182 research outputs found
Easiness Amplification and Uniform Circuit Lower Bounds
We present new consequences of the assumption that time-bounded algorithms can be "compressed" with non-uniform circuits. Our main contribution is an "easiness amplification" lemma for circuits. One instantiation of the lemma says: if n^{1+e}-time, tilde{O}(n)-space computations have n^{1+o(1)} size (non-uniform) circuits for some e > 0, then every problem solvable in polynomial time and tilde{O}(n) space has n^{1+o(1)} size (non-uniform) circuits as well. This amplification has several consequences:
* An easy problem without small LOGSPACE-uniform circuits. For all e > 0, we give a natural decision problem, General Circuit n^e-Composition, that is solvable in about n^{1+e} time, but we prove that polynomial-time and logarithmic-space preprocessing cannot produce n^{1+o(1)}-size circuits for the problem. This shows that there are problems solvable in n^{1+e} time which are not in LOGSPACE-uniform n^{1+o(1)} size, the first result of its kind. We show that our lower bound is non-relativizing, by exhibiting an oracle relative to which the result is false.
* Problems without low-depth LOGSPACE-uniform circuits. For all e > 0, 1 < d < 2, and e < d we give another natural circuit composition problem computable in tilde{O}(n^{1+e}) time, or in O((log n)^d) space (though not necessarily simultaneously) that we prove does not have SPACE[(log n)^e]-uniform circuits of tilde{O}(n) size and O((log n)^e) depth. We also show SAT does not have circuits of tilde{O}(n) size and log^{2-o(1)}(n) depth that can be constructed in log^{2-o(1)}(n) space.
* A strong circuit complexity amplification. For every e > 0, we give a natural circuit composition problem and show that if it has tilde{O}(n)-size circuits (uniform or not), then every problem solvable in 2^{O(n)} time and 2^{O(sqrt{n log n})} space (simultaneously) has 2^{O(sqrt{n log n})}-size circuits (uniform or not). We also show the same consequence holds assuming SAT has tilde{O}(n)-size circuits. As a corollary, if n^{1.1} time computations (or O(n) nondeterministic time computations) have tilde{O}(n)-size circuits, then all problems in exponential time and subexponential space (such as quantified Boolean formulas) have significantly subexponential-size circuits. This is a new connection between the relative circuit complexities of easy and hard problems
On the (Non) NP-Hardness of Computing Circuit Complexity
The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function f and a size parameter k, is the circuit complexity of f at most k? This is the definitive problem of circuit synthesis, and it has been studied since the 1950s. Unlike many problems of its kind, MCSP is not known to be NP-hard, yet an efficient algorithm for this problem also seems very unlikely: for example, MCSP in P would imply there are no pseudorandom functions.
Although most NP-complete problems are complete under strong "local" reduction notions such as poly-logarithmic time projections, we show that MCSP is provably not NP-hard under O(n^(1/2-epsilon))-time projections, for every epsilon > 0. We prove that the NP-hardness of MCSP under (logtime-uniform) AC0 reductions would imply extremely strong lower bounds: NP notsubset P/poly and E notsubset i.o.-SIZE(2^(delta * n)) for some delta > 0 (hence P = BPP also follows). We show that even the NP-hardness of MCSP under general polynomial-time reductions would separate complexity classes: EXP != NP cap P/poly, which implies EXP != ZPP. These results help explain why it has been so difficult to prove that MCSP is NP-hard.
We also consider the nondeterministic generalization of MCSP: the Nondeterministic Minimum Circuit Size Problem (NMCSP), where one wishes to compute the nondeterministic circuit complexity of a given function. We prove that the Sigma_2 P-hardness of NMCSP, even under arbitrary polynomial-time reductions, would imply EXP notsubset P/poly
Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems
A frontier open problem in circuit complexity is to prove P^{NP} is not in SIZE[n^k] for all k; this is a necessary intermediate step towards NP is not in P_{/poly}. Previously, for several classes containing P^{NP}, including NP^{NP}, ZPP^{NP}, and S_2 P, such lower bounds have been proved via Karp-Lipton-style Theorems: to prove C is not in SIZE[n^k] for all k, we show that C subset P_{/poly} implies a "collapse" D = C for some larger class D, where we already know D is not in SIZE[n^k] for all k.
It seems obvious that one could take a different approach to prove circuit lower bounds for P^{NP} that does not require proving any Karp-Lipton-style theorems along the way. We show this intuition is wrong: (weak) Karp-Lipton-style theorems for P^{NP} are equivalent to fixed-polynomial size circuit lower bounds for P^{NP}. That is, P^{NP} is not in SIZE[n^k] for all k if and only if (NP subset P_{/poly} implies PH subset i.o.- P^{NP}_{/n}).
Next, we present new consequences of the assumption NP subset P_{/poly}, towards proving similar results for NP circuit lower bounds. We show that under the assumption, fixed-polynomial circuit lower bounds for NP, nondeterministic polynomial-time derandomizations, and various fixed-polynomial time simulations of NP are all equivalent. Applying this equivalence, we show that circuit lower bounds for NP imply better Karp-Lipton collapses. That is, if NP is not in SIZE[n^k] for all k, then for all C in {Parity-P, PP, PSPACE, EXP}, C subset P_{/poly} implies C subset i.o.-NP_{/n^epsilon} for all epsilon > 0. Note that unconditionally, the collapses are only to MA and not NP.
We also explore consequences of circuit lower bounds for a sparse language in NP. Among other results, we show if a polynomially-sparse NP language does not have n^{1+epsilon}-size circuits, then MA subset i.o.-NP_{/O(log n)}, MA subset i.o.-P^{NP[O(log n)]}, and NEXP is not in SIZE[2^{o(m)}]. Finally, we observe connections between these results and the "hardness magnification" phenomena described in recent works
Accelerated swell testing of artificial sulfate bearing lime stabilised cohesive soils
This paper reports on the physico-chemical response of two lime stabilised sulfate bearing artificial soils subject to the European Accelerated Volumetric Swell Test (EN13286-49). At various intervals during the test, a specimen was removed and subject to compositional and microstructural analysis. Ettringite was formed by both soils types, but with significant differences in crystal morphology. Ettringite crystals formed from kaolin based soils were very small, colloidal in size and tended to form on the surface of other particles. Conversely, those formed from montmorillonite were relatively large and typically formed away from the surface in the pore solution. It was concluded that the mechanism by which ettringite forms is determined by the hydroxide ion concentration in the pore solution and the fundamental structure of the bulk clay. In the kaolin soil, ettringite forms by a topochemical mechanism and expands by crystal swelling. In the montmorillonite soil, it forms by a through-solution mechanism and crystal growth
Genome-wide association of functional traits linked with<i> Campylobacter jejuni </i>survival from farm to fork
Campylobacter jejuni is a major cause of bacterial gastroenteritis worldwide, primarily associated with the consumption of contaminated poultry. C. jejuni lineages vary in host range and prevalence in human infection, suggesting differences in survival throughout the poultry processing chain. From 7,343 MLST-characterised isolates, we sequenced 600 C. jejuni and C. coli isolates from various stages of poultry processing and clinical cases. A genome-wide association study (GWAS) in C. jejuni ST-21 and ST-45 complexes identified genetic elements over-represented in clinical isolates that increased in frequency throughout the poultry processing chain. Disease-associated SNPs were distinct in these complexes, sometimes organised in haplotype blocks. The function of genes containing associated elements was investigated, demonstrating roles for cj1377c in formate metabolism, nuoK in aerobic survival and oxidative respiration, and cj1368-70 in nucleotide salvage. This work demonstrates the utility of GWAS for investigating transmission in natural zoonotic pathogen populations and provides evidence that major C. jejuni lineages have distinct genotypes associated with survival, within the host specific niche, from farm to fork. </p
Oncolytic and immunostimulatory efficacy of a targeted oncolytic poxvirus expressing human GM-CSF following intravenous administration in a rabbit tumor model
Targeted oncolytic poxviruses hold promise for the treatment of cancer. Arming these agents with immunostimulatory cytokines (for example, granulocyte-monocyte colony-stimulating factor; GM-CSF) can potentially increase their efficacy and/or alter their safety. However, due to species-specific differences in both human GM-CSF (hGM-CSF) activity and poxviruses immune avoidance proteins, the impact of hGM-CSF expression from an oncolytic poxvirus cannot be adequately assessed in murine or rat tumor models. We developed a rabbit tumor model to assess toxicology, pharmacodynamics, oncolytic efficacy and tumor-specific immunity of hGM-CSF expressed from a targeted oncolytic poxvirus JX-963. Recombinant purified hGM-CSF protein stimulated a leukocyte response in this model that paralleled effects of the protein in humans. JX-963 replication and targeting was highly tumor-selective after i.v. administration, and intratumoral replication led to recurrent, delayed systemic viremia. Likewise, hGM-CSF was expressed and released into the blood during JX-963 replication in tumors, but not in tumor-free animals. hGM-CSF expression from JX-963 was associated with significant increases in neutrophil, monocyte and basophil concentrations in the peripheral blood. Finally, tumor-specific cytotoxic T lymphocytes (CTL) were induced by the oncolytic poxvirus, and expression of hGM-CSF from the virus enhanced both tumor-specific CTL and antitumoral efficacy. JX-963 had significant efficacy against both the primary liver tumor as well as metastases; no significant organ toxicity was noted. This model holds promise for the evaluation of immunostimulatory transgene-armed oncolytic poxviruses, and potentially other viral species
Overcoming leakage in scalable quantum error correction
Leakage of quantum information out of computational states into higher energy
states represents a major challenge in the pursuit of quantum error correction
(QEC). In a QEC circuit, leakage builds over time and spreads through
multi-qubit interactions. This leads to correlated errors that degrade the
exponential suppression of logical error with scale, challenging the
feasibility of QEC as a path towards fault-tolerant quantum computation. Here,
we demonstrate the execution of a distance-3 surface code and distance-21
bit-flip code on a Sycamore quantum processor where leakage is removed from all
qubits in each cycle. This shortens the lifetime of leakage and curtails its
ability to spread and induce correlated errors. We report a ten-fold reduction
in steady-state leakage population on the data qubits encoding the logical
state and an average leakage population of less than
throughout the entire device. The leakage removal process itself efficiently
returns leakage population back to the computational basis, and adding it to a
code circuit prevents leakage from inducing correlated error across cycles,
restoring a fundamental assumption of QEC. With this demonstration that leakage
can be contained, we resolve a key challenge for practical QEC at scale.Comment: Main text: 7 pages, 5 figure
Measurement-induced entanglement and teleportation on a noisy quantum processor
Measurement has a special role in quantum theory: by collapsing the
wavefunction it can enable phenomena such as teleportation and thereby alter
the "arrow of time" that constrains unitary evolution. When integrated in
many-body dynamics, measurements can lead to emergent patterns of quantum
information in space-time that go beyond established paradigms for
characterizing phases, either in or out of equilibrium. On present-day NISQ
processors, the experimental realization of this physics is challenging due to
noise, hardware limitations, and the stochastic nature of quantum measurement.
Here we address each of these experimental challenges and investigate
measurement-induced quantum information phases on up to 70 superconducting
qubits. By leveraging the interchangeability of space and time, we use a
duality mapping, to avoid mid-circuit measurement and access different
manifestations of the underlying phases -- from entanglement scaling to
measurement-induced teleportation -- in a unified way. We obtain finite-size
signatures of a phase transition with a decoding protocol that correlates the
experimental measurement record with classical simulation data. The phases
display sharply different sensitivity to noise, which we exploit to turn an
inherent hardware limitation into a useful diagnostic. Our work demonstrates an
approach to realize measurement-induced physics at scales that are at the
limits of current NISQ processors
Non-Abelian braiding of graph vertices in a superconducting processor
Indistinguishability of particles is a fundamental principle of quantum
mechanics. For all elementary and quasiparticles observed to date - including
fermions, bosons, and Abelian anyons - this principle guarantees that the
braiding of identical particles leaves the system unchanged. However, in two
spatial dimensions, an intriguing possibility exists: braiding of non-Abelian
anyons causes rotations in a space of topologically degenerate wavefunctions.
Hence, it can change the observables of the system without violating the
principle of indistinguishability. Despite the well developed mathematical
description of non-Abelian anyons and numerous theoretical proposals, the
experimental observation of their exchange statistics has remained elusive for
decades. Controllable many-body quantum states generated on quantum processors
offer another path for exploring these fundamental phenomena. While efforts on
conventional solid-state platforms typically involve Hamiltonian dynamics of
quasi-particles, superconducting quantum processors allow for directly
manipulating the many-body wavefunction via unitary gates. Building on
predictions that stabilizer codes can host projective non-Abelian Ising anyons,
we implement a generalized stabilizer code and unitary protocol to create and
braid them. This allows us to experimentally verify the fusion rules of the
anyons and braid them to realize their statistics. We then study the prospect
of employing the anyons for quantum computation and utilize braiding to create
an entangled state of anyons encoding three logical qubits. Our work provides
new insights about non-Abelian braiding and - through the future inclusion of
error correction to achieve topological protection - could open a path toward
fault-tolerant quantum computing
Suppressing quantum errors by scaling a surface code logical qubit
Practical quantum computing will require error rates that are well below what
is achievable with physical qubits. Quantum error correction offers a path to
algorithmically-relevant error rates by encoding logical qubits within many
physical qubits, where increasing the number of physical qubits enhances
protection against physical errors. However, introducing more qubits also
increases the number of error sources, so the density of errors must be
sufficiently low in order for logical performance to improve with increasing
code size. Here, we report the measurement of logical qubit performance scaling
across multiple code sizes, and demonstrate that our system of superconducting
qubits has sufficient performance to overcome the additional errors from
increasing qubit number. We find our distance-5 surface code logical qubit
modestly outperforms an ensemble of distance-3 logical qubits on average, both
in terms of logical error probability over 25 cycles and logical error per
cycle ( compared to ). To investigate
damaging, low-probability error sources, we run a distance-25 repetition code
and observe a logical error per round floor set by a single
high-energy event ( when excluding this event). We are able
to accurately model our experiment, and from this model we can extract error
budgets that highlight the biggest challenges for future systems. These results
mark the first experimental demonstration where quantum error correction begins
to improve performance with increasing qubit number, illuminating the path to
reaching the logical error rates required for computation.Comment: Main text: 6 pages, 4 figures. v2: Update author list, references,
Fig. S12, Table I
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