Lieb-Robinson Light Cone for Power-Law Interactions.

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/r^{α} at distance r? Here, we present a definitive answer to this question for all exponents α>2d and all spatial dimensions d. Schematically, information takes time at least r^{min{1,α-2d}} to propagate a distance r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

A subset of replication-dependent histone mRNAs are expressed as polyadenylated RNAs in terminally differentiated tissues.

Histone proteins are synthesized in large amounts during S-phase to package the newly replicated DNA, and are among the most stable proteins in the cell. The replication-dependent (RD)-histone mRNAs expressed during S-phase end in a conserved stem-loop rather than a polyA tail. In addition, there are replication-independent (RI)-histone genes that encode histone variants as polyadenylated mRNAs. Most variants have specific functions in chromatin, but H3.3 also serves as a replacement histone for damaged histones in long-lived terminally differentiated cells. There are no reported replacement histone genes for histones H2A, H2B or H4. We report that a subset of RD-histone genes are expressed in terminally differentiated tissues as polyadenylated mRNAs, likely serving as replacement histone genes in long-lived non-dividing cells. Expression of two genes, HIST2H2AA3 and HIST1H2BC, is conserved in mammals. They are expressed as polyadenylated mRNAs in fibroblasts differentiated in vitro, but not in serum starved fibroblasts, suggesting that their expression is part of the terminal differentiation program. There are two histone H4 genes and an H3 gene that encode mRNAs that are polyadenylated and expressed at 5- to 10-fold lower levels than the mRNAs from H2A and H2B genes, which may be replacement genes for the H3.1 and H4 proteins.

The C-terminal extension of Lsm4 interacts directly with the 3' end of the histone mRNP and is required for efficient histone mRNA degradation.

Metazoan replication-dependent histone mRNAs are the only known eukaryotic mRNAs that lack a poly(A) tail, ending instead in a conserved stem-loop sequence, which is bound to the stem-loop binding protein (SLBP) on the histone mRNP. Histone mRNAs are rapidly degraded when DNA synthesis is inhibited in S phase in mammalian cells. Rapid degradation of histone mRNAs is initiated by oligouridylation of the 3' end of histone mRNAs and requires the cytoplasmic Lsm1-7 complex, which can bind to the oligo(U) tail. An exonuclease, 3'hExo, forms a ternary complex with SLBP and the stem-loop and is required for the initiation of histone mRNA degradation. The Lsm1-7 complex is also involved in degradation of polyadenylated mRNAs. It binds to the oligo(A) tail remaining after deadenylation, inhibiting translation and recruiting the enzymes required for decapping. Whether the Lsm1-7 complex interacts directly with other components of the mRNP is not known. We report here that the C-terminal extension of Lsm4 interacts directly with the histone mRNP, contacting both SLBP and 3'hExo. Mutants in the C-terminal tail of Lsm4 that prevent SLBP and 3'hExo binding reduce the rate of histone mRNA degradation when DNA synthesis is inhibited.

Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems.

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/rα) interactions. For all power-law exponents α between d and 2d+1, where d is the dimension of the system, the protocol yields a polynomial speed-up for α>2d and a superpolynomial speed-up for α≤2d, compared to the state of the art. For all α>d, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. In addition, the protocol provides a lower bound on the gate count in digital simulations of power-law interacting systems.

Signaling and scrambling with strongly long-range interactions.

Strongly long-range interacting quantum systems-those with interactions decaying as a power law 1/r α in the distance r on a D-dimensional lattice for α ⩽ D-have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum-information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. In a step towards rectifying this problem, we prove two Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α ⩽ D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians and gives a tight lower bound for the signaling time to extensive subsets of the system for all α< D. This many-site signaling time lower bounds the scrambling time in strongly long-range interacting systems.

Locality and heating in periodically driven, power-law-interacting systems.

We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power law 1 / r α . Using linear-response theory, we show that the heating time is exponentially long as a function of the drive frequency for α > D . For systems that may not obey linear-response theory, we use a more general Magnus-like expansion to show the existence of quasiconserved observables, which imply exponentially long heating time, for α > 2 D . We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear-response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.

Locality and Digital Quantum Simulation of Power-Law Interactions.

The propagation of information in nonrelativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/r α . The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al., FOCS'18. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α > 3D (where D is the number of dimensions).

Comparative genome-wide screening identifies a conserved doxorubicin repair network that is diploid specific in Saccharomyces cerevisiae.

The chemotherapeutic doxorubicin (DOX) induces DNA double-strand break (DSB) damage. In order to identify conserved genes that mediate DOX resistance, we screened the Saccharomyces cerevisiae diploid deletion collection and identified 376 deletion strains in which exposure to DOX was lethal or severely reduced growth fitness. This diploid screen identified 5-fold more DOX resistance genes than a comparable screen using the isogenic haploid derivative. Since DSB damage is repaired primarily by homologous recombination in yeast, and haploid cells lack an available DNA homolog in G1 and early S phase, this suggests that our diploid screen may have detected the loss of repair functions in G1 or early S phase prior to complete DNA replication. To test this, we compared the relative DOX sensitivity of 30 diploid deletion mutants identified under our screening conditions to their isogenic haploid counterpart, most of which (n = 26) were not detected in the haploid screen. For six mutants (bem1Delta, ctf4Delta, ctk1Delta, hfi1Delta,nup133Delta, tho2Delta) DOX-induced lethality was absent or greatly reduced in the haploid as compared to the isogenic diploid derivative. Moreover, unlike WT, all six diploid mutants displayed severe G1/S phase cell cycle progression defects when exposed to DOX and some were significantly enhanced (ctk1Delta and hfi1Delta) or deficient (tho2Delta) for recombination. Using these and other "THO2-like" hypo-recombinogenic, diploid-specific DOX sensitive mutants (mft1Delta, thp1Delta, thp2Delta) we utilized known genetic/proteomic interactions to construct an interactive functional genomic network which predicted additional DOX resistance genes not detected in the primary screen. Most (76%) of the DOX resistance genes detected in this diploid yeast screen are evolutionarily conserved suggesting the human orthologs are candidates for mediating DOX resistance by impacting on checkpoint and recombination functions in G1 and/or early S phases.