ZX-calculus publicationshttp://zxcalculus.com/publications.rssAn up to date list of the newest publications related to the ZX-calculusen-USTue, 21 May 2024 14:57:24 GMTrfeed v1.0.0https://github.com/svpino/rfeed/blob/master/README.mdZX-calculus is Complete for Finite-Dimensional Hilbert Spaceshttp://arxiv.org/abs/2405.10896The ZX-calculus is a graphical language for reasoning about quantum computing and quantum information theory. As a complete graphical language, it incorporates a set of axioms rich enough to derive any equation of the underlying formalism. While completeness of the ZX-calculus has been established for qubits and the Clifford fragment of prime-dimensional qudits, universal completeness beyond two-level systems has remained unproven until now. In this paper, we present a proof establishing the completeness of finite-dimensional ZX-calculus, incorporating only the mixed-dimensional Z-spider and the qudit X-spider as generators. Our approach builds on the completeness of another graphical language, the finite-dimensional ZW-calculus, with direct translations between these two calculi. By proving its completeness, we lay a solid foundation for the ZX-calculus as a versatile tool not only for quantum computation but also for various fields within finite-dimensional quantum theory.Boldizsár Poór, Razin A. Shaikh and Quanlong WangFri, 17 May 2024 00:00:00 GMThttp://arxiv.org/abs/2405.10896ZX Graphical Calculus for Continuous-Variable Quantum Processeshttp://arxiv.org/abs/2405.07246Continuous-variable (CV) quantum information processing is a promising candidate for large-scale fault-tolerant quantum computation. However, analysis of CV quantum process relies mostly on direct computation of the evolution of operators in the Heisenberg picture, and the features of CV space has yet to be thoroughly investigated in an intuitive manner. One key ingredient for further exploration of CV quantum computing is the construction of a computational model that brings visual intuition and new tools for analysis. In this paper, we delve into a graphical computational model, inspired by a similar model for qubit-based systems called the ZX calculus, that enables the representation of arbitrary CV quantum process as a simple directed graph. We demonstrate the utility of our model as a graphical tool to comprehend CV processes intuitively by showing how equivalences between two distinct quantum processes can be proven as a sequence of diagrammatic transformations in certain cases. We also examine possible applications of our model, such as measurement-based quantum computing, characterization of Gaussian and non-Gaussian processes, and circuit optimization.Hironari Nagayoshi, Warit Asavanant, Ryuhoh Ide, Kosuke Fukui, Atsushi Sakaguchi, Jun-ichi Yoshikawa, Nicolas C. Menicucci and Akira FurusawaSun, 12 May 2024 00:00:00 GMThttp://arxiv.org/abs/2405.07246Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ modelhttp://arxiv.org/abs/2405.04448Quantum systems can not be efficiently simulated classically due to the presence of entanglement and nonstabilizerness, also known as quantum magic. Here we study the generation of magic under evolution by a quantum circuit. To be able to provide exact solutions, we focus on the dual-unitary XXZ model and a measure of magic called stabilizer Rényi entropy (SRE). Moreover, we focus also on long-range SRE, which cannot be removed by short-depth quantum circuits. To obtain exact solutions we use a ZX-calculus representation and graphical rules for the evaluation of the required expressions. We obtain exact results for SRE after short-time evolution in the thermodynamic limit and for long-range SRE for all times and all R\ńyi parameters for a particular partition of the state. Since the numerical evaluation of these quantities is exponentially costly in the R\'ýi parameter, we verify this numerically for low R\'eí parameters and accessible system sizes and provide numerical results for the long-range SRE in other bipartitions.Jordi Arnau Montañà López and Pavel KosTue, 07 May 2024 00:00:00 GMThttp://arxiv.org/abs/2405.04448EPOC: A Novel Pulse Generation Framework Incorporating Advanced Synthesis Techniques for Quantum Circuitshttp://arxiv.org/abs/2405.03804In this paper we propose EPOC, an efficient pulse generation framework for quantum circuits that combines ZX-Calculus, circuit partitioning, and circuit synthesis to accelerate pulse generation. Unlike previous works that focus on generating pulses from unitary matrices without exploring equivalent representations, EPOC employs a finer granularity approach by grouping quantum gates and decomposing the resulting unitary matrices into smaller ones using synthesis techniques. This enables increased parallelism and decreased latency in quantum pulses. EPOC also continuously optimizes the circuit by identifying equivalent representations, leading to further reductions in circuit latency while minimizing the computational overhead associated with quantum optimal control. We introduce circuit synthesis into the workflow of quantum optimal control for the first time and achieve a 31.74% reduction in latency compared to previous work and a 76.80% reduction compared to the gate-based method for creating pulses. The approach demonstrates the potential for significant performance improvements in quantum circuits while minimizing computational overhead.Jinglei Cheng, Yuchen Zhu, Yidong Zhou, Hang Ren, Zhixin Song and Zhiding LiangMon, 06 May 2024 00:00:00 GMThttp://arxiv.org/abs/2405.03804[Video] The how and why of translating between the circuit model and the one-way model of quantum computing 🎥https://pirsa.org/24050004In the one-way model of measurement based quantum computing, unlike the quantum circuit model, a computation is driven not by unitary gates but by successive adaptive single-qubit measurements on an entangled resource state. So-called flow properties ensure that a one-way computation, described by a measurement pattern, is deterministic overall (up to Pauli corrections on output qubits). Translations between quantum circuits and measurement patterns have been used to show universality of the one-way model, verify measurement patterns, optimise quantum circuits, and more. Yet while it is straightforward to translate a circuit into a measurement pattern, the question of algorithmic "circuit extraction" -- how to translate general measurement patterns with flow to ancilla-free circuits -- had long remained open for all but the simplest type of flow. In this talk, we will recap the one-way model of quantum computing and then explain how the problem of circuit extraction was resolved using the ZX-calculus as a common language for circuits and measurement patterns. We also discuss applications.Miriam BackensFri, 03 May 2024 00:00:00 GMThttps://pirsa.org/24050004A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computinghttp://arxiv.org/abs/2404.18369Quantum error correction is necessary for large-scale quantum computing. A promising quantum error correcting code is the surface code. For this code, fault-tolerant quantum computing (FTQC) can be performed via lattice surgery, i.e., splitting and merging patches of code. Given the frequent use of certain lattice-surgery subroutines (LaS), it becomes crucial to optimize their design in order to minimize the overall spacetime volume of FTQC. In this study, we define the variables to represent LaS and the constraints on these variables. Leveraging this formulation, we develop a synthesizer for LaS, LaSsynth, that encodes a LaS construction problem into a SAT instance, subsequently querying SAT solvers for a solution. Starting from a baseline design, we can gradually invoke the solver with shrinking spacetime volume to derive more compact designs. Due to our foundational formulation and the use of SAT solvers, LaSsynth can exhaustively explore the design space, yielding optimal designs in volume. For example, it achieves 8% and 18% volume reduction respectively over two states-of-the-art human designs for the 15-to-1 T-factory, a bottleneck in FTQC.Daniel Bochen Tan, Murphy Yuezhen Niu and Craig GidneyMon, 29 Apr 2024 00:00:00 GMThttp://arxiv.org/abs/2404.18369Constructing $\mathrmNP^\mathord#\mathrm P$-complete problems and $\mathord#\mathrm P$-hardness of circuit extraction in phase-free ZHhttp://arxiv.org/abs/2404.10913The ZH calculus is a graphical language for quantum computation reasoning. The phase-free variant offers a simple set of generators that guarantee universality. ZH calculus is effective in MBQC and analysis of quantum circuits constructed with the universal gate set Toffoli+H. While circuits naturally translate to ZH diagrams, finding an ancilla-free circuit equivalent to a given diagram is hard. Here, we show that circuit extraction for phase-free ZH calculus is $\mathord#\mathrm P$-hard, extending the existing result for ZX calculus. Another problem believed to be hard is comparing whether two diagrams represent the same process. We show that two closely related problems are $\mathrmNP^\mathord#\mathrm P$-complete. The first problem is: given two processes represented as diagrams, determine the existence of a computational basis state on which they equalize. The second problem is checking whether the matrix representation of a given diagram contains an entry equal to a given number. Our proof adapts the proof of Cook-Levin theorem to a reduction from a non-deterministic Turing Machine with access to $\mathord#\mathrm P$ oracle.Piotr MitosekTue, 16 Apr 2024 00:00:00 GMThttp://arxiv.org/abs/2404.10913Catalysing Completeness and Universalityhttp://arxiv.org/abs/2404.09915A catalysis state is a quantum state that is used to make some desired operation possible or more efficient, while not being consumed in the process. Recent years have seen catalysis used in state-of-the-art protocols for implementing magic state distillation or small angle phase rotations. In this paper we will see that we can also use catalysis to prove that certain gate sets are computationally universal, and to extend completeness results of graphical languages to larger fragments. In particular, we give a simple proof of the computational universality of the CS+Hadamard gate set using the catalysis of a $T$ gate using a CS gate, which sidesteps the more complicated analytic arguments of the original proof by Kitaev. This then also gives us a simple self-contained proof of the computational universality of Toffoli+Hadamard. Additionally, we show that the phase-free ZH-calculus can be extended to a larger complete fragment, just by using a single catalysis rule (and one scalar rule).Aleks Kissinger, Neil J. Ross and John van de WeteringMon, 15 Apr 2024 00:00:00 GMThttp://arxiv.org/abs/2404.09915Scalable spider nests (...or how to graphically grok transversal non-Clifford gates)http://arxiv.org/abs/2404.07828This is the second in a series of "graphical grokking" papers in which we study how stabiliser codes can be understood using the ZX calculus. In this paper we show that certain complex rules involving ZX diagrams, called spider nest identities, can be captured succinctly using the scalable ZX calculus, and all such identities can be proved inductively from a single new rule using the Clifford ZX calculus. This can be combined with the ZX picture of CSS codes, developed in the first "grokking" paper, to give a simple characterisation of the set of all transversal diagonal gates at the third level of the Clifford hierarchy implementable in an arbitrary CSS code.Aleks Kissinger and John van de WeteringThu, 11 Apr 2024 00:00:00 GMThttp://arxiv.org/abs/2404.07828Zero-temperature entanglement membranes in quantum circuitshttp://arxiv.org/abs/2404.02975In chaotic quantum systems, the entanglement of a region $A$ can be described in terms of the surface tension of a spacetime membrane pinned to the boundary of $A$. Here, we interpret the tension of this entanglement membrane in terms of the rate at which information "flows" across it. For any orientation of the membrane, one can define (generically nonunitary) dynamics across the membrane; we explore this dynamics in various space-time translation-invariant (STTI) stabilizer circuits in one and two spatial dimensions. We find that the flux of information across the membrane in these STTI circuits reaches a steady state. In the cases where this dynamics is nonunitary and the steady state flux is nonzero, this occurs because the dynamics across the membrane is unitary in a subspace of extensive entropy. This generalized unitarity is present in a broad class of STTI stabilizer circuits, and is also present in some special non-stabilizer models. The existence of multiple unitary (or generalized unitary) directions forces the entanglement membrane tension to be a piecewise linear function of the orientation of the membrane; in this respect, the entanglement membrane behaves like an interface in a zero-temperature classical lattice model. We argue that entanglement membranes in random stabilizer circuits that produce volume-law entanglement are also effectively at zero temperature.Grace M. Sommers, Sarang Gopalakrishnan, Michael J. Gullans and David A. HuseWed, 03 Apr 2024 00:00:00 GMThttp://arxiv.org/abs/2404.02975