Quantum News
Sign InSign Up
Home/Quantum Technology/Quantum Computing Market Analysis: Industry Trends & Investment

Quantum Computing Market Analysis: Industry Trends & Investment

Quantum computing market news: market size, industry analysis, quantum investment, market forecast. Quantum computing stocks & funding.

6,193 Articles
Updated Daily

The quantum computing market is transitioning from research to commercial reality, with projections ranging from $1 billion (2024) to $125 billion by 2032 depending on fault-tolerant system development.

Market segmentation by offering type includes quantum hardware (30%), quantum software (25%), and quantum services (45%). By application: optimization (35%), simulation (30%), machine learning (20%), and cryptography (15%).

India's Quantum Market Landscape

India's National Quantum Mission represents a ₹6,003.65 crore ($720 million) government investment through 2030-31, making it one of the top 5 government quantum programs globally. The mission aims to capture a significant share of the growing quantum market by developing indigenous capabilities across computing, communication, sensing, and materials.

India's quantum startup ecosystem received government support through NQM and NM-ICPS (National Mission on Interdisciplinary Cyber-Physical Systems). Eight startups selected in November 2024 include: QNu Labs (Bengaluru): Quantum-safe networks and QKD systems; QpiAI India (Bengaluru): Superconducting quantum computer development; Dimira Technologies (IIT Mumbai): Cryogenic cables for quantum computing; Prenishq (IIT Delhi): Precision diode-laser systems; QuPrayog (Pune): Optical atomic clocks; Quanastra (Delhi): Advanced cryogenics and superconducting detectors; Pristine Diamonds (Ahmedabad): Diamond materials for quantum sensing; Quan2D Technologies (Bengaluru): Superconducting nanowire single-photon detectors.

Tata Consultancy Services (TCS) partners with IBM on quantum computing with significant investment in quantum algorithm development. The Quantum Valley Tech Park in Andhra Pradesh represents a major public-private quantum computing investment.

Researchers Find Fermionic Quantum Error Correction Needs Extra Steps - Quantum Zeitgeist
Featured
quantum-computing

Researchers Find Fermionic Quantum Error Correction Needs Extra Steps - Quantum Zeitgeist

Fermionic platforms offer compelling architectures for quantum computing, ranging from topologically protected Majorana-based qubits to fermionic cold atoms. To achieve scalability, they require quantum error correction. The research proves that any exact and sufficiently accurate approximate fermionic quantum error correction necessarily requires non-Gaussian operations, beyond the free-fermion regime of quadratic dynamics. This is in sharp contrast to the qubit setting, where efficiently classically simulable stabilizer operations form the standard framework for quantum error correction. Specifically, the study demonstrates that the logical space of any non-trivial fermionic error-correcting code contains no pure states. Non-Gaussian Operations Essential For Strong Fermionic Error Correction Scientists at Freie Universität Berlin, collaborating with Quantum Research Centre Tsinghua University and Technology Innovation Institute, have identified a key limitation for scalable quantum computation utilising fermions. They proved that sufficiently accurate fermionic error correction requires non-Gaussian operations when Majorana distance reaches dF ≥3, a threshold previously impossible to cross. Existing codes relied on simpler free-fermion dynamics but lacked the capacity for strong logical qubit protection against accumulating errors during complex calculations. This incompatibility is rooted in Wick’s theorem which governs particle correlations, establishing that the logical space within any effective fermionic code cannot contain pure states describable by Gaussian statistics. The team quantified this limitation showing the number of necessary ‘non-Gaussian gates’ grows linearly alongside both error-protection strength and logically stored information within the system. Further analysis revealed distinctions between how fermions and bosons handle entanglement distillation, a process vital for extending communication range in quantum networks; Gaussian fermionic ope

Google News – Quantum ComputingLoading...0
Occam Foundry Gains Austin and UT Austin Support for Quantum Campusquantum-computing

Occam Foundry Gains Austin and UT Austin Support for Quantum Campus

Insider Brief PRESS RELEASE — Occam Foundry, a commercialization campus for quantum technology planned for 16.5 acres in southeastern Travis County, announces a letter of support from Austin Mayor Kirk Watson and a signed memorandum of understanding with The University of Texas at Austin, acting through the Texas Advanced Computing Center (TACC). In a letter […]

Quantum DailyLoading...0
The Quantum Coast: Meet America’s Top New Tech Hub - Commercial Observerquantum-computing

The Quantum Coast: Meet America’s Top New Tech Hub - Commercial Observer

Along the coast between Silicon Valley and Southern California, another major industry hub is forming for a new kind of technological innovation. Quantum computing utilizes quantum mechanics to vastly expand on traditional binary computing, solving devilishly complex problems exponentially quicker. And, while the technology is in its early stages, the science behind it is in development in Santa Barbara and neighboring Goleta, which are drawing some of the nation’s top tech companies and employers to an area that was known far more for tourism and a large university.SEE ALSO: Marco Caffuzzi of Latham & Watkins: 5 Questions And the rapid pace of development and rosy forecasts for eventual economic effects have already spilled into commercial real estate. Centered around the groundbreaking research at the University of California-Santa Barbara, landlords and investors are positioning themselves around the specialized quantum sector in the region. In March, Colliers helped broker a recapitalization and sale of a 733,000-square-foot tech park portfolio in Goleta to Irvine-based investment firm Praelium. The $235 million trade was one of the largest investment sales ever for Santa Barbara County. In August, Google spent $32.5 million acquiring a pair of buildings on Castilian Drive in Goleta, further expanding its sizable footprint in the area. Along with a flood of Big Tech tenancy creating a cluster of companies near cutting-edge research, these kinds of deals underscore how quantum has become a new type of tech investment play. JLL research rates the Southern California quantum ecosystem, including Santa Barbara, as a more mature one versus that of the Bay Area, and tracks roughly a dozen corporate-owned quantum facilities in the region. Google’s global center for quantum research is also in Goleta, less than 15 minutes from UC-Santa Barbara. Last year, Santa Barbara startups raised $293 million across 35 deals, a 15 percent jump from 2024. “This is a pretty niche

Google News – Quantum ComputingLoading...0
KIST Connects Korean Quantum Startups With U.S. Partners at QWC 2026quantum-computing

KIST Connects Korean Quantum Startups With U.S. Partners at QWC 2026

Insider Brief PRESS RELEASE — The Korea Institute of Science and Technology (KIST) has successfully led a delegation of South Korean quantum deep-tech startups at Quantum World Congress (QWC) 2026, establishing key international partnerships and expanding their footprint into the U.S. market. Serving as the lead organization for the quantum technology sector under South Korea‘s […]

Quantum DailyLoading...0
Pasqal Shifts French Public Collaboration Toward Commercial Quantum Computingquantum-computing

Pasqal Shifts French Public Collaboration Toward Commercial Quantum Computing

Insider Brief PRESS RELEASE — Pasqal (NASDAQ: PSQL) is announcing an evolution of the areas of its collaboration with the French public authorities to now focus on commercial applications, in line with the company’s growth strategy and innovation priorities. This evolution includes the termination of Pasqal’s participation in the defense program LSQUARE (otherwise known as […]

Quantum DailyLoading...0
5 Millionaire-Maker Quantum Computing Stocks to Buy Now - The Globe and Mail
Featured
quantum-computing

5 Millionaire-Maker Quantum Computing Stocks to Buy Now - The Globe and Mail

Key PointsIonQ and Quantinuum are leading the charge on accuracy using the trapped-ion technique.D-Wave and IBM are two top companies using the faster superconducting qubit technology.Infleqtion's neutral-atom approach could become the best of both worlds.10 stocks we like better than IonQ ›Quantum computing has the potential to be the next big technological breakthrough after artificial intelligence (AI). Companies in the field are pursuing the technology in various ways, so a basket approach (a collection of small positions across several stocks) may be the best investment option.While it's unlikely that all of them pan out, if one or two do, they could help fuel a millionaire-making portfolio. Let's look at the stocks I'd put in this quantum computing basket.Missed AI’s "Act 1"? Act 2 Could Be 15x Bigger. Most investors think they missed the AI boat because they didn't buy Nvidia in 2005. But according to our analysts, we’re only at the end of "Act 1"—the R&D phase. "Act 2" is the global rollout. Continue »Image source: Getty ImagesIonQThe first stock I'd add to a quantum basket is IonQ(NYSE: IONQ). The company uses the trapped-ion method with the added twist of embedding microwave antennas directly into its chips. This also resulted in the company achieving the best accuracy in the space, with 99.99% two-qubit gate fidelity. It also recently demonstrated what it called "the industry's first end-to-end real-time quantum error correction decoder," a significant milestone as it pushes to create a fault-tolerant quantum system.In addition to its accuracy lead, the company has made a variety of acquisitions across different areas of the quantum ecosystem. It even acquired a quantum foundry that will help it advance prototypes more quickly and scale more easily.QuantinuumAnother top quantum stock in terms of accuracy is Quantinuum(NASDAQ: QNT). It also uses the trapped-ion approach and has recorded 99.92% 2-qubit gate fidelity. With its new Sol system, meanwhile,

Google News – Quantum ComputingLoading...0
5 Millionaire-Maker Quantum Computing Stocks to Buy Now - Yahoo Finance
Featured
quantum-computing

5 Millionaire-Maker Quantum Computing Stocks to Buy Now - Yahoo Finance

5 Millionaire-Maker Quantum Computing Stocks to Buy Now Geoffrey Seiler, The Motley Fool Mon, September 28, 2026 at 7:50 AM EDT 4 min read IONQ +1.11% NVDA +0.22% Quantum computing has the potential to be the next big technological breakthrough after artificial intelligence (AI). Companies in the field are pursuing the technology in various ways, so a basket approach (a collection of small positions across several stocks) may be the best investment option. While it's unlikely that all of them pan out, if one or two do, they could help fuel a millionaire-making portfolio. Let's look at the stocks I'd put in this quantum computing basket. Missed AI's "Act 1"? Act 2 Could Be 15x Bigger. Most investors think they missed the AI boat because they didn't buy Nvidia in 2005. But according to our analysts, we're only at the end of "Act 1"—the R&D phase. "Act 2" is the global rollout. Continue » Image source: Getty Images IonQ The first stock I'd add to a quantum basket is IonQ (NYSE: IONQ). The company uses the trapped-ion method with the added twist of embedding microwave antennas directly into its chips. This also resulted in the company achieving the best accuracy in the space, with 99.99% two-qubit gate fidelity. It also recently demonstrated what it called "the industry's first end-to-end real-time quantum error correction decoder," a significant milestone as it pushes to create a fault-tolerant quantum system. In addition to its accuracy lead, the company has made a variety of acquisitions across different areas of the quantum ecosystem. It even acquired a quantum foundry that will help it advance prototypes more quickly and scale more easily. Quantinuum Another top quantum stock in terms of accuracy is Quantinuum (NASDAQ: QNT). It also uses the trapped-ion approach and has recorded 99.92% 2-qubit gate fidelity. With its new Sol system, meanwhile, it expects to hit 99.999% logical fidelity in 2027.

Google News – Quantum ComputingLoading...0
5 Millionaire-Maker Quantum Computing Stocks to Buy Now - The Motley Fool
Featured
quantum-computing

5 Millionaire-Maker Quantum Computing Stocks to Buy Now - The Motley Fool

Quantum computing has the potential to be the next big technological breakthrough after artificial intelligence (AI). Companies in the field are pursuing the technology in various ways, so a basket approach (a collection of small positions across several stocks) may be the best investment option. While it's unlikely that all of them pan out, if one or two do, they could help fuel a millionaire-making portfolio. Let's look at the stocks I'd put in this quantum computing basket. Image source: Getty Images IonQ The first stock I'd add to a quantum basket is IonQ (IONQ +1.11%). The company uses the trapped-ion method with the added twist of embedding microwave antennas directly into its chips. This also resulted in the company achieving the best accuracy in the space, with 99.99% two-qubit gate fidelity. It also recently demonstrated what it called "the industry's first end-to-end real-time quantum error correction decoder," a significant milestone as it pushes to create a fault-tolerant quantum system. ExpandNYSE: IONQIonQPremium FeatureMoneyball Superscore62/100Today's Change(1.11%) $0.50Current Price$45.48Key Data Points*:nth-last-child(-n+2)]:border-b-0">Market Cap$18BMarket cap calculated using publicly traded shares outstanding only. Does not include unlisted, private, or dual-class non-traded shares. Implied market cap may vary.Day's Range$44.12 - $46.5552wk Range$25.89 - $84.64Volume1.2MAvg Vol21.3MGross Margin-3317.96% In addition to its accuracy lead, the company has made a variety of acquisitions across different areas of the quantum ecosystem. It even acquired a quantum foundry that will help it advance prototypes more quickly and scale more easily. Quantinuum Another top quantum stock in terms of accuracy is Quantinuum (QNT +0.28%). It also uses the trapped-ion approach and has recorded 99.92% 2-qubit gate fidelity. With its new Sol system, meanwhile, it expects to hit 99.999% logical fidelity in 2027. Quantinuum is also known to have one of the best quantu

Google News – Quantum ComputingLoading...0
5 Millionaire-Maker Quantum Computing Stocks to Buy Now
Featured
quantum-computing

5 Millionaire-Maker Quantum Computing Stocks to Buy Now

Quantum computing has the potential to be the next big technological breakthrough after artificial intelligence (AI). Companies in the field are pursuing the technology in various ways, so a basket approach (a collection of small positions across several stocks) may be the best investment option. While it's unlikely that all of them pan out, if one or two do, they could help fuel a millionaire-making portfolio. Let's look at the stocks I'd put in this quantum computing basket. Image source: Getty Images IonQ The first stock I'd add to a quantum basket is IonQ (IONQ +1.11%). The company uses the trapped-ion method with the added twist of embedding microwave antennas directly into its chips. This also resulted in the company achieving the best accuracy in the space, with 99.99% two-qubit gate fidelity. It also recently demonstrated what it called "the industry's first end-to-end real-time quantum error correction decoder," a significant milestone as it pushes to create a fault-tolerant quantum system. ExpandNYSE: IONQIonQPremium FeatureMoneyball Superscore62/100Today's Change(1.11%) $0.50Current Price$45.48Key Data Points*:nth-last-child(-n+2)]:border-b-0">Market Cap$18BMarket cap calculated using publicly traded shares outstanding only. Does not include unlisted, private, or dual-class non-traded shares. Implied market cap may vary.Day's Range$44.12 - $46.5552wk Range$25.89 - $84.64Volume1.1MAvg Vol21.3MGross Margin-3317.96% In addition to its accuracy lead, the company has made a variety of acquisitions across different areas of the quantum ecosystem. It even acquired a quantum foundry that will help it advance prototypes more quickly and scale more easily. Quantinuum Another top quantum stock in terms of accuracy is Quantinuum (QNT +0.28%). It also uses the trapped-ion approach and has recorded 99.92% 2-qubit gate fidelity. With its new Sol system, meanwhile, it expects to hit 99.999% logical fidelity in 2027. Quantinuum is also known to have one of the best quantu

The Motley FoolLoading...0
Town to get millions for IBM Quantum project - Mid Hudson Newsquantum-computing

Town to get millions for IBM Quantum project - Mid Hudson News

TOWN OF POUGHKEEPSIE – The proposed IBM Quantum computing facility at the existing IBM campus on South Road (Route 9) in the town has become a financial windfall worth millions of dollars for the town.  The $54 million IBM has agreed to pay the town is separate from the Payment in Lieu of Taxes (PILOT) application that IBM submitted to the Dutchess County IDA.  If approved on Tuesday, the PILOT will require IBM to pay Dutchess County, the Town of Poughkeepsie, and the Spackenkill Union Free School District a set amount instead of annual taxes.

Google News – Quantum ComputingLoading...0
Is entanglement a property of a state rather than of the spaces, and how should "irreducible to its parts" be stated precisely?quantum-computing

Is entanglement a property of a state rather than of the spaces, and how should "irreducible to its parts" be stated precisely?

Quantum Computing is part of Stack Overflow’s open communities: specialist spaces where curiosity is welcome, knowledge is shared freely, and the best answers rise to the top. Stack Overflow for Teams is now called Stack Internal. Bring the best of human thought and AI automation together at your work. Bring the best of human thought and AI automation together at your work. Learn more Bring the best of human thought and AI automation together at your work. I'm not a mathematician and I'm trying to make sure I understand this correctly. My understanding is: (1) Hilbert spaces with ⊗ form a symmetric monoidal category, and the product is non-cartesian; (2) entanglement is a property of a state in H_A ⊗ H_B, namely one not in the image of the map from pairs of states; (3) decoherence disperses correlations into the environment, so the pair alone looks mixed while the joint state stays pure. Is this right? And is there a standard way to say a construction is "irreversible" in this setting? Thanks for contributing an answer to Quantum Computing Stack Exchange! Use MathJax to format equations. MathJax reference. To learn more, see our tips on writing great answers. By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. This comment attacks a person or group. Learn more in our Abusive behavior policy. This comment is rude or condescending. Learn more in our Code of Conduct. A problem not listed above. Try to be as specific as possible. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later.

Quantum Computing Stack ExchangeLoading...0
Restricting Trainable Lie-Algebra Growth in Equivariant Quantum Networks via Hierarchical Ancilla-Controlled Subspace Projectionsquantum-computing

Restricting Trainable Lie-Algebra Growth in Equivariant Quantum Networks via Hierarchical Ancilla-Controlled Subspace Projections

--> Quantum Physics arXiv:2609.30283 (quant-ph) [Submitted on 3 Sep 2026] Title:Restricting Trainable Lie-Algebra Growth in Equivariant Quantum Networks via Hierarchical Ancilla-Controlled Subspace Projections Authors:Ting Li, Zhiming Xiao, Qibiao Tang View a PDF of the paper titled Restricting Trainable Lie-Algebra Growth in Equivariant Quantum Networks via Hierarchical Ancilla-Controlled Subspace Projections, by Ting Li and 2 other authors View PDF HTML (experimental) Abstract:Equivariant quantum networks encode symmetry as an inductive bias, which can improve generalization and may also favor optimization convergence. Equivariance alone, however, does not constrain the noncommuting closure of trainable generators, and this closure can still grow rapidly in symmetry-preserving variational circuits. We introduce a hierarchical ancilla-controlled architecture that addresses this Lie-algebra-growth mechanism. Commuting invariant-sector projectors on the data register select parameterized operations on a shared ancilla register, where the noncommuting trainable dynamics is confined. The trainable circuit decomposes into compatible joint sectors, giving a sector-probability-weighted ancilla response and an explicit view of parameter sharing across hierarchical paths. For an ancilla dimension $d_A=2^m$ and $K_\ell$ retained layer-wise control modes, we prove the group-independent bound $\dim(\mathfrak g)\le (d_A^2-1)\prod_{\ell=1}^{L}(K_\ell+1)$. The bound is polynomial in the number of data qubits when $m$ and $K_\ell$ remain constant along a logarithmic-depth hierarchy. Particle-number and parity projectors illustrate the general construction, while a fixed Clebsch--Gordan coupling tree supplies a concrete $SU(2)$ realization with rotation-invariant scalar outputs. Finite-size state-vector simulations exhibit slower gradient-variance decay and larger initialization gradients than generic and conventional rotationally equivariant circuits over the studied system sizes.

arXiv Quantum PhysicsLoading...0
Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermionsquantum-computing

Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermions

--> Quantum Physics arXiv:2609.30285 (quant-ph) [Submitted on 3 Sep 2026] Title:Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermions Authors:Dogukan Bakircioglu, Pablo Arrighi View a PDF of the paper titled Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermions, by Dogukan Bakircioglu and Pablo Arrighi View PDF HTML (experimental) Abstract:This work provides a digital quantum simulation scheme for $1{+}1$-dimensional $SU(2)$ Yang--Mills theory with Dirac fermions. It takes the form of a quantum circuit, infinitely repeating across space and time with $\Delta_t=\Delta_x=\varepsilon$, whose wires follow lightlike propagation. The construction mirrors the logic of the standard quantum field theory approach, transposed to the discrete setting. Namely, we start from the Dirac quantum walk, restore $SU(2)$ gauge symmetry by introducing the gauge field, lift the walk to a multi-particle QCA while preserving fermionic anticommutation, and equip the gauge field with its own dynamics. Rather than relying on Clebsch--Gordan decompositions, we use the pointwise-product structure of gauge-link updates, which yields self-contained proofs of unitarity and gauge covariance in quantum-computing notation. The construction provides an explicit algorithmic formulation of the theory, whose continuum limit we discuss. Subjects: Quantum Physics (quant-ph); High Energy Physics - Lattice (hep-lat) Cite as: arXiv:2609.30285 [quant-ph]   (or arXiv:2609.30285v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2609.30285 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Dogukan Bakircioglu [view email] [v1] Thu, 3 Sep 2026 19:10:11 UTC (41 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermions, by Dogukan Bakircioglu and Pablo ArrighiView PDFHTML (experimental)TeX Sour

arXiv Quantum PhysicsLoading...0
Colored Weingarten Calculus for Block-Unitary Ensemblequantum-computing

Colored Weingarten Calculus for Block-Unitary Ensemble

--> Quantum Physics arXiv:2609.30385 (quant-ph) [Submitted on 24 Sep 2026] Title:Colored Weingarten Calculus for Block-Unitary Ensemble Authors:Daniele Iannotti, Elisa Vallini View a PDF of the paper titled Colored Weingarten Calculus for Block-Unitary Ensemble, by Daniele Iannotti and Elisa Vallini View PDF HTML (experimental) Abstract:Haar randomness is the standard null model for quantum typicality, scrambling, and random-matrix formulations of thermalization. In many physical settings, however, randomness is naturally constrained to subspaces of Hilbert space. This structure arises, in particular, both in systems with symmetry-resolved sectors and in the Eigenstate Thermalization Hypothesis (ETH), where mesoscopic energy windows define subspaces in which nearby energy eigenstates are mixed. Motivated by these settings, we consider a Block-Unitary Ensemble consisting of independently Haar-random unitaries acting on each subspace. We develop a constructive Weingarten Calculus for this ensemble, providing a unified framework across quantum information and many-body physics. This construction reveals a symmetry-resolved Schur-Weyl duality, where the relevant commutant is not the ordinary permutation algebra, but the one of color-preserving permutations. We apply this framework to quantum states under symmetry constraints and to energy-resolved ensembles for ETH. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2609.30385 [quant-ph]   (or arXiv:2609.30385v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2609.30385 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Daniele Iannotti [view email] [v1] Thu, 24 Sep 2026 18:00:35 UTC (264 KB) Full-text links: Access Paper: View a PDF of the paper titled Colored Weingarten Calculus for Block-Unitary Ensemble, by Daniele Iannotti and Elisa ValliniView PDFHTML (experimental)TeX Source view license C

arXiv Quantum PhysicsLoading...0
Classification of Generalised Triorthogonal Codes through Length 54quantum-computing

Classification of Generalised Triorthogonal Codes through Length 54

--> Quantum Physics arXiv:2609.30860 (quant-ph) [Submitted on 25 Sep 2026] Title:Classification of Generalised Triorthogonal Codes through Length 54 Authors:Adam Wills, Shubham P. Jain, Shraddha Singh View a PDF of the paper titled Classification of Generalised Triorthogonal Codes through Length 54, by Adam Wills and 2 other authors View PDF HTML (experimental) Abstract:Magic state distillation is a widely considered primitive in fault-tolerant quantum computation for the preparation of high-fidelity non-Clifford resources. The most commonly considered class of such protocols are generalised triorthogonal codes; these distil $n$ noisy input $\mathrm{T}$ states into purified third-level diagonal magic states. Extensive prior work has searched this space of protocols, often using heuristic methods that do not guarantee optimality. Existing classification work is limited to protocols distilling $k$ output $\mathrm{T}$ states with $n+k\leq 38$ (Nezami and Haah, Phys. Rev. A 106, 012437 (2022)). In this work, we significantly expand this classification to all protocols with lengths $n\leq 54$. We restrict to distance $d\geq 3$ to keep the classification to a sensible size, and because efficient searches are well understood at distance $2$ (Singh et al., arXiv:2606.28518). Moreover, our results are complementary to synthillation (Campbell and Howard, Phys. Rev. A 95, 022316 (2017)), which can distil third-level states from $\mathrm{T}$ states, but only at distance $2$. Under optimality in terms of input count, space footprint, and distance for a given output, we find $74$ optimal generalised triorthogonal protocols in our range, $65$ of which are new to the literature. To achieve our classification, we extend the classification of unital triorthogonal spaces of Nezami and Haah from length $38$ to $54$ using a directional derivative method. Using these as the stabiliser spaces, we add logical rows that satisfy the triorthogonality constraints to create full protocols. Subj

arXiv Quantum PhysicsLoading...0
Quantum-circuit simulation of three-flavor neutrino oscillations: vacuum, matter, and CP diagnosticsquantum-computing

Quantum-circuit simulation of three-flavor neutrino oscillations: vacuum, matter, and CP diagnostics

--> Quantum Physics arXiv:2609.30875 (quant-ph) [Submitted on 25 Sep 2026] Title:Quantum-circuit simulation of three-flavor neutrino oscillations: vacuum, matter, and CP diagnostics Authors:Daming Li View a PDF of the paper titled Quantum-circuit simulation of three-flavor neutrino oscillations: vacuum, matter, and CP diagnostics, by Daming Li View PDF HTML (experimental) Abstract:We simulate three-flavor neutrino oscillations on two-qubit quantum circuits. The flavor space is embedded as $\ket{00}=\nu_e$, $\ket{01}=\nu_\mu$, $\ket{10}=\nu_\tau$ with the $\ket{11}$ channel kept inert, and the input mixing parameters (NuFIT~5.3, normal ordering) follow the global fit. We verify three physical settings against analytic or exact references: vacuum propagation, reproduced by a mass-eigenstate phase circuit to $\sim 10^{-16}$; constant-density Mikheev--Smirnov--Wolfenstein (MSW) matter effects, showing resonant flavor conversion when the matter potential $A$ crosses $\Delta m^2_{31}$; and varying-density (supernova shock-shell) propagation by slicing plus second-order Suzuki--Trotter splitting, agreeing with exact evolution to $\sim 10^{-6}$. We report a Suzuki--Trotter precision--resource calibration varying order, step number, and matrix/probability error. It delimits brute-force Trotterization on solar baselines: we quantify both standard alternatives, coherence averaging and adiabatic MSW. We also compute quantum-information diagnostics from the same model parameters, namely mode entanglement and the CP asymmetry. Finally, we extend the framework to open quantum systems via a Lindblad master equation with dephasing and absorptive channels. These results provide a reproducible link between low-energy oscillation observables and quantum-information measures. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.30875 [quant-ph]   (or arXiv:2609.30875v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2609.30875 Focus to learn more ar

arXiv Quantum PhysicsLoading...0
Question about the non-cloning theoremquantum-computing

Question about the non-cloning theorem

Quantum Computing is part of Stack Overflow’s open communities: specialist spaces where curiosity is welcome, knowledge is shared freely, and the best answers rise to the top. Stack Overflow for Teams is now called Stack Internal. Bring the best of human thought and AI automation together at your work. Bring the best of human thought and AI automation together at your work. Learn more Bring the best of human thought and AI automation together at your work. The standard proof to the non-cloning theorem shows that no sequence of unitary quantum gates/base states measurements could be used to duplicate the state of some unknown qubit while preserving its state. But may it be possible to clone a qubit with some physical mechanism other than quantum gates or measurement? The proof ignores the possibility of other physical ways to extract information from the quantum system. So may it be possible to clone the full quantum state of a qubit by other means? Thanks for contributing an answer to Quantum Computing Stack Exchange! Use MathJax to format equations. MathJax reference. To learn more, see our tips on writing great answers. By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. This comment attacks a person or group. Learn more in our Abusive behavior policy. This comment is rude or condescending. Learn more in our Code of Conduct. A problem not listed above. Try to be as specific as possible. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Site design / logo © 2026 Stack Exchange Inc; user contributions licensed under CC BY-SA .

Quantum Computing Stack ExchangeLoading...0
IonQ Just Announced a Major Breakthrough. Should Investors Buy the Stock Now?quantum-computing

IonQ Just Announced a Major Breakthrough. Should Investors Buy the Stock Now?

Quantum computers have a real problem. Small errors slip into calculations all the time, and catching and fixing them fast enough has been a real issue for the industry. On Tuesday, Sept. 22, IonQ (IONQ +1.11%) said it may have found a solution to this problem. ExpandNYSE: IONQIonQPremium FeatureMoneyball Superscore62/100Today's Change(1.11%) $0.50Current Price$45.48Key Data Points*:nth-last-child(-n+2)]:border-b-0">Market Cap$18BMarket cap calculated using publicly traded shares outstanding only. Does not include unlisted, private, or dual-class non-traded shares. Implied market cap may vary.Day's Range$44.12 - $46.5552wk Range$25.89 - $84.64Volume27.6MAvg Vol21.3MGross Margin-3317.96% IonQ's statement said it has developed the industry's first end-to-end, real-time quantum error-correction decoder. Even better, this breakthrough runs on a single standard CPU. This gives IonQ a real edge in this highly competitive race. The day after the announcement, IonQ also said its Superion 256 will become the first on-premises quantum processor at Nvidia's (NVDA +0.22%) Accelerated Quantum Research Center. Image source: The Motley Fool. The stock price rose more than 11% on Wednesday, in line with the good news. IonQ remains a high-risk, speculative investment. In particular, the decoder was validated on simulated data rather than in a live system. How commercially viable quantum computing will be in the coming years remains to be seen. IonQ's valuation is also quite rich. It's deeply unprofitable as well. Investors interested in this space should recognize the sector's longer time horizon and volatility. Shares of IonQ have actually fallen more than 40% in the past year. For investors willing to stay invested for the next several years as this nascent sector finds its footing and use cases, this IonQ breakthrough is significant enough to consider buying the stock, in my opinion. Read NextSep 25, 2026 •By Parkev Tatevosian, CFAGreat News for IonQ Stock Investors!Sep 25, 2026

The Motley FoolLoading...0
A 0.11 threshold defines secure quantum data for learningquantum-computing

A 0.11 threshold defines secure quantum data for learning

Jeongho Bang of Yonsei University established a security threshold of η_(BB84)≃0.11 defining acceptable noise levels in a BB84 protocol while still allowing a machine learning model to learn data securely and within a defined sample budget. This number marks a boundary for secure machine learning, connecting the formal framework of probably-approximately-correct (PAC) learning with the practical consideration of data-path security. The research specifically applies this framework to a “BB84-like quantum label path,” linking abstract security theory to the principles of quantum key distribution. The work demonstrates that the quantum component transforms a chosen noise tolerance into a testable security condition by connecting information acquisition to measurable disturbance. PAC Learning with Budget Constraints Defines Secure Quantum Data A security threshold of 0.11 was established by the research, creating a novel connection between concepts rarely linked in existing frameworks. This operational theory of secure learning centers on an explicit stopping time, combining a trained hypothesis reaching target accuracy with a validation gate halting within a finite sample budget. The work derives a closed-form requirement for this combined PAC-within-budget guarantee, operating under an admissible random-classification-noise channel. Under assumptions of ideal single-qubit operation, authenticated classical channels, memoryless systems, basis symmetry, collective attacks, asymptotic behavior and one-way reconciliation, the standard Holevo bound provides a protocol-specific information-advantage criterion. According to the paper published in Quantum Science and Technology, “The quantum layer is not invoked to reduce distribution-free PAC sample complexity; rather, it turns a designer-chosen classical noise tolerance into a physically testable, protocol-dependent security condition by linking information acquisition to observable disturbance.” Below the ηBB84≃0.11 thresh

Quantum ZeitgeistLoading...0
Quantum algorithms gain from filtered-state preparationquantum-computing

Quantum algorithms gain from filtered-state preparation

Researchers from Sungkyunkwan University in South Korea and Xanadu in Canada detailed a new method for improving quantum algorithms in a paper published September 25, 2026, in Quantum Science and Technology. The team developed a technique designed to address a critical limitation in many quantum algorithms: accurate state preparation. This work demonstrates a framework for enhancing the overlap of input states through spectral filtering, potentially reducing runtime by more than two orders of magnitude for certain calculations, with overlap amplification exceeding a factor of one hundred. Filtered Quantum Phase Estimation for Eigenvalue Problems The success probability of quantum phase estimation hinges on initial state overlap; a new framework detailed in Quantum Science and Technology on September 25, 2026, directly addresses this limitation through filtered-state preparation. Researchers from Sungkyunkwan University and Xanadu developed a method to amplify this overlap, potentially reducing the computational cost of determining essential properties of many-body Hamiltonians, such as ground-state energy and excited spectra. The work introduces a unified framework for quantum algorithms centered on enhancing the initial connection with target eigenstates. This framework explicitly defines the trade-off between overlap amplification, the probability of successfully preparing a state, and the resources required to implement the filter itself. Analysis of Gaussian filters and a modified Krylov-subspace-based filter revealed improvements in the success-probability/overlap balance important for preparing states. The team’s approach tackles a central challenge in quantum computing: accurately estimating eigenvalues, a task where standard quantum phase estimation requires a significant initial overlap between the prepared input state and the target eigenstate. Specifically, the success probability of QPE scales with the squared overlap, meaning even small improvements in

Quantum ZeitgeistLoading...0

Related Topics

Government Quantum InitiativesQuantum Cloud ServicesQuantum Education WorkforceQuantum Software Development