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Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions
Quantum Physics · Submitted 2 Sep 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We adapt these techniques from the original setting of Clifford circuits with magic state injection to generic ZX-diagrams and show that, by interleaving this "chunked" decomposition with a ZX-calculus-based simplification strategy, we can obtain stabiliser decompositions that are many orders of magnitude smaller than existing approaches.
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The abstract, sentence by sentence
We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the `sum-of-stabilisers' method with an automated simplification strategy based on the ZX-calculus. Recently it was shown that quantum circuits can be classically simulated by expressing the non-stabiliser gates in a circuit as magic state injections and decomposing them in chunks of 2-6 states at a time, obtaining sums of (efficiently-simulable) stabiliser states with many fewer terms than the naive approach. We adapt these techniques from the original setting of Clifford circuits with magic state injection to generic ZX-diagrams and show that, by interleaving this "chunked" decomposition with a ZX-calculus-based simplification strategy, we can obtain stabiliser decompositions that are many orders of magnitude smaller than existing approaches. We illustrate this technique to perform exact norm calculations (and hence strong simulation) on the outputs of random 50- and 100-qubit Clifford+T circuits with up to 70 T-gates as well as a family of hidden shift circuits previously considered by Bravyi and Gosset with over 1000 T-gates.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the `sum-of-stabilisers' method with an automated simplification strategy based on the ZX-calculus. | contribution 1.00 | 0.94 | 0.46 | asserted 1.00 |
| s1 | Recently it was shown that quantum circuits can be classically simulated by expressing the non-stabiliser gates in a circuit as magic state injections and decomposing them in chunks of 2-6 states at a time, obtaining sums of (efficiently-simulable) stabiliser states with many fewer terms than the naive approach. | background 1.00 | 0.04 | 0.05 | asserted 1.00 |
| s2 | We adapt these techniques from the original setting of Clifford circuits with magic state injection to generic ZX-diagrams and show that, by interleaving this "chunked" decomposition with a ZX-calculus-based simplification strategy, we can obtain stabiliser decompositions that are many orders of magnitude smaller than existing approaches. | contribution 0.74 | 0.94 | 0.67 | asserted 0.99 |
| s3 | We illustrate this technique to perform exact norm calculations (and hence strong simulation) on the outputs of random 50- and 100-qubit Clifford+T circuits with up to 70 T-gates as well as a family of hidden shift circuits previously considered by Bravyi and Gosset with over 1000 T-gates. | result 0.86 | 0.95 | 0.21 | asserted 1.00 |
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The paper
Original abstract
We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the `sum-of-stabilisers' method with an automated simplification strategy based on the ZX-calculus. Recently it was shown that quantum circuits can be classically simulated by expressing the non-stabiliser gates in a circuit as magic state injections and decomposing them in chunks of 2-6 states at a time, obtaining sums of (efficiently-simulable) stabiliser states with many fewer terms than the naive approach. We adapt these techniques from the original setting of Clifford circuits with magic state injection to generic ZX-diagrams and show that, by interleaving this "chunked" decomposition with a ZX-calculus-based simplification strategy, we can obtain stabiliser decompositions that are many orders of magnitude smaller than existing approaches. We illustrate this technique to perform exact norm calculations (and hence strong simulation) on the outputs of random 50- and 100-qubit Clifford+T circuits with up to 70 T-gates as well as a family of hidden shift circuits previously considered by Bravyi and Gosset with over 1000 T-gates.
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How the literature uses it
6 arXiv papers cite this in 25 sentences
Papers citing it · 7 sentences without a confident label
Builds on it 1 paper
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In this article we build on the work of both [ref] and [ref] , by significantly improving Step [ref].
Classical simulation of quantum circuits with partial and graphical stabiliser decompositions · Introduction · 1.00
Uses its method or tool 2 papers
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We implemented our new decompositions in , the software used in [ref] , and assessed the performance of our method by benchmarking the same quantum circuits as [ref] .
Classical simulation of quantum circuits with partial and graphical stabiliser decompositions · Introduction · 0.95
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It is based on the 4 $T$-gate representation of the CCZ gate from [ref] .
Circuit Extraction for ZX-diagrams can be #P-hard · Proof of hardness of Circuit extraction · 0.89
Compares with it 1 paper
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While our method used at most 1 second for each of these, the method of [ref] required more than 1000 seconds for some.
Classical simulation of quantum circuits with partial and graphical stabiliser decompositions · Introduction · 1.00
Cites it as background 5 papers
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It has proven enormously successful in applications from equivalence checking [ref] , to circuit optimization [ref] and simulation [ref] .
Equivalence Checking of Quantum Circuits by Model Counting · Related Work · 0.92
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Arguably one of the biggest research directions is concerned with classical simulation [ref] [ref] [ref] , quantum circuit optimization [ref] [ref] [ref] and quantum circuit equality validation [ref] .
Graphical Stabilizer Decompositions for Multi-Control Toffoli Gate Dense Quantum Circuits · Applications · 0.96
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State-vector methods scale with the Hilbert-space dimension $2^n$ [ref] ; MPS and related low-rank methods are governed by entanglement and the tolerated approximation error [ref] ; and stabilizer or near-Clifford methods are governed by magic, $T$ count, or the size of an active non-Clifford subspace [ref] .
Classical Simulation and Design Frontiers for IBM's Doped Clifford Sampling Experiment · Introduction · 0.91
What it cites · 9 sentences without a confident label
Uses the method or tool of 1 paper
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Instead of the simplification strategy of Section [ref] based on local complementation, we could then use the strategy of Ref. [ref] that uses hyper-local-complementation.
Hypergraph Simplification: Linking the Path-sum Approach to the ZH-calculus · Conclusion and Future Work · 0.86
Cites as background 2 papers
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Operators of this form arise naturally in various contexts, including generic representations of Clifford+T circuits [ref] and Hamiltonian simulation via trotterisation [ref] .
A Generic Compilation Strategy for the Unitary Coupled Cluster Ansatz · Random Clifford+T circuits · 0.85
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For a review see [ref] , and for a book-length introduction see Ref. [ref] .
ZX-calculus for the working quantum computer scientist · The ZX-calculus · 1.00
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