Quantum Circuit Compilation And Hybrid Computation Using Pauli-based Computation

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Filipa C. R. Peres^1,2 and Ernesto F. Galvão^1,3

¹International Iberian Nanotechnology Laboratory (INL), Av. Mestre José Veiga, 4715-330 Braga, Portugal
²Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, rua do Campo Alegre s/n, 4169–007 Porto, Portugal
³Instituto de Física, Universidade Federal Fluminense, Avenida General Milton Tavares de Souza s/n, Niterói, Rio de Janeiro 24210-340, Brazil

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Abstract

Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a PBC on $t$ qubits. Here we propose practical ways of implementing PBC as adaptive quantum circuits and provide code to do the required classical side-processing. Our schemes reduce the number of quantum gates to $O(t^2)$ (from a previous $O(t^3 / log t)$ scaling) and space/time trade-offs are discussed which lead to a reduction of the depth from $O(t log t)$ to $O(t)$ within our schemes, at the cost of $t$ additional auxiliary qubits. We compile examples of random and hidden-shift quantum circuits into adaptive PBC circuits. We also simulate hybrid quantum computation, where a classical computer effectively extends the working memory of a small quantum computer by $k$ virtual qubits, at a cost exponential in $k$. Our results demonstrate the practical advantage of PBC techniques for circuit compilation and hybrid computation.

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Featured image: In a Pauli-based computation (PBC), the computation is driven by a sequence of at most $t$ adaptively chosen, compatible, and independent multiqubit Pauli measurements performed on an input magic state of $t$ qubits [top].
Such a PBC can be translated back into (adaptive) quantum circuits, with each Pauli measurement being performed by an appropriate sequence of Clifford gates followed by a single-qubit measurement [bottom]. We propose three different methods to carry out this translation from PBC to quantum circuits; this picture illustrates only the first of those.
These ideas can be explored to perform circuit compilation and hybrid computation.

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Popular summary

Large-scale, fault-tolerant quantum computers are expected to solve tasks that are out of reach for their classical counterparts. This enticing prospect has propelled a lot of recent research in the fields of quantum information and quantum computation.
Unfortunately, current devices are still somewhat limited in their capabilities. Thus, smart schemes are needed that allow us to trade classical for quantum resources. In our work, we explore a universal model of quantum computation known as Pauli-based computation. We show that this model can be used to compile quantum circuits dominated by Clifford gates, demonstrating helpful quantum resource savings in many cases. We also describe gains in efficiency in hybrid quantum-classical computation, where the two types of computers work together to simulate a larger quantum device. Our paper is accompanied by open-access Python code that allows users to perform both compilation and hybrid computation on arbitrary user-specified circuits described using the common Clifford+$T$ gate set.
We expect our work to be relevant for near- and intermediate-term applications, but also in the long term, as the optimization of quantum resources should be of interest even after fault-tolerant quantum computing is achieved.

► BibTeX data

@article{Peres2023quantumcircuit, doi = {10.22331/q-2023-10-03-1126}, url = {https://doi.org/10.22331/q-2023-10-03-1126}, title = {Quantum circuit compilation and hybrid computation using {P}auli-based computation}, author = {Peres, Filipa C. R. and Galv{~{a}}o, Ernesto F.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1126}, month = oct, year = {2023}<br /> }

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Cited by

[1] Michael Zurel, Lawrence Z. Cohen, and Robert Raussendorf, “Simulation of quantum computation with magic states via Jordan-Wigner transformations”, arXiv:2307.16034, (2023).

[2] Qiuhao Chen, Yuxuan Du, Qi Zhao, Yuling Jiao, Xiliang Lu, and Xingyao Wu, “Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning”, arXiv:2204.06904, (2022).

[3] Filipa C. R. Peres, “Pauli-based model of quantum computation with higher-dimensional systems”, Physical Review A 108 3, 032606 (2023).

[4] Michael Zurel, Cihan Okay, and Robert Raussendorf, “Simulating quantum computation with magic states: how many “bits” for “it”?”, arXiv:2305.17287, (2023).

[5] Mark Koch, Richie Yeung, and Quanlong Wang, “Speedy Contraction of ZX Diagrams with Triangles via Stabiliser Decompositions”, arXiv:2307.01803, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-10-04 03:09:33). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-10-04 03:09:31).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2023-10-03-1126/

Time Stamp: October 3, 2023

Time Stamp: Dec 20, 2023

Quantum circuit compilation and hybrid computation using Pauli-based computation

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