Flow-preserving ZX-calculus Rewrite Rules for Optimisation and Obfuscation

• URL: http://arxiv.org/abs/2304.08166v2
• Date: Thu, 31 Aug 2023 07:00:41 GMT
• Title: Flow-preserving ZX-calculus Rewrite Rules for Optimisation and Obfuscation
• Authors: Tommy McElvanney (University of Birmingham), Miriam Backens (University of Birmingham)
• Abstract summary: We introduce several ZX-calculus rewrite rules that increase the number of qubits and preserve the existence of Pauli flow. We also give the first flow-preserving rewrite rule that allows measurement angles to be changed arbitrarily.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on a resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense, with Pauli flow being the most general of these. Computations, represented as measurement patterns, may be rewritten to optimise resource use and for other purposes. Such rewrites need to preserve the existence of flow to ensure the new pattern can still be implemented deterministically. The majority of existing work in this area has focused on rewrites that reduce the number of qubits, yet it can be beneficial to increase the number of qubits for certain kinds of optimisation, as well as for obfuscation. In this work, we introduce several ZX-calculus rewrite rules that increase the number of qubits and preserve the existence of Pauli flow. These rules can be used to transform any measurement pattern into a pattern containing only (general or Pauli) measurements within the XY-plane. We also give the first flow-preserving rewrite rule that allows measurement angles to be changed arbitrarily, and use this to prove that the `neighbour unfusion' rule of Staudacher et al. preserves the existence of Pauli flow. This implies it may be possible to reduce the runtime of their two-qubit-gate optimisation procedure by removing the need to regularly run the costly gflow-finding algorithm.

Related papers

• Floquetifying stabiliser codes with distance-preserving rewrites [0.0]
  ZX calculus is a graphical language for representing and rewriting quantum circuits. Applying rewrites to a circuit that implements an error-correcting code can change its distance. We define the notion of distance-preserving rewrites that enable the transformation of error-correcting codes without changing their distance.
  arXiv  Detail & Related papers  (2024-10-22T17:56:26Z)
• Pauli Flow on Open Graphs with Unknown Measurement Labels [0.0]
  One-way quantum computation, or measurement-based quantum computation, is a universal model of quantum computation alternative to the circuit model. It is known how to efficiently determine the existence of Pauli flow given an open graph together with a measurement labelling. We show that, in the case of X and Z measurements only, flow existence corresponds to the right-invertibility of a matrix derived from the adjacency matrix.
  arXiv  Detail & Related papers  (2024-08-12T11:19:27Z)
• Qubit Number Optimization for Restriction Terms of QUBO Hamiltonians [62.997667081978825]
  It is mathematically allowed to ask for fractional values of $R$. We show how they can reduce the number of qubits needed to implement the restriction hamiltonian even further. Finally, we characterize the response of DWave's Advantage$_$system4.1 Quantum Annealer (QA) when faced with the implementation of FRCs.
  arXiv  Detail & Related papers  (2023-06-12T08:25:56Z)
• Graphix: optimizing and simulating measurement-based quantum computation on local-Clifford decorated graph [0.0]
  We introduce an open-source software library Graphix, which optimize and simulates measurement-based quantum computation (MBQC) By combining the measurement calculus with an efficient graph state simulator, Graphix allows the classical preprocessing of Pauli measurements in the measurement patterns.
  arXiv  Detail & Related papers  (2022-12-22T18:58:20Z)
• Complete Flow-Preserving Rewrite Rules for MBQC Patterns with Pauli Measurements [0.0]
  We show that introducing new Z-measured qubits, connected to any subset of the existing qubits, preserves the existence of Pauli flow. We prove that any MBQC-like stabilizer ZX-diagram with Pauli flow can be rewritten into this canonical form.
  arXiv  Detail & Related papers  (2022-05-04T11:42:20Z)
• Deep Equilibrium Optical Flow Estimation [80.80992684796566]
  Recent state-of-the-art (SOTA) optical flow models use finite-step recurrent update operations to emulate traditional algorithms. These RNNs impose large computation and memory overheads, and are not directly trained to model such stable estimation. We propose deep equilibrium (DEQ) flow estimators, an approach that directly solves for the flow as the infinite-level fixed point of an implicit layer.
  arXiv  Detail & Related papers  (2022-04-18T17:53:44Z)
• GMFlow: Learning Optical Flow via Global Matching [124.57850500778277]
  We propose a GMFlow framework for learning optical flow estimation. It consists of three main components: a customized Transformer for feature enhancement, a correlation and softmax layer for global feature matching, and a self-attention layer for flow propagation. Our new framework outperforms 32-iteration RAFT's performance on the challenging Sintel benchmark.
  arXiv  Detail & Related papers  (2021-11-26T18:59:56Z)
• Self Normalizing Flows [65.73510214694987]
  We propose a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer. This reduces the computational complexity of each layer's exact update from $mathcalO(D3)$ to $mathcalO(D2)$. We show experimentally that such models are remarkably stable and optimize to similar data likelihood values as their exact gradient counterparts.
  arXiv  Detail & Related papers  (2020-11-14T09:51:51Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• LiteFlowNet3: Resolving Correspondence Ambiguity for More Accurate Optical Flow Estimation [99.19322851246972]
  We introduce LiteFlowNet3, a deep network consisting of two specialized modules to address the problem of optical flow estimation. LiteFlowNet3 not only achieves promising results on public benchmarks but also has a small model size and a fast runtime.
  arXiv  Detail & Related papers  (2020-07-18T03:30:39Z)
• There and back again: A circuit extraction tale [0.0]
  We give the first circuit-extraction algorithm to work for one-way computations containing measurements in all three planes. The algorithm is efficient and the resulting circuits do not contain ancillae. We bring together several known rewrite rules for measurement patterns and formalise them in a unified notation using the ZX-calculus.
  arXiv  Detail & Related papers  (2020-03-03T17:45:09Z)

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.