Generators and Relations for 2-Qubit Clifford+T Operators
- URL: http://arxiv.org/abs/2204.02217v3
- Date: Wed, 15 Nov 2023 11:01:41 GMT
- Title: Generators and Relations for 2-Qubit Clifford+T Operators
- Authors: Xiaoning Bian (Dalhousie University), Peter Selinger (Dalhousie
University)
- Abstract summary: We give a presentation by generators and relations of the group of Clifford+T operators on two qubits.
The proof relies on an application of the Reidemeister-Schreier theorem to an earlier result of Greylyn, and has been formally verified in the proof assistant Agda.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We give a presentation by generators and relations of the group of Clifford+T
operators on two qubits. The proof relies on an application of the
Reidemeister-Schreier theorem to an earlier result of Greylyn, and has been
formally verified in the proof assistant Agda.
Related papers
- Mutual transformations of arbitrary ternary qubit trees by Clifford gates [55.2480439325792]
It is shown that ternary qubit trees with the same number of nodes can be transformed by the naturally defined sequence of Clifford gates into each other or into standard representation as 1D chain corresponding to Jordan-Wigner transform.
arXiv Detail & Related papers (2024-04-25T15:54:32Z) - Clifford circuits over non-cyclic abelian groups [0.0]
We show that every Clifford circuit can be efficiently classically simulated.
We additionally provide circuits for a universal quantum computing scheme based on local two-qudit Clifford gates and magic states.
arXiv Detail & Related papers (2024-02-21T18:26:25Z) - The Clifford theory of the $n$-qubit Clifford group [0.0]
Recent applications have made use of the representation theory of the Clifford group.
We find an unexpected correspondence between irreducible characters of the $n$-qubit Clifford group and those of the $(n+1)$-qubit Clifford group.
arXiv Detail & Related papers (2023-07-11T21:21:31Z) - Generators and Relations for 3-Qubit Clifford+CS Operators [0.0]
We give a presentation by generators and relations of the group of 3-qubit Clifford+CS operators.
We show that the 3-qubit Clifford+CS group, which is of course infinite, is the amalgamated product of three finite subgroups.
arXiv Detail & Related papers (2023-06-14T14:23:46Z) - General ordering theorem [0.0]
We prove the General Ordering Theorem (GOT), which establishes a relation among any pair of orderings.
We show that it acts on operators satisfying generic (i.e. operatorial) commutation relations.
Remarkably, it establishes a formal relation between these two theorems, and it provides compact expressions for them, unlike the notoriously complicated ones currently known.
arXiv Detail & Related papers (2023-02-02T17:49:35Z) - Duality theory for Clifford tensor powers [0.7826806223782052]
The representation theory of the Clifford group is playing an increasingly prominent role in quantum information theory.
In this paper, we provide a unified framework for the duality approach that also covers qubit systems.
arXiv Detail & Related papers (2022-08-02T18:27:17Z) - Bias-Robust Bayesian Optimization via Dueling Bandit [57.82422045437126]
We consider Bayesian optimization in settings where observations can be adversarially biased.
We propose a novel approach for dueling bandits based on information-directed sampling (IDS)
Thereby, we obtain the first efficient kernelized algorithm for dueling bandits that comes with cumulative regret guarantees.
arXiv Detail & Related papers (2021-05-25T10:08:41Z) - PRover: Proof Generation for Interpretable Reasoning over Rules [81.40404921232192]
We propose a transformer-based model that answers binary questions over rule-bases and generates the corresponding proofs.
Our model learns to predict nodes and edges corresponding to proof graphs in an efficient constrained training paradigm.
We conduct experiments on synthetic, hand-authored, and human-paraphrased rule-bases to show promising results for QA and proof generation.
arXiv Detail & Related papers (2020-10-06T15:47:53Z) - Generative Language Modeling for Automated Theorem Proving [94.01137612934842]
This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans might be addressable via generation from language models.
We present an automated prover and proof assistant, GPT-f, for the Metamath formalization language, and analyze its performance.
arXiv Detail & Related papers (2020-09-07T19:50:10Z) - Learning to Prove Theorems by Learning to Generate Theorems [71.46963489866596]
We learn a neural generator that automatically synthesizes theorems and proofs for the purpose of training a theorem prover.
Experiments on real-world tasks demonstrate that synthetic data from our approach improves the theorem prover.
arXiv Detail & Related papers (2020-02-17T16:06:02Z) - Joint measurability meets Birkhoff-von Neumann's theorem [77.34726150561087]
We prove that joint measurability arises as a mathematical feature of DNTs in this context, needed to establish a characterisation similar to Birkhoff-von Neumann's.
We also show that DNTs emerge naturally from a particular instance of a joint measurability problem, remarking its relevance in general operator theory.
arXiv Detail & Related papers (2018-09-19T18:57:45Z)
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.