One of the challenges of quantum computers in the near- and mid- term is the limited number of qubits we can use for computations. Finding methods that achieve useful quantum improvements under size ...limitations is thus a key question in the field. In this vein, it was recently shown that a hybrid classical-quantum method can help provide polynomial speed-ups to classical divide-and-conquer algorithms, even when only given access to a quantum computer much smaller than the problem itself. In this work, we study the hybrid divide-and-conquer method in the context of tree search algorithms, and extend it by including quantum backtracking, which allows better results than previous Grover-based methods. Further, we provide general criteria for polynomial speed-ups in the tree search context, and provide a number of examples where polynomial speed ups, using arbitrarily smaller quantum computers, can be obtained. We provide conditions for speedups for the well known algorithm of DPLL, and we prove threshold-free speed-ups for the PPSZ algorithm (the core of the fastest exact Boolean satisfiability solver) for well-behaved classes of formulas. We also provide a simple example where speed-ups can be obtained in an algorithm-independent fashion, under certain well-studied complexity-theoretical assumptions. Finally, we briefly discuss the fundamental limitations of hybrid methods in providing speed-ups for larger problems.
In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring ...problem is finding a transformation from a given source graph state to a desired target graph state using only local operations. Recently it has been shown that deciding transformability is already NP-hard. In this paper, we present a CNF encoding for both local and non-local graph state operations, corresponding to one- and two-qubit Clifford gates and single-qubit Pauli measurements. We use this encoding in a bounded-model-checking set-up to synthesize the desired transformation. For a completeness threshold, we provide an upper bound on the length of the transformation if it exists. We evaluate the approach in two settings: the first is the synthesis of the ubiquitous GHZ state from a random graph state where we can vary the number of qubits, while the second is based on a proposed 14 node quantum network. We find that the approach is able to synthesize transformations for graphs up to 17 qubits in under 30 minutes.
Saturation is considered the state-of-the-art method for computing fixpoints with decision diagrams. We present a relatively simple decision diagram operation called REACH that also computes ...fixpoints. In contrast to saturation, it does not require a partitioning of the transition relation. We give sequential algorithms implementing the new operation for both binary and multi-valued decision diagrams, and moreover provide parallel counterparts. We implement these algorithms and experimentally compare their performance against saturation on 692 model checking benchmarks in different languages. The results show that the REACH operation often outperforms saturation, especially on transition relations with low locality. In a comparison between parallelized versions of REACH and saturation we find that REACH obtains comparable speedups up to 16 cores, although falls behind saturation at 64 cores. Finally, in a comparison with the state-of-the-art model checking tool ITS-tools we find that REACH outperforms ITS-tools on 29% of models, suggesting that REACH can be useful as a complementary method in an ensemble tool.
The ability to distribute high-quality entanglement between remote parties is a necessary primitive for many quantum communication applications. A large range of schemes for realizing the ...long-distance delivery of remote entanglement has been proposed, both for bipartite and multipartite entanglement. For assessing the viability of these schemes, knowledge of the time at which entanglement is delivered is crucial. Specifically, if the communication task requires multiple remote-entangled quantum states and these states are generated at different times by the scheme, the earlier states will need to wait and thus their quality will decrease while being stored in an (imperfect) memory. For the remote-entanglement delivery schemes which are closest to experimental reach, this time assessment is challenging, as they consist of nondeterministic components such as probabilistic entanglement swaps. For many such protocols even the average time at which entanglement can be distributed is not known exactly, in particular when they consist of feedback loops and forced restarts. In this work, we provide improved analytical bounds on the average and on the quantiles of the completion time of entanglement distribution protocols in the case that all network components have success probabilities lower bounded by a constant. A canonical example of such a protocol is a nested quantum repeater scheme which consists of heralded entanglement generation and entanglement swaps. For this scheme specifically, our results imply that a common approximation to the mean entanglement distribution time, the 3-over-2 formula, is in essence an upper bound to the real time. Our results rely on a novel connection with reliability theory.
One of the challenges of quantum computers in the near- and mid- term is the limited number of qubits we can use for computations. Finding methods that achieve useful quantum improvements under size ...limitations is thus a key question in the field. In this vein, it was recently shown that a hybrid classical-quantum method can help provide polynomial speed-ups to classical divide-and-conquer algorithms, even when only given access to a quantum computer much smaller than the problem itself. In this work, we study the hybrid divide-and-conquer method in the context of tree search algorithms, and extend it by including quantum backtracking, which allows better results than previous Grover-based methods. Further, we provide general criteria for polynomial speed-ups in the tree search context, and provide a number of examples where polynomial speed ups, using arbitrarily smaller quantum computers, can be obtained. We provide conditions for speedups for the well known algorithm of DPLL, and we prove threshold-free speed-ups for the PPSZ algorithm (the core of the fastest exact Boolean satisfiability solver) for well-behaved classes of formulas. We also provide a simple example where speed-ups can be obtained in an algorithm-independent fashion, under certain well-studied complexity-theoretical assumptions. Finally, we briefly discuss the fundamental limitations of hybrid methods in providing speed-ups for larger problems.
Objective
Tregs are crucial for immune regulation, and environment‐driven adaptation of effector (e)Tregs is essential for local functioning. However, the extent of human Treg heterogeneity in ...inflammatory settings is unclear.
Methods
We combined single‐cell RNA‐ and TCR‐sequencing on Tregs derived from three to six patients with juvenile idiopathic arthritis (JIA) to investigate the functional heterogeneity of human synovial fluid (SF)‐derived Tregs from inflamed joints. Confirmation and suppressive function of the identified Treg clusters was assessed by flow cytometry.
Results
Four Treg clusters were identified; incoming, activated eTregs with either a dominant suppressive or cytotoxic profile, and GPR56+CD161+CXCL13+ Tregs. Pseudotime analysis showed differentiation towards either classical eTreg profiles or GPR56+CD161+CXCL13+ Tregs supported by TCR data. Despite its most differentiated phenotype, GPR56+CD161+CXCL13+ Tregs were shown to be suppressive. Furthermore, BATF was identified as an overarching eTreg regulator, with the novel Treg‐associated regulon BHLHE40 driving differentiation towards GPR56+CD161+CXCL13+ Tregs, and JAZF1 towards classical eTregs.
Conclusion
Our study reveals a heterogeneous population of Tregs at the site of inflammation in JIA. SF Treg differentiate to a classical eTreg profile with a more dominant suppressive or cytotoxic profile that share a similar TCR repertoire, or towards GPR56+CD161+CXCL13+ Tregs with a more distinct TCR repertoire. Genes characterising GPR56+CD161+CXCL13+ Tregs were also mirrored in other T‐cell subsets in both the tumor and the autoimmune setting. Finally, the identified key regulators driving SF Treg adaptation may be interesting targets for autoimmunity or tumor interventions.
We show that human regulatory T cells (Tregs) within the inflamed arthritic joint differentiate locally and are functionally heterogeneous. Tregs differentiate towards either classical effector Tregs or towards GRP56+CD161+CXCL13+ Tregs, supported by TCR data. Novel predicted drivers of local Treg differentiation include JAZF1 for classical effector Tregs and BHLHE40 for GRP56+CD161+CXCL13+ Tregs.
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