Alphabeta MathHow statement and proof provenance work
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The Pauli matrices
Definition
In the ordered computational basis of Qubit spaces and states, define the identity and Pauli endomorphisms of by
The displayed sign in fixes all later orientation and rotation conventions.
Remarks
The adjoint, product, and trace identities are proved in Pauli matrix algebra and trace identities.
Depends on
Used by
- Costed coherent evaluation of cyclic group powers Algorithm
- Dense-coding procedure Algorithm
- Exact success amplification by attenuating the good branch Algorithm
- QC24 State Preparation Algorithm
- Qubit teleportation procedure Algorithm
- Reversible embedding of a Boolean circuit Algorithm
- Stabilizer encoder by symplectic elimination Algorithm
- A symmetrized acceptance polynomial can exceed one between Hamming layers Counterexample
- Ancilla-free Rz approximation problem and T-count Definition
- Bloch coordinate maps Definition
- Clifford+T gate library and exact matrices Definition
- CNOT and Control-Target Order Definition
- Exact one-qubit gates and rotations Definition
- Finite toric-code Hamiltonian Definition
- Multi-Control Activation Pattern Definition
- Pauli measurement branch semantics Definition
- Pauli-path energy barrier Definition
- Phase aware n qubit pauli group Definition
- Phase-aware binary Clifford tableau Definition
- QAOA circuit and expected combinatorial objective Definition
- Square planar surface code Definition
- Toffoli and Fredkin gates Definition
- Toric star and plaquette checks Definition
- A one-query exact algorithm on a two-point OR promise Example
- Bloch coordinates of |0> and H|0> Example
- Cancelling identity padding fixes the LCU scale Example
- Pauli commutator and binary symplectic sign Example
- Stabilizer measurement on |0⟩ in the X basis Example
- Steane seven-qubit CSS code Example
- Teleportation branch and Pauli correction Example
- Three-Ising-anyon braid matrices are Clifford Example
- Two-term LCU postselection is input dependent Example
- A Finite Four-Round Verified Shor Correction Circuit Lemma
- Adaptive J angle and Pauli-frame update Lemma
- Clifford+T Is Dense Projectively on One Qubit Lemma
- CNOT Pauli action Lemma
- Computational basis states have an extended stabilizer tableau Lemma
- Exact Gray-code synthesis of multiplexed y- and z-axis rotations Lemma
- Finite Verified Steane Magic States and T Injection Lemma
- Fresh-target NOT and OR gadgets Lemma
…and 44 more results.
Dependency tree · two levels
5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- John Preskill, Quantum Computation, Chapter 2: Foundations I: States and Ensembles (updated July 2015) (standard reference, not scraped)
- Ronald de Wolf, Quantum Computing: Lecture Notes, arXiv:1907.09415v6 (2026-08-27) (standard reference, not scraped)
- Aram Harrow, 6.443/8.371/18.436 Quantum Information Science II, Lecture 1: Quantum states and operations (2018) (standard reference, not scraped)