ZX-calculus publicationshttp://zxcalculus.com/publications.rssAn up to date list of the newest publications related to the ZX-calculusen-USMon, 30 Sep 2024 15:02:09 GMTrfeed v1.0.0https://github.com/svpino/rfeed/blob/master/README.mdFusion and flow: formal protocols to reliably build photonic graph stateshttp://arxiv.org/abs/2409.13541Photonics offers a promising platform for implementations of measurement-based quantum computing. Recently proposed fusion-based architectures aim to achieve universality and fault-tolerance. In these approaches, computation is carried out by performing fusion and single-qubit measurements on a resource graph state. The verification of these architectures requires linear algebraic, probabilistic, and control flow structures to be combined in a unified formal language. This paper develops a framework for photonic quantum computing by bringing together linear optics, ZX calculus, and dataflow programming. We characterize fusion measurements that induce Pauli errors and show that they are correctable using a novel flow structure for fusion networks. We prove the correctness of new repeat-until-success protocols for the realization of arbitrary fusions and provide a graph-theoretic proof of universality for linear optics with entangled photon sources. The proposed framework paves the way for the development of compilation algorithms for photonic quantum computing.Giovanni de Felice, Boldizsár Poór, Lia Yeh and William CashmanFri, 20 Sep 2024 00:00:00 GMThttp://arxiv.org/abs/2409.13541Parallel Quantum Circuit Extraction from MBQC-Patternshttps://dx.doi.org/10.1109/IPDPSW63119.2024.00179In the model of measurement-based quantum computing (MBQC), computations are performed via sequential measurements on a highly entangled graph state. MBQC is a natural model for photonic quantum computing and has been shown to be useful for tasks like optimization and verification of general quantum computations. Therefore, it is often necessary to translate between MBQC and the predominantly used quantum circuit model in a fast and reliable way. While there are algorithms with linear complexity to extract quantum circuits from measurement patterns using additional ancilla qubits, efficient ancilla-free extraction has shown to be more costly. We develop strategies to parallelize an existing extraction algorithm based on ZX-calculus by exploiting the graph structure of measurement patterns and evaluate the performance on patterns obtained from a benchmark set of quantum circuits. Our results suggest that possible parallelization speedups are closely related to the graph structure of a pattern.Marcel Quanz, Korbinian Staudacher and Karl FürlingerSun, 15 Sep 2024 00:00:00 GMThttps://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=10596505&casa_token=IvO5I8HAAmsAAAAA:s1XrQZcpF079508i5_tYXIbnybpxOWLWMuGULR-iMG0gI6LUZh9bw2OHBsaAOUYTySpqIi-jHwo&tag=1Smarter k-Partitioning of ZX-Diagrams for Improved Quantum Circuit Simulationhttp://arxiv.org/abs/2409.00828We introduce a novel method for strong classical simulation of quantum circuits based on optimally k-partitioning ZX-diagrams, reducing each part individually, and then efficiently cross-referencing their results to conclude the overall probability amplitude of the original circuit. We then analyse how this method fares against the alternatives for circuits of various size, shape, and interconnectedness and demonstrate how it is often liable to outperform those alternatives in speed by orders of magnitude.Matthew SutcliffeSun, 01 Sep 2024 00:00:00 GMThttp://arxiv.org/abs/2409.00828Magic of the Heisenberg Picturehttp://arxiv.org/abs/2408.16047Magic quantifies the non-Clifford operations required for preparing a state on quantum processors and sets bounds on the classical computational complexity of simulating quantum dynamics. We study a magic resource theory for operators, which is dual to that describing states. We identify that the stabilizer Rényi entropy analog in operator space is a good magic monotone satisfying the usual conditions, while inheriting efficient computability properties and providing a tight lower-bound to the minimum number of non-Clifford gates in a circuit. It is operationally well-defined as quantifying how well one can approximate an operator with one that has only few Pauli strings; analogous to the relation between entanglement entropy and tensor-network truncation. An immediate advantage is that the operator stabilizer entropies exhibit inherent locality through a Lieb-Robinson bound, making them particularly suited for studying local dynamic magic generation in many-body systems. We compute this quantity analytically in two distinct regimes. First, we show that random evolution or circuits typically have approximately maximal magic in the Heisenberg picture for all R\ńyi indices, and evaluate the Page correction. Second, harnessing both dual unitarity and ZX graphical calculus, we compute the operator stabilizer entropy evolution for an interacting integrable XXZ circuit. In this case, magic quickly saturates to a constant; a distinct Heisenberg picture phenomena and suggestive of a connection to integrability. We argue that this efficiently computable operator magic monotone reveals structural properties of many-body magic generation, and can inspire novel Clifford-assisted tensor network methods.Neil Dowling, Pavel Kos and Xhek TurkeshiWed, 28 Aug 2024 00:00:00 GMThttp://arxiv.org/abs/2408.16047Redefining Lexicographical Ordering: Optimizing Pauli String Decompositions for Quantum Compilinghttp://arxiv.org/abs/2408.00354In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we propose a novel algorithm for the synthesis of trotterized time-evolution operators that results in circuits with significantly fewer gates than previous solutions. Our synthesis procedure takes the qubit connectivity of a target quantum computer into account. As a result, the generated quantum circuit does not require routing, and no additional CNOT gates are needed to run the resulting circuit on a target device. We compare our algorithm against Paulihedral and TKET, and show a significant improvement for randomized circuits and different molecular ansatzes. We also investigate the Trotter error introduced by our ordering of the terms in the Hamiltonian versus default ordering and the ordering from the baseline methods and conclude that our method on average does not increase the Trotter error.Qunsheng Huang, David Winderl, Arianne Meijer-van de Griend and Richie YeungThu, 01 Aug 2024 00:00:00 GMThttp://arxiv.org/abs/2408.00354Enhancing Encoding Rate through Alternate Floquetificationhttps://dx.doi.org/10.23919/CCC63176.2024.10661713Quantum error correction codes protect quantum systems against environmental noise, enabling fault-tolerant quantum computing. Among various codes, color codes have received considerable attention for their geometric locality, high error thresholds, and transversal logical operators. A canonical example is the [[4,2,2]] code implemented on a square lattice, which identifies single-qubit errors through four-qubit check measurements. By applying Floquetification to the [[4,2,2]] color code, a [[12,2,2]] Floquet code based on a double hexagon lattice has recently been developed, leading to a decrease in measurement weight from four to two. However, the aforementioned improvement is offset by a decrease in the encoding rate from 1/2 to 1/6, thus requiring an increased number of physical qubits. In this work, we provide a Floquetification process tailored for the [[4,2,2]] code. This leads to a new [[10,4,2]] Floquet code on a double pentagon lattice that not only retains weight two measurements but also enhances the encoding rate compared to the [[12,2,2]] Floquet code.Yabo Wang, Yunlong Xiao, Kishor Bharti and Bo QiSun, 28 Jul 2024 00:00:00 GMThttps://ieeexplore.ieee.org/abstract/document/10661713Qubit-count optimization using ZX-calculushttp://arxiv.org/abs/2407.10171We propose several methods for optimizing the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing, as much as possible, the gadgetization of Hadamard gates, which is a procedure used by some $T$-count optimizers to circumvent Hadamard gates at the expense of additional qubits. We prove the NP-hardness of this problem and we present an algorithm for solving it. We also propose a more general approach to optimize the number of qubits by showing how it relates to the problem of finding a minimal-width path-decomposition of the graph associated with a given ZX-diagram. This approach can be used to optimize the number of qubits for any computational model that can natively be depicted in ZX-calculus, such as the Pauli Fusion computational model which can represent lattice surgery operations. We also show how this method can be used to efficiently optimize the number of qubits in a quantum circuit by using the ZX-calculus as an intermediate representation.Vivien VandaeleSun, 14 Jul 2024 00:00:00 GMThttp://arxiv.org/abs/2407.10171The XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetimehttp://arxiv.org/abs/2407.08566Analyzing and developing new quantum error-correcting schemes is one of the most prominent tasks in quantum computing research. In such efforts, introducing time dynamics explicitly in both analysis and design of error-correcting protocols constitutes an important cornerstone. In this work, we present a graphical formalism based on tensor networks to capture the logical action and error-correcting capabilities of any Clifford circuit with Pauli measurements. We showcase the formalism on new Floquet codes derived from topological subsystem codes, which we call XYZ ruby codes. Based on the projective symmetries of the building blocks of the tensor network we develop a framework of Pauli flows. Pauli flows allow for a graphical understanding of all quantities entering an error correction analysis of a circuit, including different types of QEC experiments, such as memory and stability experiments. We lay out how to derive a well-defined decoding problem from the tensor network representation of a protocol and its Pauli flows alone, independent of any stabilizer code or fixed circuit. Importantly, this framework applies to all Clifford protocols and encompasses both measurement- and circuit-based approaches to fault tolerance. We apply our method to our new family of dynamical codes which are in the same topological phase as the 2+1d color code, making them a promising candidate for low-overhead logical gates. In contrast to its static counterpart, the dynamical protocol applies a Z3 automorphism to the logical Pauli group every three timesteps. We highlight some of its topological properties and comment on the anyon physics behind a planar layout. Lastly, we benchmark the performance of the XYZ ruby code on a torus by performing both memory and stability experiments and find competitive circuit-level noise thresholds of 0.18%, comparable with other Floquet codes and 2+1d color codes.Julio C. Magdalena de la Fuente, Josias Old, Alex Townsend-Teague, Manuel Rispler, Jens Eisert and Markus MüllerThu, 11 Jul 2024 00:00:00 GMThttp://arxiv.org/abs/2407.08566Hybrid Quantum-Classical Machine Learning with String Diagramshttp://arxiv.org/abs/2407.03673Central to near-term quantum machine learning is the use of hybrid quantum-classical algorithms. This paper develops a formal framework for describing these algorithms in terms of string diagrams: a key step towards integrating these hybrid algorithms into existing work using string diagrams for machine learning and differentiable programming. A notable feature of our string diagrams is the use of functor boxes, which correspond to a quantum-classical interfaces. The functor used is a lax monoidal functor embedding the quantum systems into classical, and the lax monoidality imposes restrictions on the string diagrams when extracting classical data from quantum systems via measurement. In this way, our framework provides initial steps toward a denotational semantics for hybrid quantum machine learning algorithms that captures important features of quantum-classical interactions.Alexander Koziell-Pipe and Aleks KissingerThu, 04 Jul 2024 00:00:00 GMThttp://arxiv.org/abs/2407.03673Automated reasoning in quantum circuit compilationhttps://spin-web.github.io/SPIN2024/assets/preproceedings/SPIN2024-paper6.pdfAutomated reasoning techniques have been proven of immense importance in classical applications like formal verification, circuit design and probabilistic inference. The domain of quantum computing poses new challenges of a different nature, such as the compilation of quantum circuits, which involves ``quantum-hard'' tasks such as the simulation, optimization, synthesis, and equivalence checking of quantum circuits. We ask the question of how effective the methods motivated by classical automated reasoning can be for quantum compilation. We assess their current applicability to this new domain by discussing the recent advances. In particular, we focus on three core automated reasoning approaches: decision diagrams, satisfiability and graphical calculus-based methods. In this survey, we explain in a manner accessible to those unfamiliar with quantum computing concepts how these prominent automated reasoning methods have found numerous applications in quantum circuit compilation. We find that surprisingly all considered reasoning methods, while originally developed for classical purposes, can excel at various compilation tasks for even universal quantum circuits.Dimitrios Thanos, Alejandro Villoria, Sebastiaan Brand, Arend-Jan Quist, Jingyi Mei, Tim Coopmans and Alfons LaarmanThu, 04 Jul 2024 00:00:00 GMThttps://spin-web.github.io/SPIN2024/assets/preproceedings/SPIN2024-paper6.pdf