Power of Uninitialized Qubits in Shallow Quantum Circuits

We study the computational power of shallow quantum circuits with O(log n) initialized and n^{O(1)} uninitialized ancillary qubits, where n is the input length and the initial state of the uninitialized ancillary qubits is arbitrary. First, we show that such a circuit can compute any symmetric function on n bits that is classically computable in polynomial time. Then, we regard such a circuit as an oracle and show that a polynomial-time classical algorithm with the oracle can estimate the elements of any unitary matrix corresponding to a constant-depth quantum circuit on n qubits. Since it seems unlikely that these tasks can be done with only O(log n) initialized ancillary qubits, our results give evidences that adding uninitialized ancillary qubits increases the computational power of shallow quantum circuits with only O(log n) initialized ancillary qubits. Lastly, to understand the limitations of uninitialized ancillary qubits, we focus on near-logarithmic-depth quantum circuits with them and show the impossibility of computing the parity function on n bits

Classically Simulating Quantum Circuits with Local Depolarizing Noise

We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small constant rate is applied to each qubit at the end of computation. We show that, under this noise model, if an approximate value of the noise rate is known, any CT-ECS circuit with an anti-concentrated output probability distribution is classically simulatable. This indicates that the presence of small noise drastically affects the classical simulatability of CT-ECS circuits. Then, we consider an extension of the noise model where the noise rate can vary with each qubit, and provide a similar sufficient condition for classically simulating CT-ECS circuits with anti-concentrated output probability distributions

Divide-and-conquer verification method for noisy intermediate-scale quantum computation

Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langle\psi_t|\hat{\rho}_{\rm out}|\psi_t\rangle$ between an actual $n$-qubit output state $\hat{\rho}_{\rm out}$ obtained from the noisy intermediate-scale quantum computation and the ideal output state (i.e., the target state) $|\psi_t\rangle$. Although the direct fidelity estimation method requires $O(2^n)$ copies of $\hat{\rho}_{\rm out}$ on average, our method requires only $O(D^32^{12D})$ copies even in the worst case, where $D$ is the denseness of $|\psi_t\rangle$. For logarithmic-depth quantum circuits on a sparse chip, $D$ is at most $O(\log{n})$, and thus $O(D^32^{12D})$ is a polynomial in $n$. By using the IBM Manila 5-qubit chip, we also perform a proof-of-principle experiment to observe the practical performance of our method.Comment: 17 pages, 7 figures, v3: Added a proof-of-principle experiment (Sec. IV) and improved Sec. V, Accepted for publication in Quantu

Cryptochrome and Period Proteins Are Regulated by the CLOCK/BMAL1 Gene: Crosstalk between the PPARs/RXRα-Regulated and CLOCK/BMAL1-Regulated Systems

Feeding and the circadian system regulate lipid absorption and metabolism, and the expression of enzymes involved in lipid metabolism is believed to be directly controlled by the clock system. To investigate the interaction between the lipid metabolism system and the circadian system, we analyzed the effect of a CLOCK/BMAL1 heterodimer on the transcriptional regulation of PPAR-controlled genes through PPAR response elements (PPREs). Transcription of acyl-CoA oxidase, cellular retinol binding protein II (CRBPII), and 3-hydroxy-3-methylglutaryl coenzyme A (HMG-CoA) synthase was altered by CLOCK/BMAL1, and transcriptional activity via PPRE by PPARs/RXRα was enhanced by CLOCK/BMAL1 and/or by PPARs ligand/activators. We also found that CLOCK/BMAL1-mediated transcription of period (PER) and cryptochrome (CRY) was modulated by PPARα/RXRα. These results suggest that there may be crosstalk between the PPARs/RXRα-regulated system and the CLOCK/BMAL1-regulated system

Statins Activate Human PPARα Promoter and Increase PPARα mRNA Expression and Activation in HepG2 Cells

Statins increase peroxisome proliferator-activated receptor α (PPARα) mRNA expression, but the mechanism of this increased PPARα production remains elusive. To examine the regulation of PPARα production, we examined the effect of 7 statins (atorvastatin, cerivastatin, fluvastatin, pitavastatin, pravastatin, rosuvastatin, and simvastatin) on human PPARα promoter activity, mRNA expression, nuclear protein levels, and transcriptional activity. The main results are as follows. (1) Majority of statins enhanced PPARα promoter activity in a dose-dependent manner in HepG2 cells transfected with the human PPARα promoter. This enhancement may be mediated by statin-induced HNF-4α. (2) PPARα mRNA expression was increased by statin treatment. (3) The PPARα levels in nuclear fractions were increased by statin treatment. (4) Simvastatin, pravastatin, and cerivastatin markedly enhanced transcriptional activity in 293T cells cotransfected with acyl-coenzyme A oxidase promoter and PPARα/RXRα expression vectors. In summary, these data demonstrate that PPARα production and activation are upregulated through the PPARα promoter activity by statin treatment

The signaling pathway of Campylobacter jejuni-induced Cdc42 activation: Role of fibronectin, integrin beta1, tyrosine kinases and guanine exchange factor Vav2

<p>Abstract</p> <p>Background</p> <p>Host cell invasion by the foodborne pathogen <it>Campylobacter jejuni </it>is considered as one of the primary reasons of gut tissue damage, however, mechanisms and key factors involved in this process are widely unclear. It was reported that small Rho GTPases, including Cdc42, are activated and play a role during invasion, but the involved signaling cascades remained unknown. Here we utilised knockout cell lines derived from fibronectin^-/-, integrin-beta1^-/-, focal adhesion kinase (FAK)^-/-and Src/Yes/Fyn^-/-deficient mice, and wild-type control cells, to investigate <it>C. jejuni</it>-induced mechanisms leading to Cdc42 activation and bacterial uptake.</p> <p>Results</p> <p>Using high-resolution scanning electron microscopy, GTPase pulldowns, G-Lisa and gentamicin protection assays we found that each studied host factor is necessary for induction of Cdc42-GTP and efficient invasion. Interestingly, filopodia formation and associated membrane dynamics linked to invasion were only seen during infection of wild-type but not in knockout cells. Infection of cells stably expressing integrin-beta1 variants with well-known defects in fibronectin fibril formation or FAK signaling also exhibited severe deficiencies in Cdc42 activation and bacterial invasion. We further demonstrated that infection of wild-type cells induces increasing amounts of phosphorylated FAK and growth factor receptors (EGFR and PDGFR) during the course of infection, correlating with accumulating Cdc42-GTP levels and <it>C. jejuni </it>invasion over time. In studies using pharmacological inhibitors, silencing RNA (siRNA) and dominant-negative expression constructs, EGFR, PDGFR and PI3-kinase appeared to represent other crucial components upstream of Cdc42 and invasion. siRNA and the use of Vav1/2^-/-knockout cells further showed that the guanine exchange factor Vav2 is required for Cdc42 activation and maximal bacterial invasion. Overexpression of certain mutant constructs indicated that Vav2 is a linker molecule between Cdc42 and activated EGFR/PDGFR/PI3-kinase. Using <it>C. jejuni </it>mutant strains we further demonstrated that the fibronectin-binding protein CadF and intact flagella are involved in Cdc42-GTP induction, indicating that the bacteria may directly target the fibronectin/integrin complex for inducing signaling leading to its host cell entry.</p> <p>Conclusion</p> <p>Collectively, our findings led us propose that <it>C. jejuni </it>infection triggers a novel fibronectin→integrin-beta1→FAK/Src→EGFR/PDGFR→PI3-kinase→Vav2 signaling cascade, which plays a crucial role for Cdc42 GTPase activity associated with filopodia formation and enhances bacterial invasion.</p