Trade-off between Noise and Banding in a Quantum Adder with Qudits

• URL: http://arxiv.org/abs/2310.11514v1
• Date: Tue, 17 Oct 2023 18:22:23 GMT
• Title: Trade-off between Noise and Banding in a Quantum Adder with Qudits
• Authors: Gaurang Agrawal, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, Aditi Sen De
• Abstract summary: Quantum addition based on the quantum Fourier transform can be an integral part of a quantum circuit. We analytically prove an upper bound on the number of the controlled rotation gates required to accomplish the quantum addition up to an arbitrary defect. We demonstrate that utilizing magnetic fields to prepare an initial state that evolves according to a one-dimensional spin chain can be a potential technique to implement quantum addition circuits in many-body systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum addition based on the quantum Fourier transform can be an integral part of a quantum circuit and proved to be more efficient than the existing classical ripple carry adder. Our study includes identifying the quantum resource required in a quantum adder in any arbitrary dimension and its relationship with the performance indicator in the presence of local noise acting on the circuit and when a limited number of controlled rotation operations is permitted, a procedure known as banding. We analytically prove an upper bound on the number of the controlled rotation gates required to accomplish the quantum addition up to an arbitrary defect in the fidelity between the desired and imperfect output. When the environment interacts with individual qudits, we establish a connection between quantum coherence and fidelity of the output. Interestingly, we demonstrate that when banding is employed in the presence of noise, approximate circuits of constant depth outperform circuits with a higher number of controlled rotations, establishing a complementary relationship between the approximate quantum adder and the strength of the noise. We exhibit that utilizing magnetic fields to prepare an initial state that evolves according to a one-dimensional spin chain for a specific amount of time can be a potential technique to implement quantum addition circuits in many-body systems.

Related papers

• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories [0.0]
  We show a new method to treat open quantum-spin lattices, based on the solution of the open-system dynamics. We validate this approach in the paradigmatic case of the phase transitions of the dissipative 2D XYZ lattice, subject to spontaneous decay.
  arXiv  Detail & Related papers  (2022-09-27T13:23:38Z)
• Numerical hardware-efficient variational quantum simulation of a soliton solution [0.0]
  We discuss the capabilities of quantum algorithms with special attention paid to a hardware-efficient variational eigensolver. A delicate interplay between magnetic interactions allows one to stabilize a chiral state that destroys the homogeneity of magnetic ordering. We argue that, while being capable of correctly reproducing a uniform magnetic configuration, the hardware-efficient ansatz meets difficulties in providing a detailed description to a noncollinear magnetic structure.
  arXiv  Detail & Related papers  (2021-05-13T11:58:18Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Floquet engineering of continuous-time quantum walks: towards the simulation of complex and next-to-nearest neighbor couplings [0.0]
  We apply the idea of Floquet engineering in the context of continuous-time quantum walks on graphs. We define periodically-driven Hamiltonians which can be used to simulate the dynamics of certain target quantum walks. Our work provides explicit simulation protocols that may be used for directing quantum transport, engineering the dispersion relation of one-dimensional quantum walks or investigating quantum dynamics in highly connected structures.
  arXiv  Detail & Related papers  (2020-12-01T12:46:56Z)
• Many-body quantum lock-in amplifier [0.0]
  We present a protocol for achieving an entanglement-enhanced lock-in amplifier. By selecting suitable input states and readout operations, the frequency and amplitude of an unknown alternating field can be simultaneously extracted. Our study may point out a new direction for measuring time-dependent signals with many-body quantum systems.
  arXiv  Detail & Related papers  (2020-10-14T07:24:39Z)
• Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
  Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling. We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
  arXiv  Detail & Related papers  (2020-05-05T20:11:53Z)
• Nonadiabatic geometric quantum computation with optimal control on superconducting circuits [7.703593898562321]
  We propose a nonadiabatic geometric quantum computation scheme on superconducting circuits. Our scheme provides a promising step towards fault-tolerant solid-state quantum computation.
  arXiv  Detail & Related papers  (2020-04-21T08:34:08Z)

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.