Quantum Computing

A classical computer stores information in bits — 0 or 1. A quantum computer stores information in qubits, which can be in a superposition of 0 and 1 simultaneously. The power isn’t that a qubit is “both at once” in any naive sense — it’s that you can process an exponentially large space of possibilities in parallel and then extract answers via interference, amplifying correct paths and canceling wrong ones. When this works, certain problems that would take a classical computer the age of the universe can be solved in minutes.

When it works. The catch is that quantum states are extraordinarily fragile. The slightest interaction with the environment destroys the superposition — a process called decoherence. Building a useful quantum computer means fighting thermodynamics at every scale.

Core Concepts

Superposition

A qubit can exist in a linear combination of |0⟩ and |1⟩: |ψ⟩ = α|0⟩ + β|1⟩. The coefficients α and β are complex numbers; |α|² + |β|² = 1. Measurement collapses the state to 0 (probability |α|²) or 1 (probability |β|²). Before measurement, the qubit is in superposition — it has probability amplitudes, not definite values.

Entanglement

Two qubits can be entangled such that measuring one instantly determines the other’s state, regardless of distance. A two-qubit entangled state cannot be described as two independent qubits — it requires a joint description. Entanglement is the resource that allows quantum computers to maintain correlations across many qubits simultaneously, enabling the parallel processing that classical systems can’t replicate.

Interference

Quantum algorithms are sequences of quantum gates that manipulate probability amplitudes. Correct answers get amplified (constructive interference); wrong answers cancel (destructive interference). The art of quantum algorithm design is engineering interference to concentrate probability mass on correct solutions. This is why quantum speedup isn’t automatic — most problems don’t have this structure.

Decoherence and Error Correction

Any interaction with the environment collapses quantum states. At room temperature, qubits decohere in nanoseconds. Current superconducting quantum computers operate near absolute zero (15 millikelvin — colder than deep space). Even so, qubit errors occur with every gate operation. Quantum error correction encodes one logical qubit across many physical qubits so that errors can be detected and corrected without measuring (and thereby destroying) the logical state. See concept-quantum-error-correction.

Hardware Landscape (2025–2026)

Google Willow (105 qubits)

The most publicized quantum result of late 2024/2025. Willow completed a benchmark calculation in 5 minutes that would take a classical supercomputer 10²⁵ years — 10 billion times longer than the age of the universe. This is a quantum supremacy demonstration, not a practical application.

More significant: Google’s Quantum Echoes algorithm (published in Nature, 2025) achieved verifiable quantum advantage — 13,000× faster than classical on a repeated algorithm that can be run on other quantum platforms, confirming it’s not an artifact of the benchmark. Google claims a path to practical applications within 5 years from this result.

Key Willow advance: error rates improve as the system scales — the more qubits used for error correction, the lower the logical error rate. This is the first strong experimental evidence that quantum error correction can break even and then dominate at scale.

IBM (Nighthawk + roadmap)

IBM Nighthawk (delivered end of 2025): 120 qubits with 218 next-generation tunable couplers, allowing 30% more circuit complexity than the prior generation. IBM partnered with RIKEN to use the IBM Quantum Heron processor alongside the Fugaku supercomputer to simulate molecules beyond the ability of classical computers alone (June 2025, “utility scale” — first time IBM used that phrase).

IBM’s updated roadmap (June 2025): fault-tolerant quantum computer by 2029. Quantum advantage (industry consensus) expected before end of 2026.

Quantinuum Helios (trapped ion)

Launched commercially November 2025. Claims to be the most accurate commercial quantum system available. Early testers include SoftBank and JPMorgan Chase, who ran “commercially relevant research.” Trapped-ion systems (like Quantinuum and IonQ) have lower qubit counts than superconducting systems but dramatically higher gate fidelity.

IonQ / Ansys — First Practical Advantage

March 2025: IonQ and Ansys ran a medical device simulation on IonQ’s 36-qubit computer that outperformed classical high-performance computing by 12 percent — one of the first documented cases of quantum computing delivering practical advantage in a real-world application. Small but not synthetic.

Fujitsu / RIKEN — 256 Qubits

April 2025: 256-qubit superconducting quantum computer — four times the size of their 2023 system. Plans for a 1,000-qubit machine in 2026.

Microsoft Majorana 1 and Amazon Ocelot (2025)

Both Microsoft and Amazon announced new quantum chips in 2025. Microsoft’s Majorana 1 uses topological qubits — a fundamentally different approach that, if it works at scale, would provide inherently more stable qubits (error rates reduce without exponential overhead). Amazon Ocelot is a superconducting approach with novel error-correction architecture.

Error Correction Progress — “A Tsunami”

2025 saw what one researcher called “a tsunami” of quantum error correction progress:

• 120 peer-reviewed papers in the first 10 months of 2025, up from 36 in all of 2024 — a >3× increase
• Error rates reached record lows of 0.000015% per gate operation
• QuEra (Harvard-adjacent startup) published algorithmic fault tolerance techniques that reduce QEC overhead by up to 100×, potentially making fault-tolerant quantum computing practical years earlier than roadmaps assumed

Error correction is the central bottleneck. A 1,000-physical-qubit machine with high error rates has less computational utility than a 100-qubit machine with very low error rates.

What Quantum Computers Can Actually Do

Yes — Clear Quantum Speedup

• Molecular simulation: Quantum mechanics is the right tool for simulating quantum mechanics. Simulating electron configurations of molecules (for drug discovery, materials design, catalyst optimization) maps naturally onto quantum hardware. IBM/RIKEN demonstrated this at utility scale June 2025.
• Integer factoring (Shor’s algorithm): Exponential speedup over classical. Cracks RSA encryption. Not yet demonstrated at the scale needed to break current key lengths, but the algorithmic proof is complete.
• Search (Grover’s algorithm): Quadratic speedup over classical brute-force search. Useful but less dramatic than Shor.
• Quantum key distribution: Quantum communication, not computation — unbreakable encryption keys; interception is detectable via quantum no-cloning theorem.

Not Yet — Needs Error Correction Scale

• Cracking current RSA-2048 encryption would require ~4,000 logical qubits, which translates to ~4 million physical qubits with current error rates. We have ~1,000 physical qubits. This is the “harvest now, decrypt later” threat: nation-states may be archiving encrypted data today to decrypt when quantum computers reach scale.
• Large-scale drug discovery optimization
• Full financial portfolio optimization

No — Not Helpful

• Running classical algorithms faster (quantum computers are slower than classical for classical tasks)
• Machine learning training (marginal benefit at best for current ML paradigms)
• General-purpose computation

Cryptography Implications

Threat: Shor’s algorithm factors large integers exponentially faster than classical methods. RSA and elliptic-curve cryptography (ECC) — the foundations of TLS, SSH, and almost all modern encryption — are vulnerable once fault-tolerant quantum computers exist at scale. Timeline uncertainty spans from 5 to 20+ years.

Response — Post-Quantum Cryptography (PQC): NIST standardized its first post-quantum cryptographic algorithms in 2024: CRYSTALS-Kyber (key encapsulation), CRYSTALS-Dilithium (signatures), and FALCON. These are lattice-based problems believed to be hard for both classical and quantum computers. Migration has begun across government and critical infrastructure.

Quantum advantage for defense: Quantum key distribution (QKD) creates provably secure channels — any interception disturbs the quantum states, making eavesdropping detectable in principle.

Investment and Market (2025)

• Equity funding: **$3.77billion\ast \ast infirst9monthsof2025(vs$1.3B in all of 2024 — nearly 3× annualized increase)
• Government investment: **$10billion\ast \ast globallybyApril2025(vs$1.8B in all of 2024)
• The commercialization phase has accelerated dramatically — SoftBank, JPMorgan, Airbus, BASF, and pharmaceutical companies are running early workloads

The Benchmark Controversy

Google Willow’s 10²⁵-year benchmark solves a deliberately constructed mathematical problem (random circuit sampling) optimized to be hard for classical computers and easy for quantum ones. Critics note it has no practical use. Google acknowledges this, but argues it demonstrates two things: (1) quantum processors can maintain coherence at this scale; (2) error rates improve with scaling. The Quantum Echoes verifiable advantage (2025) is a more robust result because it’s transferable to other platforms.

This connects to a deep question: what counts as solving a problem? Quantum computers excel on problems with quantum structure; most real-world problems don’t obviously have that structure. The killer app has not yet materialized.

Confidence Levels

• Quantum speedup on molecular simulation: established (IBM/RIKEN utility-scale demonstration, June 2025)
• Practical quantum advantage over HPC: emerging (IonQ/Ansys 12% improvement, March 2025)
• Cracking RSA before 2030: speculative (physical qubit counts still orders of magnitude short)
• Fault-tolerant quantum computing by 2029: emerging (IBM roadmap; depends on QEC scaling progress)
• Quantum computing transforming drug discovery: theoretical (clear pathway; not yet demonstrated)

See Also

• concept-quantum-error-correction — the core technical barrier; 2025 saw 3× acceleration in papers
• concept-quantum-entanglement — the resource that makes quantum speedup possible; also why FTL communication is impossible
• concept-quantum-measurement-problem — why does measurement collapse the wavefunction? The deepest conceptual puzzle in quantum mechanics, distinct from quantum computing
• concept-holographic-error-correction — quantum error correction has deep connections to the holographic principle; surface codes are related to AdS/CFT
• concept-halting-problem — what problems are in principle unsolvable? Quantum computing expands the tractable set but not the computable set; Turing undecidability remains
• concept-godel-incompleteness — the same structure: there are truths that cannot be proven; quantum computing addresses complexity but not incompleteness
• concept-aging-telomeres — molecular simulation on quantum hardware may accelerate telomere biology research; quantum drug discovery is the most credible near-term medical application

Cross-Realm Surprise

Google Willow’s benchmark result — 5 minutes vs. 10²⁵ years — is not a useful computation. It was engineered to be hard for classical computers. This is the same structure as concept-halting-problem: Turing constructed an artificial problem (self-referential halting) to prove a fundamental limit. In both cases, the constructed problem reveals something deep about the substrate: Turing’s about the limits of computation; Willow’s about the nature of quantum resources. The questions “what can this machine do?” and “what is this machine doing?” are not the same question — and in both quantum computing and computability theory, the gap between them has shaped the field.