Robust Quantum Gate Complexity: Foundations

• URL: http://arxiv.org/abs/2404.15828v2
• Date: Fri, 26 Apr 2024 08:59:58 GMT
• Title: Robust Quantum Gate Complexity: Foundations
• Authors: Johannes Aspman, Vyacheslav Kungurtsev, Jakub Marecek,
• Abstract summary: We propose a new approach inspired by the closed quantum optimal control and its connection to geometric interpretations. We present the appropriate problem definitions of robustness in the context of quantum control, focusing on its broader implications for gate complexity.
• Score: 5.274477003588407
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimal control of closed quantum systems is a well studied geometrically elegant set of computational theory and techniques that have proven pivotal in the implementation and understanding of quantum computers. The design of a circuit itself corresponds to an optimal control problem of choosing the appropriate set of gates (which appear as control operands) in order to steer a qubit from an initial, easily prepared state, to one that is informative to the user in some sense, for e.g., an oracle whose evaluation is part of the circuit. However, contemporary devices are known to be noisy, and it is not certain that a circuit will behave as intended. Yet, although the computational tools exist in broader optimal control theory, robustness of adequate operation of a quantum control system with respect to uncertainty and errors has not yet been broadly studied in the literature. In this paper, we propose a new approach inspired by the closed quantum optimal control and its connection to geometric interpretations. To this end, we present the appropriate problem definitions of robustness in the context of quantum control, focusing on its broader implications for gate complexity.

Related papers

• Error-mitigated Geometric Quantum Control over an Oscillator [2.7382619198694886]
  Quantum information is fragile to environmental- and operational-induced imperfections. We propose a robust scheme based on quantum optimal control via the functional theory. Our scheme provides a promising alternative for fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2025-01-24T09:13:24Z)
• Traversing Quantum Control Robustness Landscapes: A New Paradigm for Quantum Gate Engineering [0.0]
  We introduce the Quantum Control Robustness Landscape (QCRL), a conceptual framework that maps control parameters to noise susceptibility. By navigating through the level sets of the QCRL, our Robustness-Invariant Pulse Variation (RIPV) algorithm allows for the variation of control pulses while preserving robustness. Numerical simulations demonstrate that our single- and two-qubit gates exceed the quantum error correction threshold even with substantial noise.
  arXiv  Detail & Related papers  (2024-12-27T05:56:38Z)
• Stochastic optimal control of open quantum systems [0.0]
  We address the generic problem of optimal quantum state preparation for open quantum systems. We propose a corresponding algorithm, which we call Quantum Diffusion Control (QDC)
  arXiv  Detail & Related papers  (2024-10-24T10:47:42Z)
• Quantum control by the environment: Turing uncomputability, Optimization over Stiefel manifolds, Reachable sets, and Incoherent GRAPE [56.47577824219207]
  In many practical situations, the controlled quantum systems are open, interacting with the environment. In this note, we briefly review some results on control of open quantum systems using environment as a resource.
  arXiv  Detail & Related papers  (2024-03-20T10:09:13Z)
• Quantum Optimal Control without Arbitrary Waveform Generators [1.572727650614088]
  We show that arbitrary control of a quantum system can be achieved by simply turning on and off the control fields in a proper sequence. We demonstrate the flexibility and robustness of the resulting control protocol, and apply it to superconducting quantum circuits.
  arXiv  Detail & Related papers  (2022-09-20T17:27:27Z)
• Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
  We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
  arXiv  Detail & Related papers  (2022-04-12T19:39:31Z)
• Resource Optimisation of Coherently Controlled Quantum Computations with the PBS-calculus [55.2480439325792]
  Coherent control of quantum computations can be used to improve some quantum protocols and algorithms. We refine the PBS-calculus, a graphical language for coherent control inspired by quantum optics.
  arXiv  Detail & Related papers  (2022-02-10T18:59:52Z)
• Error-Tolerant Geometric Quantum Control for Logical Qubits with Minimal Resource [4.354697470999286]
  We propose a new fast and robust geometric scheme, with the decoherence-free-subspace encoding, and present its physical implementation on superconducting quantum circuits. Our scheme can consolidate both error suppression methods for logical-qubit control, which sheds light on the future large-scale quantum computation.
  arXiv  Detail & Related papers  (2021-12-16T12:10:41Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• QUANTIFY: A framework for resource analysis and design verification of quantum circuits [69.43216268165402]
  QUANTIFY is an open-source framework for the quantitative analysis of quantum circuits. It is based on Google Cirq and is developed with Clifford+T circuits in mind. For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits.
  arXiv  Detail & Related papers  (2020-07-21T15:36:25Z)
• Quantum Geometric Machine Learning for Quantum Circuits and Control [78.50747042819503]
  We review and extend the application of deep learning to quantum geometric control problems. We demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
  arXiv  Detail & Related papers  (2020-06-19T19:12:14Z)

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.