Relating Measurement Patterns to Circuits via Pauli Flow

  title={Relating Measurement Patterns to Circuits via Pauli Flow},
  author={Will Simmons},
  • Will Simmons
  • Published 13 September 2021
  • Computer Science
  • ArXiv
The one-way model of Measurement-Based Quantum Computing and the gate-based circuit model give two different presentations of how quantum computation can be performed. There are known methods for converting any gate-based quantum circuit into a one-way computation, whereas the reverse is only efficient given some constraints on the structure of the measurement pattern. Causal flow and generalised flow have already been shown as sufficient, with efficient algorithms for identifying these… 

Figures and Tables from this paper

Circuit Extraction for ZX-diagrams can be #P-hard

This paper proves that any oracle that takes as input a ZX-diagram description of a unitary and produces samples of the output of the associated quantum computation enables efficient probabilistic solutions to NP-complete problems.

Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements

This work shows that introducing new Z -measured qu bits, connected to any subset of the existing qubits, preserves the existence of Pauli flow, and gives a unique canonical form for stabilizer ZX-diagrams inspired by recent work of Hu & Khesin.

Characterising Determinism in MBQCs involving Pauli Measurements

A new characterisation of determinism in measurement-based quantum computing, called Extended Pauli Flow, is introduced that is necessary and sufficient for robust determinism.

Phase-free ZX diagrams are CSS codes (...or how to graphically grok the surface code)

In this paper, we demonstrate a direct correspondence between phase-free ZX diagrams, a graphical notation for representing and manipulating a certain class of linear maps on qubits, and



Optimization of One-Way Quantum Computation Measurement Patterns

A new scheme is proposed to perform the optimization techniques simultaneously on patterns with flow and only gflow based on their geometries, and it is shown that the time complexity of the proposed approach is improved over the previous ones.

There and back again: A circuit extraction tale

This work gives the first circuit-extraction algorithm to work for one-way computations containing measurements in all three planes and having gflow, and brings together several known rewrite rules for measurement patterns and formalise them in a unified notation using the ZX-calculus.

Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus

A simplification strategy for ZX-diagrams is given based on the two graph transformations of local complementation and pivoting and it is shown that the resulting reduced diagram can be transformed back into a quantum circuit.

Generalized flow and determinism in measurement-based quantum computation

We extend the notion of quantum information flow defined by Danos and Kashefi (2006 Phys. Rev. A 74 052310) for the one-way model (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 910) and present a

Finding flows in the one-way measurement model

The one-way measurement model is a framework for universal quantum computation in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A

Finding Optimal Flows Efficiently

A polynomial time algorithm is introduced that outputs an optimal gflow of a given graph and thus finds an optimal correction strategy to the nondeterministic evolution due to measurements.

Towards Large-scale Functional Verification of Universal Quantum Circuits

  • M. Amy
  • Computer Science, Physics
  • 2018
A framework for the formal specification and verification of quantum circuits based on the Feynman path integral is introduced, and the algorithm is shown to give a polynomial-time decision procedure for checking the equivalence of Clifford group circuits.

Global Quantum Circuit Optimization

A new connection between two MBQC depth optimisation procedures, known as the maximally delayed generalised flow and signal shifting, is presented, which will allow an MBZC qubit optimisation procedure known as compactification to be applied to a large class of pattern including all those obtained from any arbitrary quantum circuit.

Reducing the number of non-Clifford gates in quantum circuits

We present a method for reducing the number of non-Clifford quantum gates, in particularly T-gates, in a circuit, an important task for efficiently implementing fault-tolerant quantum computations.

ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity

A new graphical calculus is presented that is sound and complete for universal quantum computation by demonstrating the reduction of any diagram to an easily describable normal form, which suggests that this calculus will be significantly more convenient for reasoning about the interplay between classical non-linear behaviour and purely quantum operations.