Tailoring Fault-Tolerance to Quantum Algorithms

• URL: http://arxiv.org/abs/2404.11953v1
• Date: Thu, 18 Apr 2024 07:15:15 GMT
• Title: Tailoring Fault-Tolerance to Quantum Algorithms
• Authors: Zhuangzhuang Chen, Narayanan Rengaswamy,
• Abstract summary: We develop a solve-and-stitch algorithm to synthesize physical realizations of Clifford Trotter circuits. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead.
• Score: 3.836669717540222
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known $[\![ n,n-2,2 ]\!]$ error-detecting code family. Our analysis shows that this family implements Trotter circuits with optimal depth, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. The solve-and-stitch algorithm has the potential to scale beyond this specific example and hence provide a principled approach to tailored fault-tolerance in quantum computing.

Related papers

• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code [0.0]
  Many current quantum error correcting codes that achieve full fault-tolerance suffer from having low ratios of logical to physical qubits and significant overhead. We propose a middle ground: constructions in the [[n,n-2,2]] quantum error detecting code that can detect any error from a single faulty gate.
  arXiv  Detail & Related papers  (2024-08-27T07:25:36Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Automated error correction in superdense coding, with implementation on superconducting quantum computer [0.28675177318965034]
  We present a task-specific error-correction technique that provides a complete protection over a restricted set of quantum states. Specifically, we give an automated error correction in Superdense Coding algorithms utilizing n-qubit generalized Bell states. We experimentally realize our automated error correction technique for three different types of superdense coding algorithm on a 7-qubit superconducting IBM quantum computer and also on a 27-qubit quantum simulator in the presence of noise.
  arXiv  Detail & Related papers  (2022-10-27T04:02:13Z)
• On proving the robustness of algorithms for early fault-tolerant quantum computers [0.0]
  We introduce a randomized algorithm for the task of phase estimation and give an analysis of its performance under two simple noise models. We calculate that the randomized algorithm can succeed with arbitrarily high probability as long as the required circuit depth is less than 0.916 times the dephasing scale.
  arXiv  Detail & Related papers  (2022-09-22T21:28:12Z)
• A Quantum Algorithm for Computing All Diagnoses of a Switching Circuit [73.70667578066775]
  Faults are by nature while most man-made systems, and especially computers, work deterministically. This paper provides such a connecting via quantum information theory which is an intuitive approach as quantum physics obeys probability laws.
  arXiv  Detail & Related papers  (2022-09-08T17:55:30Z)
• Establishing trust in quantum computations [0.0]
  We introduce a technique for measuring the fidelity with which an as-built quantum computer can execute an algorithm. Our technique converts the algorithm's quantum circuits into a set of closely related circuits whose success rates can be efficiently measured.
  arXiv  Detail & Related papers  (2022-04-15T17:44:30Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Efficient realization of quantum algorithms with qudits [0.70224924046445]
  We propose a technique for an efficient implementation of quantum algorithms with multilevel quantum systems (qudits) Our method uses a transpilation of a circuit in the standard qubit form, which depends on the parameters of a qudit-based processor. We provide an explicit scheme of transpiling qubit circuits into sequences of single-qudit and two-qudit gates taken from a particular universal set.
  arXiv  Detail & Related papers  (2021-11-08T11:09:37Z)
• Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms [55.41644538483948]
  We provide the first complete characterization of sources of error in a neutral-atom quantum computer. We develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace. Our protocols can be implemented in the near-term using state-of-the-art neutral atom platforms with qubits encoded in both alkali and alkaline-earth atoms.
  arXiv  Detail & Related papers  (2021-05-27T23:29:53Z)

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.