# qubit: stability of classical shadows under gate-dependent noise

<< Expectation values of observables are routinely estimated using so-called classical shadows—the outcomes of randomized bases measurements on a repeatedly prepared quantum state. In order to trust the accuracy of shadow estimation in practice, it is crucial to understand the behavior of the estimators under realistic noise. >>

<< In this Letter, (AA) prove that any shadow estimation protocol involving Clifford unitaries is stable under gate-dependent noise for observables with bounded stabilizer norm—originally introduced in the context of simulating Clifford circuits. In contrast, (They) demonstrate with concrete examples that estimation of “magic” observables can lead to highly misleading results in the presence of miscalibration errors and a worst case bias scaling exponentially in the system size. >>

AA << further find that so-called robust shadows, aiming at mitigating noise, can introduce a large bias in the presence of gate-dependent noise compared to unmitigated classical shadows. Nevertheless, (AA) guarantee the functioning of robust shadows for a more general noise setting than in previous works. On a technical level, (They) identify average noise channels that affect shadow estimators and allow for a more fine-grained control of noise-induced biases. >>️

Raphael Brieger, Markus Heinrich, et al. Stability of Classical Shadows under Gate-Dependent Noise. Phys. Rev. Lett. 134, 090801. Mar 4, 2025. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.090801  arXiv: 2310.19947v3 [quant-ph]. Feb 19, 2025.   https://arxiv.org/abs/2310.19947

Also: qubit, in FonT  https://flashontrack.blogspot.com/search?q=qubit  noise, ai (artificial intell) (bot), in https://www.inkgmr.net/kwrds.html   

Keywords: qubit, noise, realistic noise, shadows, robust shadows

# qubit: communication power of a noisy qubit.

<< A fundamental limitation of quantum communication is that a single qubit can carry at most one bit of classical information. For an important class of quantum communication channels, known as entanglement breaking, this limitation holds even if the sender and receiver share entangled particles. But does this mean that, for the purpose of communicating classical messages, a noisy entanglement-breaking qubit channel can be replaced by a noisy bit channel? >>

Here AA << answer the question in the negative. (They) introduce a game, similar to the Monty Hall problem in classical statistics, where a sender assists a receiver in finding a valuable item (the “prize”) hidden in one of four possible boxes, while avoiding a hazardous item (the “bomb”) hidden in one of the remaining three boxes. (AA) show that no classical strategy using a noisy bit channel can ensure that the bomb is avoided, even if the sender and receiver share arbitrary amounts of randomness. >>

<< In contrast, communication of a qubit through a class of noisy entanglement-breaking channels, which (They) call quantum not channels, allows the players to deterministically avoid the bomb and to find the prize with a guaranteed nonzero probability. >>

AA << findings show that the communication of classical messages through a noisy entanglement-breaking qubit channel assisted by quantum entanglement cannot, in general, be simulated by communication through a noisy bit channel assisted by classical correlations. >>️

Giulio Chiribella, Saptarshi Roy, et al. Communication Power of a Noisy Qubit. Phys. Rev. Lett. 134, 080803. Feb 28, 2025. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.080803     arXiv: 2405.17946v2 [quant-ph]. https://arxiv.org/abs/2405.17946  

Also: qubit, in https://flashontrack.blogspot.com/search?q=qubit  game, in  https://flashontrack.blogspot.com/search?q=game  noise, in  https://flashontrack.blogspot.com/search?q=noise 

Keywords: qubit, games, noise

# qubit: to simulate 16 futures simultaneously by quantum superposition, the beginning

<< Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. >>

AA << demonstrate interference of two 16-dimensional quantum states, representing statistical futures of (the) process, with a visibility of 0.96 ± 0.02. >>

Farzad Ghafari, Nora Tischler, et al.
Interfering trajectories in experimental quantum-enhanced stochastic simulation. Nature  Comm Volume 10, Article number: 1630 (2019)

https://www.nature.com/articles/s41467-019-08951-2   

Gu Mile. Scientists build a machine to generate quantum superposition of possible futures. School of Physical and Mathematical Sciences, Nanyang Technological University.  April 9, 2019.

https://m.phys.org/news/2019-04-scientists-machine-quantum-superposition-futures.html   

# qubit: an energy control approach to build quantum computers: quickly jump two rungs at a time without spilling any water from the glass

<< Dr. Sergey Danilin, (..) describes quantum control-the process of using chips like transmons to build quantum computers-by extending the "climbing a ladder" analogy. "To get a useful quantum system, you need to imagine climbing a ladder while holding a glass of water-it works if one does it smoothly, but if you do it too fast, the water spills. Certainly, this requires a special skill."  (..)  in the quantum world, the trick for climbing the ladder quickly without spilling any water is by carefully jumping two rungs at a time. >>

Life on the edge in the quantum world. Aalto University. Feb 8, 2019

https://m.phys.org/news/2019-02-life-edge-quantum-world.html

Antti Vepsalainen, Sergey Danilin,  Gheorghe Sorin Paraoanu. Superadiabatic population transfer in a three-level superconducting circuit. Science Advances  Feb 8, 2019:
Vol. 5, no. 2, eaau5999
doi: 10.1126/sciadv.aau5999

http://advances.sciencemag.org/content/5/2/eaau5999

Also

https://flashontrack.blogspot.com/search?q=%23+qubit

# qucpu: a quantum computer in a silicon chip seems closer to reality

AA << demonstrate an integrated device platform incorporating a silicon metal-oxide-semiconductor double quantum dot that is capable of single-spin addressing and control via electron spin resonance, combined with high-fidelity spin readout in the singlet-triplet basis. >>

M. A. Fogarty, K. W. Chan, et al. Integrated silicon qubit platform with single-spin addressability, exchange control and single-shot singlet-triplet readout. Nature Comm. volume 9, Article number: 4370  Oct 30, 2018.

https://www.nature.com/articles/s41467-018-06039-x

Tests show integrated quantum chip operations possible. University of New South Wales. Oct 30, 2018.

https://m.phys.org/news/2018-10-quantum-chip.html

# game: pulsating as a Toffoli gate: Parrondo's paradox with a three-state coin (heads, tails, and a side)

<< Parrondo's paradox - an apparent paradox in which two losing strategies combine to make a winning strategy - can emerge as a coin game with a single coin in the quantum realm, but only when the coin has three states (heads, tails, and a side) rather than the conventional two. >>

<< In the new study, [AA] have demonstrated a Parrondo's game using a three-state coin, which they represent with a qutrit, a quantum system with three states. >>

Lisa Zyga. Parrondo's paradox with a three-sided coin. Phys.org. July 11, 2018.

https://m.phys.org/news/2018-07-parrondo-paradox-three-sided-coin.html

Jishnu Rajendran, Colin Benjamin. Playing a true Parrondo's game with a three-state coin on a quantum walk. EPL. 2018; 122(4). June 28.

http://iopscience.iop.org/article/10.1209/0295-5075/122/40004/meta

https://arxiv.org/abs/1710.04033

Also

"Toffoli gate"

# qubit: three-qubit operation with the Toffoli gate for scalable semiconductor quantum processors. Mar 4, 2018.

https://flashontrack.blogspot.com/2018/03/qubit-three-qubit-operation-with.html

FonT

quando lessi per la prima volta in bibliografia circa il "Parrondo Game"  mi venne in mente una strategia che avevo immaginato e piu' volte usato a suo tempo - da meta'  anni '70 a tutti gli anni '80 (e oltre) - composta da una sorta di "tit-for-tat stocastico" cioe' una strategia di gioco di  "cooperazione/ defezione" con decisioni di scelta pilotate da "lancio di moneta" all'interno di due (e poi anche tre) scenari riconducibili al tipo Parrondo ... in pratica la generazione di scenari senz'altro di  "frontiera", evolutivi,  immediatamente generabili all'interno di situazioni (se-si-puo-dire ... or, namely, "sire-die-soup") del tipo "standard", supposte "lineari".  Anzicheforse.

1668 - ramificata tinnula (di carmina fluitantia). Jun 9, 2005.

https://inkpi.blogspot.com/2005/06/1668-ramificata-tinnula-di-carmina.html

"charlie"

https://inkpi.blogspot.com/search?q=charlie

# qubit: three-qubit operation with the Toffoli gate for scalable semiconductor quantum processors

<< The Toffoli gate is a three-qubit operation that changed the state of a target qubit conditioned on the state of two control qubits. It can be used for universal reversible classical computation, (..) >>

<< As a result, a single-step Toffoli gate can reduce the number of quantum operations dramatically, which can break the limit of coherence time and improve the efficiency of quantum computing >>

University of Science and Technology of China. Experimentally demonstrated a Toffoli gate in a semiconductor three-qubit system. March 1, 2018

https://m.phys.org/news/2018-03-experimentally-toffoli-gate-semiconductor-three-qubit.html

Hai-Ou Li, Gang Cao, et al. Controlled Quantum Operations of a Semiconductor Three-Qubit System. Phys. Rev. Applied 2018; 9.024015. doi: 10.1103/ PhysRevApplied.9.024015. Feb 15, 2018.

https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.9.024015

# qubit-ai: inside the qubit AI neural “black boxes”

<< Neural networks’ powers of prediction have fueled the recent AI boom, but it can be hard to explain how they reach their decisions. A new technique aimed at uncovering the inner workings of language processing networks is just the latest effort to shed some light on these “black boxes.” >>

<< Going a step further, some researchers are trying to create AI able to explain its decisions to lay people, not just experts >>

Edd Gent. Machines Are Getting Smarter—Now They Should Explain Themselves. Sep 19, 2017

https://singularityhub.com/2017/09/19/machines-are-getting-smarter-now-they-should-explain-themselves/

FonT

"but it can be hard to explain how they [AI machines] reach their decisions"

An easy prediction: "Qubit AI  Machines" will never fully explain themselves.

# qubit: the flip-flop quantum processor, the begin

AA << introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields >>

<< to encode quantum information in the electron-nuclear spin states of 31P [phosphorus] donors in silicon, and to realize fast, high-fidelity, electrically driven universal quantum gates >>

<< a credible pathway to the construction of a large-scale quantum processor, where atomic-size spin qubits are integrated with silicon nanoelectronic devices, in a platform that does not require atomic-scale precision in the qubit placement [..] and, with realistic assumptions on noise and imperfections, are predicted to achieve error rates compatible with fault-tolerant quantum error correction >>

Guilherme Tosi, Fahd A. Mohiyaddin, et al. Silicon quantum processor with robust long-distance qubit couplings. Nature Comm 8, 2017; 450 Sept 06, 2017 doi: 10.1038/s41467-017-00378-x

https://www.nature.com/articles/s41467-017-00378-x

<< a new way to define a 'spin qubit' that uses both the electron and the nucleus of the atom. Crucially, this new qubit can be controlled using electric signals, instead of magnetic ones. Electric signals are significantly easier to distribute and localise within an electronic chip >>

Flip-flop qubits: Radical new quantum computing design invented. Sept 6, 2017

https://scienmag.com/flip-flop-qubits-radical-new-quantum-computing-design-invented/

Fiona MacDonald,  Mike McRae. Breaking: An Entirely New Type of Quantum Computing Has Been Invented. "It's amazing no one had thought of it before."  Sep 6, 2017

http://www.sciencealert.com/breaking-a-brand-new-type-of-qubit-has-been-unveiled-and-it-finally-makes-quantum-computers-scalable

also

# ai-bot: 352 predictions of when machines will make humans obsolete. Sep 2, 2017

http://flashontrack.blogspot.it/2017/09/ai-bot-352-predictions-of-when-machines.html

Bill Berry, Michael Stipe, Peter Buck, Michael Mills (R.E.M.).  "Begin The Begin". In: "Lifes Rich Pageant" (1986)

https://en.m.wikipedia.org/wiki/Begin_the_Begin

https://m.youtube.com/watch?v=7XaoF8bDMcM

# e-qubit: quantum algorithm(s) ready to leap out

<< I tell my students that 2017 is the year of braiding. >> Leo Kouwenhoven

Davide Castelvecchi. Quantum computers ready to leap out of the lab in 2017. Nature. Volume: 541,  Pages: 9–10 Date publ.: 05 Jan. 2017 DOI:  doi :10.1038/541009a

http://www.nature.com/news/quantum-computers-ready-to-leap-out-of-the-lab-in-2017-1.21239

FonT: quando "the (qubit) year of braiding" sara' realta', i sistemi di crittografia entreranno in stati di  ampia e risonante fibrillazione, immagino ...

# s-phys: "entanglement entropy of a qubit", the begin ...

<< All systems are fundamentally quantum systems (..) but the means of describing in a quantum sense the chaotic behavior of, say, air molecules in an evacuated room, remains limited >>

<< To investigate, [AA] devised an experiment using three quantum bits, the basic computational units of the quantum computer >>

<< By manipulating these qubits with electronic pulses, [AA] caused them to interact, rotate and evolve in the quantum analog of a highly sensitive classical [chaotic] system >>

<< The result is a map of entanglement entropy of a qubit that, over time, comes to strongly resemble that of classical dynamics — the regions of entanglement in the quantum map resemble the regions of chaos on the classical map >>

Sonia Fernandez. Researchers at UCSB blur the line between classical and quantum physics by connecting chaos and entanglement.  Monday, July 11, 2016

http://www.news.ucsb.edu/2016/017014/entanglement-chaos

C. Neill, P. Roushan, et al.  Ergodic dynamics and thermalization in an isolated quantum system. Nature Physics (2016) DOI: doi:10.1038/nphys3830. Published online 11 July 2016

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3830.html

# s-phys-tech-bot: crackin' as a snap

<< If quantum computers existed, they would revolutionize computing as we know it. Based on fundamental properties of matter, the potential power of these theoretical workhorses would solve problems in a new way, cracking extremely complex spy codes and precisely modeling chemical systems in a snap. >>

http://www.eurekalert.org/pub_releases/2015-12/acs-aqs112415.php

Joseph M. Zadrozny, Jens Niklas, et al  Millisecond Coherence Time in a Tunable Molecular Electronic Spin Qubit. ACS Central Science, 2015; DOI: 10.1021/acscentsci.5b00338

http://pubs.acs.org/doi/full/10.1021/acscentsci.5b00338