detail & Related papers  (2022-09-22T21:54:28Z)
• Improving Quantum Simulation Efficiency of Final State Radiation with Dynamic Quantum Circuits [1.3375143521862154]
  We make use of a new quantum hardware capability called dynamical quantum computing to improve the scaling of the QPS algorithm. We modify the quantum parton shower circuit to incorporate mid-circuit qubit measurements, resets, and quantum operations conditioned on classical information.
  arXiv  Detail & Related papers  (2022-03-18T15:31:19Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Deterministic and Entanglement-Efficient Preparation of Amplitude-Encoded Quantum Registers [0.533024001730262]
  A classical vector $mathbfb$ is encoded in the amplitudes of a quantum state. An arbitrary state of $Q$ qubits generally requires approximately $2Q$ entangling gates. We present a deterministic (nonvariational) algorithm that allows one to flexibly reduce the quantum resources required for state preparation.
  arXiv  Detail & Related papers  (2021-10-26T07:37:54Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)
• Cost-efficient QFA Algorithm for Quantum Computers [0.0]
  We present a modified Moore-Crutchfield quantum finite automaton (MCQFA) algorithm for the language $mathttMOD_p$. We obtain shorter quantum programs using fewer basis gates compared to the implementation of the original algorithm given in the literature.
  arXiv  Detail & Related papers  (2021-07-05T20:41:18Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.