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Abstract Photonic graph states are important for measurement- and fusion-based quantum computing, quantum networks, and sensing. They can in principle be generated deterministically by using emitters to create the requisite entanglement. Finding ways to minimize the number of entangling gates between emitters and understanding the overall optimization complexity of such protocols is crucial for practical implementations. Here, we address these issues using graph theory concepts. We develop optimizers that minimize the number of entangling gates, reducing them by up to 75% compared to naive schemes for moderately sized random graphs. While the complexity of optimizing emitter-emitter CNOT counts is likely NP-hard, we are able to develop heuristics based on strong connections between graph transformations and the optimization of stabilizer circuits. These patterns allow us to process large graphs and still achieve a reduction of up to 66% in emitter CNOTs, without relying on subtle metrics such as edge density. We find the optimal emission orderings and circuits to prepare unencoded and encoded repeater graph states of any size, achieving global minimization of emitter and CNOT resources despite the average NP-hardness of both optimization problems. We further study the locally equivalent orbit of graphs. Although enumerating orbits is#P complete for arbitrary graphs, we analytically calculate the size of the orbit of repeater graphs and find a procedure to generate the orbit for any repeater size. Finally, we inspect the entangling gate cost of preparing any graph from a given orbit and show that we can achieve the same optimal CNOT count across the orbit. 

In this paper, we introduce the concept of quasi-metaparticles based on the theory of metaparticles, the zero modes of the metastring. We apply the concept of quasi-metaparticles to the problem of non-Fermi liquids and the properties of strange metals. In particular, we point out that the quasi-metaparticle Green’s function interpolates between the canonical quasi-particle Green’s function and the result found in the context of the SYK model, which presents an exactly solvable model without quasiparticles. The linear dependence of resistivity with temperature is reproduced in the SYK limit. Also, the Cooper mechanism is possible in the quasi-metaparticle case. Finally, the new parameter that characterizes quasi-metaparticles can be extracted from ARPES data. Thus, the quasi-metaparticle could be a useful new concept in the study of strange metals and high-temperature superconductivity. 

Quantum memories play a key role in facilitating tasks within quantum networks and quantum information processing, including secure communications, advanced quantum sensing, and distributed quantum computing. Progress in characterizing large nuclear-spin registers coupled to defect electronic spins has been significant, but selecting memory qubits remains challenging due to the multitude of possible assignments. Numerical simulations for evaluating entangling gate fidelities encounter obstacles, restricting research to small registers, while experimental investigations are time-consuming and often limited to well-understood samples. Here we present an efficient methodology for systematically assessing the controllability of defect systems coupled to nuclear-spin registers. We showcase the approach by investigating the generation of entanglement links between silicon monovacancy or divacancy centers in Si⁢C and randomly selected sets of nuclear spins within the two-species (13⁢C and 29⁢Si) nuclear register. We quantify the performance of entangling gate operations and present the achievable gate fidelities, considering both the size of the register and the presence of unwanted nuclear spins. We find that some control sequences perform better than others depending on the number of target versus bath nuclei. This efficient approach is a guide for both experimental investigation and engineering, facilitating the high-throughput exploration of suitable defect systems for quantum memories. 

Photonic parity projection plays an important role in photonic quantum information processing. Nondestructive parity projections normally require high-fidelity controlled- $Z$gates between photonic and matter qubits, which can be experimentally demanding. In this paper, we propose a nearly deterministic parity projection protocol on two photonic qubits which only requires stable matter-photon controlled-phase gates. We also demonstrate that our protocol can tolerate moderate Gaussian phase errors in the controlled-phase gates as well as Pauli errors on the matter qubits. The fact that our protocol does not require perfect controlled- $Z$gates makes it more amenable to experimental implementation. Although we focus on photonic qubits, our protocol can be applied to any physical system or circuit with imperfect controlled- $Z$gates. Our protocol also provides a new optimization space for parity projection operations on various physical platforms, which is potentially beneficial for achieving high-fidelity parity projection operations. Published by the American Physical Society2024 

We propose and analyze deterministic protocols to generate qudit photonic graph states from quantum emitters. We show that our approach can be applied to generate any qudit graph state and we exemplify it by constructing protocols to generate one- and two-dimensional qudit cluster states, absolutely maximally entangled states, and logical states of quantum error-correcting codes. Some of these protocols make use of time-delayed feedback, while others do not. The only additional resource requirement compared to the qubit case is the ability to control multilevel emitters. These results significantly broaden the range of multiphoton entangled states that can be produced deterministically from quantum emitters. Published by the American Physical Society2024 

Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZ ${}_M$-like states with minimal cross-talk. We introduce the $M$-tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZ ${}_M$-like states of up to $M=10$qubits within time constraints that saturate bounds on $M$-way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary $M$-tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary $M$-tangling power which incorporates the impact of electronic dephasing errors on the $M$-way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation.