Quantum computing is a model of computation that stores and manipulates information in quantum mechanical systems, using superposition, entanglement, and interference to solve certain problems with far fewer operations than any known classical method. Its basic unit is the qubit, a two-level quantum system that, unlike a classical bit, can sit in a superposition of 0 and 1 until it is measured [1]. A register of n qubits is described by 2^n complex amplitudes, and a quantum algorithm works by arranging those amplitudes so that paths leading to wrong answers cancel and paths leading to the right answer reinforce.

The idea dates to the early 1980s. Richard Feynman argued in 1982 that simulating quantum systems on classical computers is exponentially expensive, and that a computer built from quantum components would be the natural tool for the job [2]. David Deutsch formalized the universal quantum computer in 1985 [3]. The field acquired urgency in 1994, when Peter Shor showed that a quantum computer could factor integers and compute discrete logarithms in polynomial time, breaking the assumptions behind most deployed public-key cryptography [4][5].

Quantum computing intersects artificial intelligence in three distinct ways that are frequently conflated. Proposals grouped under quantum machine learning claim quantum hardware could accelerate training or inference, a claim that has repeatedly failed to survive careful analysis. In the opposite direction, classical machine learning has become a working component inside quantum computers, most visibly in neural network decoders for error correction. And a sufficiently large quantum computer would break the cryptography protecting the infrastructure AI systems run on, which is why standards bodies began replacing those algorithms in 2024. As of mid-2026, no quantum computer has run a commercially useful program faster than classical hardware in a way the wider research community treats as settled. IBM said in November 2025 that it "anticipates that the first cases of verified quantum advantage will be confirmed by the wider community by the end of 2026" [6], and DARPA runs a program whose entire purpose is to determine whether any approach can reach useful scale by 2033 [7].

How a quantum computer works

A qubit is any two-level quantum system that can be prepared, manipulated, and read out: the energy levels of a superconducting circuit, the electronic states of a trapped ion, the polarization of a photon, or the spin of an electron in silicon. Its defining property is that it can occupy a superposition of its two basis states until measurement, at which point it yields a single classical outcome with a probability set by the amplitudes [1].

Multiple qubits can be entangled, meaning their joint state cannot be factored into independent descriptions of each qubit, so measuring one constrains the others [1]. Entanglement is what makes the state space of a quantum register exponentially large rather than a collection of n independent coins, and it is the resource most quantum algorithms consume.

Computation proceeds by applying quantum gates, unitary operations analogous to classical logic gates but reversible. A small set of them, typically single-qubit rotations plus a two-qubit entangling gate such as controlled-NOT, is universal: any quantum computation can be compiled into a circuit built from that set [8]. Measurement at the end of the circuit collapses the state and returns ordinary bits, so an algorithm must be designed so that the bits it returns are the ones worth having. This is a real constraint rather than a formality, and it eliminates several proposed speedups outright.

The engineering problem is decoherence. Qubits lose superposition and entanglement through interaction with their environment, and every gate introduces error [1]. The best reported two-qubit gate error rates sit at a few parts in ten thousand to a few parts in a thousand depending on the platform [9][10], which is why IBM's late-2025 flagship processor is specified for circuits of up to about 5,000 two-qubit gates rather than millions [6]. Nearly everything about the current state of the field follows from that number.

Algorithms and where the speedups actually are

The set of quantum algorithms with proven asymptotic advantage is narrower than popular coverage suggests [11], and the size of the advantage varies enormously.

Algorithm	Year	Problem	Speedup over best known classical
Quantum simulation [2]	1982 (concept)	Simulating quantum systems	Exponential for suitable Hamiltonians
Shor's algorithm [4][5]	1994	Integer factoring, discrete logarithm	Exponential: polynomial time versus sub-exponential
Grover's algorithm [12]	1996	Unstructured search over N items	Quadratic: O(sqrt(N)) versus O(N)
HHL [13]	2008	Sampling from solutions of sparse linear systems	Exponential in system size, subject to heavy caveats

Shor's result is the headline and the reason governments fund the field. Grover's algorithm, which finds a marked item in an unstructured list of N in about sqrt(N) steps [12], is far more general but only quadratic, and a quadratic gain has to be paid for out of the very large constant-factor overhead of running anything on error-corrected hardware [14][15]. Quantum simulation of chemistry and materials is the application closest to Feynman's original motivation and the one most researchers consider likeliest to pay off first, although a 2023 analysis co-authored by researchers at Google, Caltech, Columbia, and elsewhere concluded that for the central task of ground-state energy estimation, "evidence for such an exponential advantage across chemical space has yet to be found" [16].

The HHL algorithm, published by Aram Harrow, Avinatan Hassidim, and Seth Lloyd, prepares a quantum state encoding the solution to a sparse linear system in time polylogarithmic in the system size [13]. It is the root of most quantum machine learning proposals and the clearest illustration of how fragile these speedups are.

Hardware modalities

No single qubit technology has won. In November 2025 DARPA selected eleven companies for Stage B of its Quantum Benchmarking Initiative: Atom Computing, Diraq, IBM, IonQ, Nord Quantique, Photonic Inc., Quantinuum, Quantum Motion, QuEra Computing, Silicon Quantum Computing, and Xanadu [17]. That roster spans superconducting, trapped-ion, neutral-atom, photonic, and silicon-spin hardware, which is a fair map of the approaches under serious evaluation.

Modality	Physical qubit	Representative organizations	Notes
Superconducting circuits	Microwave resonant circuits at millikelvin temperatures	Google, IBM, Nord Quantique	Fast gates, mature fabrication, requires dilution refrigeration
Trapped ions	Individual ions held in electromagnetic traps	Quantinuum, IonQ	Highest reported gate fidelities, all-to-all connectivity, slower gates
Neutral atoms	Atoms held in optical tweezer arrays	QuEra Computing, Atom Computing	Scales easily in qubit count; thousands of sites demonstrated
Photonics	Photons in waveguides and interferometers	Xanadu	Natural fit with optical networking; deterministic two-qubit gates are hard, since entangling operations are typically probabilistic
Silicon spin qubits	Electron or nuclear spins in silicon	Diraq, Quantum Motion, Silicon Quantum Computing, Photonic Inc.	Reuses semiconductor manufacturing, very small device footprint
Topological	Proposed non-local encodings in hybrid semiconductor-superconductor devices	Microsoft	Promises intrinsic error protection; the experimental claims are disputed

Superconducting and trapped-ion systems have produced most of the headline results. Quantinuum's Helios, launched in November 2025, uses 98 barium-137 ion qubits in a quantum charge-coupled device architecture, with a rotatable storage ring giving all-to-all connectivity; it reports single-qubit gate infidelity of 2.5(1) x 10^-5 and two-qubit gate infidelity of 7.9(2) x 10^-4 [9]. Neutral atoms lead on raw count: a Caltech group led by Manuel Endres, publishing in Nature in 2025, reported an array of more than 6,100 neutral atoms held in roughly 12,000 tweezer sites, with a hyperfine coherence time of 12.6 seconds and imaging survival of 99.989% [18].

Error correction and the road to fault tolerance

Physical qubits are too noisy to run long computations directly. Quantum error correction spreads one logical qubit across many physical qubits so errors can be detected and corrected without measuring, and thereby destroying, the encoded state. The dominant scheme has been the surface code, a two-dimensional stabilizer code set out in practical form by Austin Fowler, Matteo Mariantoni, John Martinis, and Andrew Cleland in 2012 [8].

Surface codes only help when physical error rates fall below a threshold. Above it, adding qubits makes things worse; below it, logical error falls off exponentially with code distance. In December 2024 Google reported crossing that line with its 105-qubit Willow chip. A distance-7 surface code using 101 qubits reached an error rate of 0.143% +/- 0.003% per correction cycle, and increasing the code distance by two suppressed logical error by a factor of 2.14 +/- 0.02; the logical qubit outlived its best constituent physical qubit by a factor of 2.4 +/- 0.3 [19]. Real-time decoding at distance-5 ran with an average latency of 63 microseconds against a 1.1 microsecond cycle time. Repetition-code tests out to distance-29 exposed the next obstacle: rare correlated error events occurring roughly once per hour [19].

IBM has committed instead to quantum low-density parity check codes, which trade the surface code's strictly local connectivity for longer-range couplings between qubits; its experimental Loon processor, unveiled in November 2025, is the company's demonstration of the processor components fault tolerance requires, and IBM separately reported decoding errors in real time in under 480 nanoseconds using qLDPC codes [6][20]. IBM's published roadmap targets IBM Quantum Starling in 2029, described as running "100 million quantum operations using 200 logical qubits," followed by Blue Jay at 1 billion operations over 2,000 logical qubits, built at a data center in Poughkeepsie, New York [20]. Its November 2025 Nighthawk processor carries 120 qubits and 218 tunable couplers [6].

The scale required for the famous applications remains daunting. Craig Gidney and Martin Ekerå estimated in 2019 that factoring a 2048-bit RSA key would take 20 million noisy qubits running for 8 hours [14]. Gidney's 2025 revision cut that to fewer than a million noisy qubits running for under a week, a reduction achieved through approximate residue arithmetic, yoked surface codes, and magic state cultivation [15]. Either figure is three to four orders of magnitude beyond any device built to date.

Quantum advantage claims and the classical counterattack

Headline demonstrations of quantum advantage have repeatedly been followed by classical algorithm improvements that narrow or erase the gap, although the most recent claims have not yet drawn a published refutation. The pattern is consistent enough to be one of the most useful things to know about the field.

Year	Claim	Classical response
2019	Google's 53-qubit Sycamore samples a random circuit in about 200 seconds; Google estimates roughly 10,000 years for a state-of-the-art classical supercomputer [21]	IBM estimates about two and a half days on the Summit supercomputer using secondary storage, at far higher fidelity [22]; in 2021 Feng Pan, Keyang Chen, and Pan Zhang generate one million uncorrelated samples in 15 hours on 512 GPUs [23]
2023	IBM reports "evidence for the utility of quantum computing before fault tolerance" on a 127-qubit Eagle processor [24]	Tomislav Begušić, Johnnie Gray, and Garnet Kin-Lic Chan reproduce the results classically, and faster, using sparse Pauli dynamics and tensor networks [25]
2024	Zuchongzhi 3.0, a 105-qubit Chinese superconducting processor, samples an 83-qubit circuit in a few hundred seconds, estimated at 6.4 x 10^9 years on Frontier [10]	No published refutation at time of writing
2024	Google's Willow, a 105-qubit chip, performs a random circuit sampling computation "in under five minutes that would take one of today's fastest supercomputers 10 septillion (that is, 10^25) years" [26]	No published refutation at time of writing
2025	Google's Quantum Echoes algorithm, built on out-of-time-order correlators, reported as running "13,000 times faster on Willow than the best classical algorithm on one of the world's fastest supercomputers" [27][28]	Google researchers and collaborators argued in April 2026 that tensor networks with belief propagation, a leading classical alternative, cannot feasibly reproduce the experiment [29]

Random circuit sampling, the benchmark behind the 2019 and 2024 claims, is a stress test rather than an application, which is part of why Google presented the 2025 Quantum Echoes result differently. That algorithm measures how quantum information spreads through a system, and Google demonstrated it on nuclear magnetic resonance data for molecules of 15 and 28 atoms, arguing it could contribute to drug discovery and materials characterization [27]. Google also stressed verifiability, by which it meant a result that can be repeated on its own quantum computer or any other of the same caliber to get the same answer [27].

Quantum machine learning: the case for skepticism

The claim that quantum computers will accelerate AI is the most oversold part of the field, and the reasons are well documented.

Scott Aaronson's 2015 commentary "Read the fine print" set out four caveats that apply to HHL and to the machine learning algorithms built on top of it [11]. The input vector must be loadable into a quantum state quickly, which generally requires a quantum RAM holding structure that ordinary data does not have. The matrix must admit efficient Hamiltonian simulation. It must be well conditioned. And, most damagingly, the output is a quantum state rather than a list of numbers: "learning the value of any specific entry x_i will, in general, require repeating the algorithm roughly n times, which would once again kill the exponential speedup" [11]. Any one of these failing removes the exponential advantage.

Three later results hollowed out the near-term case further:

Dequantization. In 2018 Ewin Tang, then an undergraduate, produced a classical algorithm matching the quantum recommendation system of Kerenidis and Prakash up to polynomial factors, showing the claimed exponential speedup was an artifact of comparing unequal input assumptions [30]. A wave of similar dequantization results followed for other HHL-derived algorithms.
Barren plateaus. Jarrod McClean and colleagues at Google showed in 2018 that for a broad class of randomly initialized parameterized quantum circuits, gradients vanish exponentially with qubit count, leaving a flat loss landscape that classical optimizers cannot climb [31]. The variational circuits that dominate near-term quantum machine learning are exactly the models affected.
The simulability trap. A 2025 paper in Nature Communications by M. Cerezo, Zoë Holmes, and colleagues gathered evidence that the structural choices used to escape barren plateaus also tend to make the model classically simulable, "provided that one can collect some classical data from quantum devices during an initial data acquisition phase" [32]. If a circuit is trainable, there is a fair chance it is also unnecessary.

Maria Schuld and Nathan Killoran argued in 2022 that quantum advantage may be the wrong goal for the subfield altogether, since classical machine learning is empirically powerful but theoretically hard to study while quantum computing has no practical benchmarks at realistic scale and leans on theory instead [33]. None of this proves quantum machine learning is impossible, but the burden of proof sits with its proponents, and the mechanisms proposed so far have not carried it.

Machine learning inside the quantum stack

Traffic in the other direction has been more productive. Decoding an error-correcting code means inferring which physical errors occurred from a stream of syndrome measurements, a pattern-recognition problem over noisy correlated data, which is the kind of thing neural networks handle well.

Google DeepMind and Google Quantum AI built AlphaQubit, a recurrent transformer-based decoder for the surface code, reported in Nature in 2024. It outperformed state-of-the-art algorithmic decoders on real data from Google's Sycamore processor at code distances 3 and 5, and held its accuracy on simulated data out to distance 11 [34]. The author list includes Demis Hassabis and Pushmeet Kohli, and the paper frames the result as a learned model beating hand-designed algorithms by picking up noise correlations those algorithms assume away [34]. The practical constraint is latency: a decoder has to keep pace with a microsecond-scale correction cycle [19].

Learning shows up elsewhere in the stack as well: the same Google experiment that produced the Quantum Echoes result used its correlator measurements to perform Hamiltonian learning, inferring the parameters of the system being probed [28]. On present evidence the relationship runs more strongly from AI to quantum computing than the other way around.

Cryptography and the post-quantum transition

Shor's algorithm is why quantum computing has a policy dimension. RSA, Diffie-Hellman, and elliptic-curve cryptography all rest on problems Shor's algorithm solves efficiently, so an adversary that records encrypted traffic today could decrypt it once such a machine exists. That risk, plus the years it takes to replace cryptography in deployed systems, is why the transition started well before the hardware did.

The NIST standardization process moved first. On 13 August 2024 NIST released its first three finalized post-quantum standards [35]:

Standard	Algorithm name	Original submission	Function
FIPS 203	ML-KEM	CRYSTALS-Kyber	General encryption and key encapsulation
FIPS 204	ML-DSA	CRYSTALS-Dilithium	Digital signatures
FIPS 205	SLH-DSA	SPHINCS+	Backup signature scheme, hash-based

NIST mathematician Dustin Moody urged administrators "to start integrating them into their systems immediately, because full integration will take time" [35]. In March 2025 NIST selected HQC, a code-based scheme, as a fifth algorithm and a backup for ML-KEM, chosen specifically because it rests on error-correcting codes rather than lattices, so a break of one family would not take down both [36].

Migration deadlines are now written into United States federal guidance. NIST's draft internal report IR 8547 proposes that classical public-key schemes at the 112-bit security level, which covers currently deployed RSA and elliptic-curve parameters, be deprecated after 2030 and disallowed after 2035, matching National Security Memorandum 10's target of widespread post-quantum adoption by 2035 [37]. The threat is asymmetric across primitives: symmetric encryption and hash functions need only larger parameters, and lattice-based privacy techniques such as homomorphic encryption are themselves candidates for quantum resistance.

Recent developments, 2025 and 2026

The 2025 Nobel Prize in Physics went to John Clarke, Michel H. Devoret, and John M. Martinis on 7 October 2025 "for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit," recognizing experiments from 1984 and 1985 on Josephson junctions that underpin superconducting qubits [38]. Devoret's listed affiliations at the time of the award included Google Quantum AI [38]. On 18 March 2026 ACM named Charles H. Bennett of IBM Research and Gilles Brassard of the Université de Montréal recipients of the 2025 A.M. Turing Award, citing the BB84 quantum key distribution protocol of 1984, quantum teleportation in 1993, and entanglement distillation in 1996 [39].

Microsoft's topological program drew sustained criticism. The company announced its Majorana 1 chip on 19 February 2025, claiming eight topological qubits on an architecture it said offered a path to a million qubits on a single chip [40]. On 24 June 2026 Nature published a Matters Arising critique by Henry Legg of the University of St Andrews, "On the robustness of topological gap detection via transport," arguing that shifting the measurement window changed whether a device region passed Microsoft's topological gap test, that favorable results had been reported selectively, and that data-processing errors affected the analysis [41]. Microsoft's published reply described the issue as a "minor off-by-one-pixel bug" in its processing and said it stands by its results and roadmap [42].

Two large companies broadened their hardware bets. On 24 March 2026 Google Quantum AI said it would add neutral atom research alongside superconducting qubits, hiring Adam Kaufman to lead a team in Boulder, Colorado and citing foundational work by its portfolio company QuEra. Google framed the platforms as complementary, since "superconducting processors are easier to scale in the time dimension (circuit depth), while neutral atoms are easier to scale in the space dimension (qubit count)" [43]. On 23 July 2026 IBM announced an agreement to acquire HRL Laboratories, jointly owned by Boeing and General Motors, for its silicon-spin qubit, sensing, and materials work; terms were not disclosed and the deal was expected to close by the end of the third quarter of 2026 [44].

Application results are becoming more concrete, if still modest. On 6 July 2026 Oak Ridge National Laboratory, Cleveland Clinic, and IBM reported computing nine molecular configurations of FLiBe, a fluorine-lithium-beryllium material relevant to tritium extraction in fusion reactors, using a quantum-centric supercomputing approach in which quantum and classical machines each take part of the problem [45]. That shape, hybrid and narrow and checked against classical methods rather than replacing them, is the realistic near-term picture of the field.

See also

References

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Editing: Quantum computing