搜索结果：Deutsche

Khosravi, Drnovšek and Moslehian [\textit{Filomat, 2012}] derived Buzano inequality for Hilbert C*-modules. Using this inequality we derive Deutsch entropic uncertainty principle for Hilbert C*-modules over commutative unital C*-algebras.

We present a novel approach to quantum algorithms, by taking advantage of modular values, i.e., complex and unbounded quantities resulting from specific post-selected measurement scenarios. Our focus is on the problem of ascertaining whether a given function acting on a set of binary values is constant (uniformly yielding outputs of either all 0 or all 1), or balanced (a situation wherein half of the outputs are 0 and the other half are 1). Such problem can be solved by relying on the Deutsch-Jozsa algorithm. The proposed method, relying on the use of modular values, provides a high number of degrees of freedom for optimizing the new algorithm inspired from the Deutsch-Jozsa one. In particular, we explore meticulously the choices of the pre- and post-selected states. We eventually test the novel theoretical algorithm on a quantum computing platform. While the outcomes are currently not on par with the conventional approach, they nevertheless shed light on potential for future improvements, especially with less-optimized algorithms. We are thus confidend that the proposed proof of concept could prove its validity in bridging quantum algorithms and modular values research fields.

We show that one can implement the Deutsch-Josza algorithm, one of the first and simplest quantum algorithms, in a fault-tolerant manner using the smallest quantum error-detecting code -- the $[[4,2,2]]$ code -- without any ancillae. We implemented the algorithm on a trapped-ion quantum computer with and without fault-tolerant encoding and compared the results. With approximately $99 \%$ confidence, we found that the fault-tolerant implementation provided a noise reduction for all oracles. Averaged across all oracles, the reduction in error rate was nearly $90 \%$.

Deutsch's algorithm is the first quantum algorithm to show the advantage over the classical algorithm. Here we generalize Deutsch's problem to $n$ functions and propose a new quantum algorithm with indefinite causal order to solve this problem. The new algorithm not only reduces the number of queries to the black-box by half over the classical algorithm, but also significantly reduces the number of required quantum gates over the Deutsch's algorithm. We experimentally demonstrate the algorithm in a stable Sagnac loop interferometer with common path, which overcomes the obstacles of both phase instability and low fidelity of Mach-Zehnder interferometer. The experimental results have shown both an ultra-high and robust success probability $\sim 99.7\%$. Our work opens up a new path towards solving the practical problems with indefinite casual order quantum circuits.

Measurement-based quantum computing (MBQC), an alternate paradigm for formulating quantum algorithms, can lead to potentially more flexible and efficient implementations as well as to theoretical insights on the role of entanglement in a quantum algorithm. Using the graph-theoretical ZX-calculus, we describe and apply a general scheme for reformulating quantum circuits as MBQC implementations. After illustrating the method using the two-qubit Deutsch-Jozsa algorithm, we derive a ZX graph-diagram that encodes a general MBQC implementation for the three-qubit Deutsch-Jozsa algorithm. This graph describes an 11-qubit cluster state on which single-qubit measurements are used to execute the algorithm. Particular sets of choices of the axes for the measurements can be used to implement any realization of the oracle. In addition, we derive an equivalent lattice cluster state for the algorithm.

Let $(Ω, μ)$, $(Δ, ν)$ be measure spaces and $\{τ_α\}_{α\in Ω}$, $\{ω_β\}_{β\in Δ}$ be 1-bounded continuous Parseval frames for a Hilbert space $\mathcal{H}$. Then we show that \begin{align} (1) \quad \quad \quad \quad \log (μ(Ω)ν(Δ))\geq S_τ(h)+S_ω(h)\geq -2 \log \left(\frac{1+\displaystyle \sup_{α\in Ω, β\in Δ}|\langleτ_α, ω_β\rangle|}{2}\right) , \quad \forall h \in \mathcal{H}_τ\cap \mathcal{H}_ω, \end{align} where \begin{align*} &\mathcal{H}_τ:= \{h_1 \in \mathcal{H}: \langle h_1 , τ_α\rangle eq 0, α\in Ω\}, \quad \mathcal{H}_ω:= \{h_2 \in \mathcal{H}: \langle h_2, ω_β\rangle eq 0, β\in Δ\},\\ &S_τ(h):= -\displaystyle\int\limits_Ω\left|\left \langle \frac{h}{\|h\|}, τ_α\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, τ_α\right\rangle \right|^2\,dμ(α), \quad \forall h \in \mathcal{H}_τ, \\ & S_ω(h):= -\displaystyle\int\limits_Δ\left|\left \langle \frac{h}{\|h\|}, ω_β\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, ω_β\right\rangle \right|^2\,dν(β), \quad \forall h \in \mathcal{H}_ω. \end{align*} We call Inequality (1) as \textbf{Continuous Deutsch Uncertainty Principle}. Inequality (1) improves the uncertainty principle obtained by

Let $\{f_j\}_{j=1}^n$ and $\{g_k\}_{k=1}^m$ be Parseval p-frames for a finite dimensional Banach space $\mathcal{X}$. Then we show that \begin{align} (1) \quad\quad\quad\quad \log (nm)\geq S_f (x)+S_g (x)\geq -p \log \left(\displaystyle\sup_{y \in \mathcal{X}_f\cap \mathcal{X}_g, \|y\|=1}\left(\max_{1\leq j\leq n, 1\leq k\leq m}|f_j(y)g_k(y)|\right)\right), \quad \forall x \in \mathcal{X}_f\cap \mathcal{X}_g, \end{align} where \begin{align*} &\mathcal{X}_f:= \{z\in \mathcal{X}: f_j(z) eq 0, 1\leq j \leq n\}, \quad \mathcal{X}_g:= \{w\in \mathcal{X}: g_k(w) eq 0, 1\leq k \leq m\},\\ &S_f (x):= -\sum_{j=1}^{n}\left|f_j\left(\frac{x}{\|x\|}\right)\right|^p\log \left|f_j\left(\frac{x}{\|x\|}\right)\right|^p, \quad S_g (x):= -\sum_{k=1}^{m}\left|g_k\left(\frac{x}{\|x\|}\right)\right|^p\log \left|g_k\left(\frac{x}{\|x\|}\right)\right|^p, \quad \forall x \in \mathcal{X}_g. \end{align*} We call Inequality (1) as \textbf{Functional Deutsch Uncertainty Principle}. For Hilbert spaces, we show that Inequality (1) reduces to the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We also derive a dual of Inequality (1).

As traditional chip miniaturization slows, researchers have found a way to pack more computing power into the same space by stacking silicon circuits in multiple layers。 The new process uses ultra-thin silicon membranes and low-temperature manufacturing techniques to overcome a major obstacle that has long blocked the production of true 3D chips

NASA’s Fermi telescope has detected what may be the first confirmed gamma-ray signal from a superluminous supernova — one of the most extreme explosions in the universe。 Scientists believe the blast was powered by a rapidly spinning magnetar, an exotic neutron star with unbelievably strong magnetic fields。 The event, called SN 2017egm, erupted 440

"We look forward to working with Roscosmos on a collaborative approach to address the leaks

NASA’s PExT terminal has shown that spacecraft can seamlessly communicate through multiple government and commercial networks, a major step beyond traditional single-network systems。 The mission is now expanding to test new capabilities that could help create a more flexible, reliable communications infrastructure for future space missions

Scientists working at CERN’s Large Hadron Collider may be seeing the strongest hints yet of physics beyond the Standard Model — the decades-old theory that explains the fundamental particles and forces of the universe。 By studying incredibly rare particle transformations called “penguin decays,” researchers found behavior that doesn’t fully match t

Scientists at Lawrence Livermore National Laboratory recreated part of the intense chaos inside a nuclear fireball to better understand how radioactive fallout forms。 Their experiments revealed that the way vaporized materials cool can dramatically change the particles that eventually form, especially for volatile elements like cesium

Astronomers have finally cracked the mystery behind a strange class of repeating cosmic signals that has baffled scientists for years。 Using Australia’s ASKAP radio telescope, researchers traced the bursts to a rare stellar duo in which a dense white dwarf is relentlessly siphoning material from a nearby red dwarf companion。 As the stolen matter sp

Scientists have uncovered a surprising new way to control superconductivity — the mysterious phenomenon where electricity flows with zero energy loss。 By pairing twisted layers of graphene with a synthetic diamond material, researchers were able to effectively switch superconductivity on and off by tweaking how electrons interact with their surroun

A lightweight new X-ray telescope could finally give scientists something they’ve never had before: a complete chemical map of the Moon。 Researchers used detailed mission simulations to show that a compact telescope orbiting the Moon could identify key elements across the entire lunar surface, helping reveal how the Moon formed and evolved

Scientists have proposed a new method for finding tightly bound supermassive black hole pairs by searching for stars that flash repeatedly as their light is magnified by the black holes’ gravity。 The timing and brightness of these bursts could provide a unique fingerprint of black holes slowly spiraling toward a future collision

A team at the University of Minnesota discovered that changing a metal film's thickness by just a few nanometers can dramatically alter how it behaves electronically。 The finding reveals a surprising new way to control metals and could help power future advances in electronics, catalysis, and quantum technology

A team at the University of Chicago has discovered a surprisingly simple way to create powerful quantum states that are normally difficult to produce。 By making small adjustments to the energy levels of atoms inside an optical cavity, researchers can generate a wide variety of highly entangled states without adding complicated hardware