PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations

• URL: http://arxiv.org/abs/2002.09387v2
• Date: Mon, 31 Aug 2020 18:16:43 GMT
• Title: PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations
• Authors: Alexandre Cl\'ement and Simon Perdrix
• Abstract summary: We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations. We equip the language with an equational theory, which is proved to be sound and complete. We consider applications like the implementation of controlled permutations and the unrolling of loops.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations. Coherent control, and in particular indefinite causal order, is known to enable multiple computational and communication advantages over classically ordered models like quantum circuits. The PBS-calculus is inspired by quantum optics, in particular the polarising beam splitter (PBS for short). We formalise the syntax and the semantics of the PBS-diagrams, and we equip the language with an equational theory, which is proved to be sound and complete: two diagrams are representing the same quantum evolution if and only if one can be transformed into the other using the rules of the PBS-calculus. Moreover, we show that the equational theory is minimal. Finally, we consider applications like the implementation of controlled permutations and the unrolling of loops.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Completeness of qufinite ZXW calculus, a graphical language for finite-dimensional quantum theory [0.11049608786515838]
  We introduce the qufinite ZXW calculus - a graphical language for reasoning about finite-dimensional quantum theory. We prove the completeness of this calculus by demonstrating that any qufinite ZXW diagram can be rewritten into its normal form. Our work paves the way for a comprehensive diagrammatic description of quantum physics, opening the doors of this area to the wider public.
  arXiv  Detail & Related papers  (2023-09-22T17:23:58Z)
• LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits [58.720142291102135]
  We introduce the LOv-calculus, a graphical language for reasoning about linear optical quantum circuits. Two LOv-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LOv-calculus.
  arXiv  Detail & Related papers  (2022-04-25T16:59:26Z)
• 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)
• Quantum Fokker-Planck Master Equation for Continuous Feedback Control [0.0]
  Measurement and feedback control are essential features of quantum science, with applications ranging from quantum technology protocols to information-to-work conversion in quantum thermodynamics. Here we present a formalism for continuous quantum measurement and feedback, both linear and nonlinear. Our main result is a quantum Fokker-Planck master equation describing the joint dynamics of a quantum system and a detector with finite bandwidth. For fast measurements, we derive a Markovian master equation for the system alone, amenable to analytical treatment.
  arXiv  Detail & Related papers  (2021-10-18T10:25:23Z)
• LQP: The Dynamic Logic of Quantum Information [77.34726150561087]
  This paper introduces a dynamic logic formalism for reasoning about information flow in composite quantum systems. We present a finitary syntax, a relational semantics and a sound proof system for this logic. As applications, we use our system to give formal correctness for the Teleportation protocol and for a standard Quantum Secret Sharing protocol.
  arXiv  Detail & Related papers  (2021-10-04T12:20:23Z)
• The Logic of Quantum Programs [77.34726150561087]
  We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound quantum systems.
  arXiv  Detail & Related papers  (2021-09-14T16:08:37Z)
• Foundations for Near-Term Quantum Natural Language Processing [0.17205106391379021]
  We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP) We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure. We provide references for supporting empirical evidence and formal statements concerning mathematical generality.
  arXiv  Detail & Related papers  (2020-12-07T14:49:33Z)
• Theory of Ergodic Quantum Processes [0.0]
  We consider general ergodic sequences of quantum channels with arbitrary correlations and non-negligible decoherence. We compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are metastable and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned.
  arXiv  Detail & Related papers  (2020-04-29T18:00:03Z)

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.