Quantum Computing

error-corrected quantum computers with far fewer qubits, and where the field stands

Quantum computers make errors constantly, so a machine that runs long, useful programs has to correct its own mistakes as it computes. The leading approach is expensive: each reliable logical qubit is built from hundreds to thousands of noisy physical qubits. Our group designs error-correcting codes that store many logical qubits in far fewer physical ones, and works out how to compute with them.

28 times fewer qubits at the same code distance

Our [[90,21,11]] code: 90 data qubits hold 21 logical qubits.

Surface code at the same distance 11: one 11 × 11 patch per logical qubit, 2,541 data qubits in all.

Data qubits only: each design needs roughly as many extra qubits again to measure its checks. A code of distance d can correct any (d − 1)/2 errors, rounded down. Distance is a first measure of protection; the full comparison under realistic noise is in the papers.

There is a catch. Packed this tightly, logical qubits overlap on the same physical qubits, so acting on one without disturbing the others becomes the hard part. Much of our recent work is about that catch.

How many qubits does a useful quantum computer need?

The field’s standard yardstick is factoring a 2048-bit RSA number with Shor’s algorithm. Published estimates have fallen from about a billion physical qubits in 2012 to under 100,000 today, or about 13,000 for a machine willing to run for decades. The two most recent drops, both in 2026, came from replacing the surface code with high-rate quantum LDPC codes, the family of codes we design.

Physical qubits needed to factor a 2048-bit RSA number, by year of the estimate

surface codehigh-rate qLDPC codeshardware that exists today

Sources and assumptions
Year Qubits Runtime Code Paper
2012 about 1 billion about a day surface Fowler et al.
2019 20 million 8 hours surface Gidney & Ekerå
2025 under 1 million under a week surface Gidney
2026 under 100,000 about a month qLDPC Webster et al. (Iceberg Quantum)
2026 about 13,000 decades at 1 ms cycles; about 100 days with ~100,000 atoms qLDPC Cain et al. (Oratomic, Caltech)

All are designs on paper. They assume physical error rates near 0.1% and differ in what they assume about connectivity and speed: the superconducting-style designs assume 1 µs error-correction cycles, while Cain et al. assume 1 ms cycles for atoms, which is why their smallest design runs for decades. The dashed line marks 6,100 atoms held in one array (Caltech, 2025), held but not yet used for computation.

These are designs on paper: no machine this large exists yet, and runtimes range from hours to decades. Still, the trend is why high-rate codes have moved from theory papers into company roadmaps.

Inside a fault-tolerant quantum computer

A fault-tolerant quantum computer is several machines working together. The blueprint shows the main parts of a design built on high-rate codes, how far the field has come on each, and what is still open. Parts where our group contributes are tagged.

CompilerTurns a program into a schedule of logical operations. simulated at full scaleour work MemoryStores logical qubits in high-rate qLDPC code blocks. shown on small devicesour work Logic unitMeasures, entangles and teleports logical qubits. simulated at full scaleour work Magic-state factorySupplies the magic states that make the machine universal. shown on small devicesour work DecoderReads the check results and infers corrections, in real time. shown on small devices Physical qubits and connectivityThe qubits themselves, and the links that let distant qubits interact. shown on small devicesour work FoundationsTheory of what is possible: thresholds, limits and overheads. theoryour work

Bars fill in four steps: proposed, simulated at full scale, shown on small devices, running at useful scale. Select a part to see who is filling it in and what is still open. Status as of October 2026.

Compiler

Simulated at full scale. Full designs and resource estimates exist; compilers for qLDPC machines are just appearing.

Decides which logical qubits meet, in what order, and when to call for magic states, so that a program runs in as little time and space as possible.

Progress across the field

Open problems

  • Compile real programs onto high-rate code blocks: which logical qubits share a block, and when they move.
  • Report qubits and runtime together, under common assumptions, so that designs can be compared.
  • Find useful applications beyond factoring that fit early fault-tolerant machines.

Our workWith support from Microsoft's Quantum Pioneers Program, we are building on logical spectroscopy toward hardware-aware compilation for qLDPC codes. Details under “Logical operations”

Memory

Shown on small devices. Small qLDPC codes run on superconducting and trapped-ion hardware; no large qLDPC memory exists yet.

Holds most logical qubits most of the time, correcting errors every cycle. High-rate codes make it the cheapest part of the machine per logical qubit.

Progress across the field

Open problems

  • Find the best codes at realistic sizes, where rate, distance, check weight and block size pull against each other.
  • Certify the distance of large codes, a computationally hard problem in general.
  • Keep the full distance during measurement circuits, and cope with atom loss and leakage.
  • Fit long-range checks onto chips and atom arrays without slowing the cycle.

Our workDesign rules for compact ultra-high-rate codes, codes with a complete basis of light logical operators, and families of codes built by lifting. Details under “Error-correcting codes”

Logic unit

Simulated at full scale. Logic on hardware so far uses surface codes or small codes.

Carries out logical operations, mostly by code surgery: temporarily attaching extra qubits that measure chosen logical operators. In a high-rate block it must reach one logical qubit without disturbing the rest.

Progress across the field

Open problems

  • Measure any chosen logical qubits cheaply, quickly and in parallel. Surgery costs grow with the weight of the logical operator, and each measurement takes about d rounds.
  • Verify that large gadgets are fault tolerant; estimating their fault distance becomes prohibitive for big blocks.
  • Find fast logic for qLDPC codes: transversal, single-shot or symmetry-based gates.

Our workLogical spectroscopy gives every logical qubit a label and an explicit operator; frame width measures how light a complete set of them can be; lifting carries surgery gadgets across code families. Details under “Logical operations”

Magic-state factory

Shown on small devices. Logical distillation and cultivation have run on neutral-atom and superconducting hardware.

Easy operations alone cannot run every algorithm. The factory prepares special magic states and feeds the logic unit one for each hard gate, such as a T gate.

Progress across the field

Open problems

  • Make magic states as fast as a high-rate processor consumes them, without a factory larger than the memory.
  • Get them into qLDPC blocks efficiently and in parallel.
  • Turn constant-overhead distillation and transversal non-Clifford gates for qLDPC codes from theory into practical protocols.

Our workCCZ state cultivation makes the magic states behind Toffoli gates directly inside high-rate qLDPC codes, at lower cost per state than converting cultivated T states. Details under “Magic states and universal computation”

Decoder

Shown on small devices. Real-time decoding has run on hardware for surface codes; qLDPC decoders look fast enough on paper.

A classical co-processor that receives check results every cycle and infers which errors occurred. It has to keep pace with the machine, or the computation stalls.

Progress across the field

Open problems

  • Decode during logical operations, not just storage, faster than the machine's reaction time.
  • Scale to tens of thousands of qubits on practical classical hardware.
  • Handle realistic noise: correlated errors, leakage and atom loss.

Physical qubits and connectivity

Shown on small devices. Hundreds of qubits run below threshold, thousands can be held, and long-range links work on small chips.

High-rate codes need checks that connect distant qubits. Atom arrays move atoms, superconducting chips route long couplers through extra layers, and ion traps shuttle ions between zones.

Progress across the field

Open problems

  • Grow from hundreds to tens of thousands of qubits while keeping error rates near 0.1% or lower.
  • Make long-range connectivity fast and reliable: atom-array cycles of milliseconds must shrink, and multilayer chips must be built at scale.
  • Understand noise beyond simple models, including correlated bursts and leakage.

Our workWith Jacob Covey's group, two qubits stored in each ytterbium atom; and Floquet codes that protect qubits with simple repeated measurements. Details under “Hardware and dynamics”

Foundations

Why fault tolerance works at all, how much noise each code can survive in principle, and how small the overhead can be.

Progress across the field

Open problems

  • Pin down thresholds and decodability under realistic circuit-level and coherent noise.
  • Close the gap between optimal decoding and what fast decoders achieve.
  • Define code families with a well-defined large-size limit for algebraic qLDPC codes.

Our workExact coherent information for noisy codes, a hierarchy of Rényi measures, and new mixed-state phases, which together characterize the best any decoder could do. Details under “Noise and thresholds”

Our work in detail

Select a heading to expand it, or show all.

Error-correcting codes

The surface code stores one logical qubit per patch, and each patch grows with the square of the distance. High-rate quantum LDPC codes break that pattern: each check still involves only a handful of qubits, but checks can reach across the block, so one block can hold dozens or hundreds of logical qubits. The hard part is that block size, encoding rate, distance and check weight all pull against each other.

  • Design principles for ultra-high-rate quantum codes (2026, with Koki Okada, Nishad Maskara, Kenta Kasai and Hengyun Zhou) turns these trade-offs into design rules. One finding: at a realistic 0.1% physical error rate, heavier checks are often worth it, because they buy larger distance in a small block. The resulting codes, such as [[90,21,11]], [[140,31,15]] and [[200,43,20]], need only a few data qubits per logical qubit.
  • Designing group-valued codes (2026) builds codes such as [[1088,128,22]] and [[1024,256,24]] with a complete, regular basis of logical operators about as light as the distance allows, and shows why this is impossible for a common class of codes built on odd-order groups.
  • Lifting lifted-product codes (2026, with Yuta Hirasaki) grows a code into a family that keeps its local structure. It finds codes with better parameters than previously reported, and takes a first step toward code families with a well-defined large-size limit.

Logical operations

Packing many logical qubits into one block creates a new problem. To compute, you need to know where each logical qubit lives, how it is labeled, and how to act on it without disturbing its neighbors. For Abelian lifted-product codes, which include many of the best high-rate designs, the row-reduction shortcut that works for simpler product codes can fail.

  • Logical spectroscopy (2026) fixes this for Abelian lifted-product codes. Like a prism splitting light into colors, it splits the code’s algebra into small independent pieces, solves each one, and reassembles a complete, labeled set of logical operators. It has been applied to codes with up to 5,000 physical qubits.
  • Full regular low-weight bases (2026) introduces the frame width: the smallest weight limit that still allows a complete canonical set of logical operators. Lighter operators make logical operations cheaper, so frame width belongs next to distance in resource estimates.
  • Lifting lifted-product codes (2026, with Ph.D. student Yuta Hirasaki) shows that surgery gadgets, the standard way to measure logical qubits, carry over across a family of codes, sometimes at lower cost.

Next, with support from a Microsoft Quantum Pioneers award, we are building on logical spectroscopy toward hardware-aware compilation for qLDPC codes.

Magic states and universal computation

The operations that come cheaply in an error-correcting code, the Clifford gates, cannot run every algorithm on their own. A universal machine also needs non-Clifford gates such as the T gate or the three-qubit Toffoli gate, which are usually made by preparing special magic states and consuming one per gate. The cost of many of the most valuable algorithms, from Shor’s factoring to simulating molecules, is counted in Toffoli gates, so cheaper Toffoli resources make the whole computation cheaper.

  • Logical CCZ state cultivation (2026, with Ph.D. student Yuta Hirasaki) makes CCZ states, the magic states behind Toffoli gates, directly inside high-rate qLDPC codes. Bivariate tricycle codes, which have CCZ gates built in, prepare two CCZ states at once, and lifting moves them into bivariate bicycle memories with larger distance. In circuit-level simulations with neutral-atom-like noise, output errors reach about 2 × 10−5 while keeping 22% of attempts, or 4 × 10−7 while keeping 9%, and the smallest factory costs less per CCZ state than cultivating T states and converting them.

Hardware and dynamics

Codes have to run on real machines, and real machines suggest new codes.

  • Two qubits per atom (npj Quantum Information 2024): with Jacob Covey’s group at Illinois, an architecture that stores two qubits in each ytterbium-171 atom, so error correction needs fewer two-atom gates.
  • Stable Floquet codes (Phys. Rev. Lett. 2024): Floquet codes protect qubits with a repeating cycle of simple two-qubit measurements. We showed that the dynamical topological order they create survives perturbations.
  • Decoding measurement-prepared states (2022): measurements can create long-range entangled states quickly, and the outcomes can be decoded by classical computation instead of repeating the experiment exponentially many times.

Noise and thresholds

Code families typically have an error threshold: below a certain noise level, bigger codes protect better; above it, no decoder can recover the information. We study thresholds as phase transitions, like water freezing, using information-theoretic quantities that do not depend on any particular decoder. This connects to our broader work on mixed-state phases of matter.

Milestones

Selected results in theory, architecture and experiment since 1980, newest first, with our group’s work marked.

2026

  1. Oct

    DARPA's quantum benchmark enters final stage Experiment

    Atom Computing, Diraq, IBM and IonQ join Microsoft and PsiQuantum in Stage C of DARPA's Quantum Benchmarking Initiative, where government experts test whether their machines can reach utility scale by 2033.

  2. Oct

    Light logical operators, by design Our group

    Codes whose complete basis of logical operators is about as light as the distance allows (exactly as light for [[1088,128,22]]), and a new code parameter, the frame width, that measures this.

  3. Oct

    Microsoft Quantum Pioneers award Our group

    One of five Software Track winners, for the project “From Logical Spectroscopy to Hardware-Aware qLDPC Compilation.”

  4. Oct

    Logical CCZ state cultivation Our group

    Magic states for Toffoli gates, the workhorse of quantum arithmetic, made directly inside high-rate qLDPC codes at lower cost than converting cultivated T states. With Ph.D. student Y. Hirasaki.

  5. Sep

    Rényi coherent information, put in order Our group

    Proves that, for independent Pauli noise, the easy-to-compute Rényi measures of decodability form an ordered hierarchy, and gives them an operational meaning. With A. Vijay and L. Colmenarez.

  6. Sep

    Design principles for ultra-high-rate codes Our group

    Rules for trading off rate, distance and check weight, leading to compact codes such as [[90,21,11]] and [[200,43,20]]. With K. Okada, N. Maskara, K. Kasai and H. Zhou.

  7. Aug

    IBM joins its first cryogenic modules Experiment

    IBM cools two linked modules as one system, with processors to be installed later in 2026, a step toward Starling, its planned 2029 fault-tolerant machine built on qLDPC codes.

  8. Aug

    Error correction at chiral topological edges Our group

    The gapless edges of two-dimensional topological phases act as approximate error-correcting codes. With Y. Song, Z. Liu, Z. Wang and B. Shi.

  9. Jul

    High-rate qLDPC processors Theory

    Caltech and Oratomic's mitten codes (rate 20%, check weight 9) come with a symmetric logical basis, so a few reusable gadgets reach every logical qubit.

  10. Jul

    Logical spectroscopy Our group

    A complete, labeled set of logical operators for Abelian lifted-product codes, found by splitting the code's algebra into small finite-field pieces.

  11. Jul

    QID 2026: qLDPC Theory and Application Our group

    Co-organized this workshop at KIAS, Seoul, with I. H. Kim and H. Kwon. Recorded talks are online.

  12. Jul

    Lifting lifted-product codes Our group

    Grows codes into families that keep their local structure, improving code parameters and carrying surgery gadgets across a family. With Ph.D. student Y. Hirasaki.

  13. Jun

    qLDPC codes reach breakeven Experiment

    IonQ runs nine codes on one trapped-ion device; some qLDPC runs match or slightly beat the lifetime of the physical qubits.

  14. Jun

    Lattice surgery on superconducting chips Experiment

    Zhejiang University entangles two distance-3 surface-code logical qubits by lattice surgery on a superconducting chip; weeks later USTC shows a logical CNOT and other Clifford gates without postselection.

  15. Apr

    Rates above one half for atom arrays Theory

    QuEra, Harvard and MIT adapt Kasai's ultra-high-rate codes, such as 580 logical qubits in 1,152 physical ones, to the way atom arrays move.

  16. Mar

    Shor's algorithm with about 10,000 atoms Theory

    Oratomic and Caltech use high-rate codes to bring cryptographically relevant Shor's algorithm down to about 10,000 atomic qubits, at the cost of long runtimes.

  17. Feb

    RSA-2048 with under 100,000 qubits Theory

    Iceberg Quantum's Pinnacle architecture swaps the surface code for qLDPC codes and cuts the estimate about tenfold, with a runtime of about a month.

  18. Feb

    Dozens of logical qubits beyond break-even Experiment

    Quantinuum computes with 48 error-corrected and up to 94 error-detected logical qubits on its 98-qubit Helios, beating unencoded circuits, though many runs rely on discarding flagged results.

2025

  1. Dec

    Magic states cultivated on hardware Experiment

    Magic state cultivation, a cheap way to make the extra ingredient that universal logic needs, is tested on a superconducting processor.

  2. Dec

    A second chip below threshold Experiment

    USTC's Zuchongzhi 3.2 runs a distance-7 surface code below threshold, with errors falling 1.4-fold per step, using microwave-only leakage control; it is the second superconducting team to do so.

  3. Dec

    Information critical phases Our group

    In noisy ZN toric codes with N > 4, a whole intermediate phase in which a fraction of the stored information survives. With Ph.D. student A. Vijay.

  4. Jun

    IBM's road to Starling Theory

    A modular design built on bivariate bicycle codes, with a belief-propagation decoder fast enough for real time; the target is 200 logical qubits by 2029.

  5. Jun

    A fault-tolerant neutral-atom architecture Experiment

    A Harvard-led team combines the key elements of universal fault-tolerant computing on up to 448 atoms, with error correction running 2.14 times below threshold.

  6. Jun

    Quantum Echoes, a contested advantage claim Experiment

    Google's Willow measures an echo-like signal (out-of-time-order correlators) on up to 103 qubits; Google estimates a 65-qubit case would take a supercomputer 13,000 times longer. Some experts question the “verifiable advantage” label.

  7. May

    RSA-2048 with under a million qubits Theory

    Gidney cuts the surface-code estimate twentyfold with better arithmetic, yoked codes and magic state cultivation, though the run takes under a week instead of 8 hours.

  8. May

    qLDPC codes on a superconducting chip Experiment

    Zhejiang University runs two qLDPC codes, including a bivariate bicycle code, on a processor with long-range couplers; logical errors, about 8–9% per cycle, are still high.

2024

  1. Dec

    Logical magic state distillation Experiment

    QuEra distills magic states encoded in color codes on a neutral-atom computer, a first on any platform.

  2. Dec

    Codes near the hashing bound Theory

    Komoto and Kasai find qLDPC codes with rates from one half to three quarters that approach the hashing bound, a long-standing benchmark, with decoding cost linear in size (in a simplified noise model).

  3. Oct

    Error threshold of SYK codes Our group

    Black-hole-inspired SYK models store information like a code; under parity-preserving noise, their threshold coincides with strong-to-weak symmetry breaking (Phys. Rev. B 2026). With J. Kim and E. Altman.

  4. Sep

    Magic state cultivation Theory

    Gidney, Shutty and Jones grow magic states in place at a cost close to that of an ordinary two-qubit gate.

  5. Sep

    Cat qubits in a repetition code Experiment

    AWS links bit-flip-resistant “cat” qubits into a repetition code, and going from distance 3 to 5 lowers the logical error slightly; the chip was announced as Ocelot in 2025.

  6. Aug

    Below threshold Experiment

    On Google's Willow chip, each step up in surface-code size cuts the logical error rate by a factor of about two, up to distance 7.

  7. Jul

    Surgery for qLDPC codes Theory

    Better ways to measure logical qubits inside high-rate codes, such as improved surgery and gauging logical operators, bring computation on them within reach.

  8. Jul

    Coherent information for all CSS codes Our group

    Extends the exact calculation to general CSS codes under incoherent Pauli noise, showing the optimal decoder reaches the fundamental threshold (Phys. Rev. A 2025). With R. Niwa.

  9. Jun

    Faster logic with transversal gates Theory

    QuEra and Harvard researchers show that logical gates can be followed by a few rounds of checks instead of d rounds, speeding up computation.

  10. Apr

    Logical qubits beat physical ones Experiment

    Microsoft and Quantinuum run trapped-ion logical qubits with error rates up to 800 times below physical ones, depending on how many flagged runs are discarded; 12 logical qubits followed in September.

  11. Mar

    6,100 atomic qubits in one array Experiment

    Caltech holds over 6,100 coherent atoms in a 12,000-site optical tweezer array (storage, not yet computation).

  12. Feb

    Two qubits in one atom Our group

    With Jacob Covey's group at Illinois, an architecture that stores two qubits in each ytterbium-171 atom and needs fewer two-atom gates (npj Quantum Information 2024).

  13. Feb

    Exact coherent information for the toric code Our group

    The first exact formula for the toric code's coherent information under noise, tying its threshold to the random-bond Ising model (Phys. Rev. Lett. 2025).

2023

  1. Dec

    48 logical qubits Experiment

    Harvard, MIT and QuEra run algorithms on up to 48 logical qubits in a reconfigurable atom array.

  2. Aug

    qLDPC codes on moving atoms Theory

    Xu et al. show that reconfigurable atom arrays can run high-rate qLDPC codes, toward constant-overhead fault tolerance.

  3. Aug

    The gross code Theory

    IBM's bivariate bicycle code stores 12 logical qubits in 288 physical qubits, about a tenth of what the surface code needs.

  4. Mar

    Stable Floquet codes Our group

    Floquet codes build protected qubits from a repeating cycle of two-qubit measurements; their dynamical topological order survives perturbations (Phys. Rev. Lett. 2024). With D. Vu, A. Lavasani and M. P. A. Fisher.

2022

  1. Nov

    Bosonic qubits pass break-even Experiment

    Yale's real-time-corrected GKP qubit in a microwave cavity lives 2.3 times longer than the system's best uncorrected qubit; a SUSTech binomial-code qubit also passes break-even.

  2. Aug

    Decoding measurement-prepared states Our group

    Long-range entangled states made by measurement can be decoded without post-selection, trading exponential repetition for polynomial classical computation.

  3. Jul

    Bigger code, fewer errors Experiment

    Google shows a distance-5 surface code slightly outperforming distance 3, the first sign of scaling.

2021

  1. Nov

    Good qLDPC codes exist Theory

    Panteleev and Kalachev build qLDPC codes whose number of logical qubits and distance both grow in proportion to size.

  2. Jul

    Floquet codes Theory

    Hastings and Haah create protected qubits from a repeating schedule of two-qubit measurements.

  3. Jul

    Real-time fault-tolerant error correction Experiment

    Honeywell (now Quantinuum) repeatedly measures, decodes and corrects errors on a seven-qubit Steane-code logical qubit in trapped ions while the computation runs.

2020

  1. Dec

    Lifted-product codes Theory

    Panteleev and Kalachev introduce lifted-product codes, the family much of our recent work builds on.

  2. Dec

    Jiuzhang: an advantage claim with light Experiment

    USTC's Jiuzhang detects up to 76 photons in Gaussian boson sampling and claims to run about 100 trillion times faster than a supercomputer simulation, the first advantage claim made with photons.

2019

  1. Oct

    Google's quantum supremacy claim Experiment

    Google's 53-qubit Sycamore samples random circuits in about 200 seconds, a task it estimated would take a supercomputer 10,000 years; in 2021 classical GPUs matched it in about 15 hours.

  2. May

    RSA-2048 with 20 million qubits Theory

    Gidney and Ekerå's surface-code estimate, with 8 hours of runtime, becomes the field's benchmark.

2018

  1. Jan

    The NISQ era Theory

    Preskill names the “noisy intermediate-scale quantum” era, separating today's error-prone devices from the fault-tolerant machines that error correction will enable.

2017

  1. Jul

    Quantum simulators pass 50 qubits Experiment

    Harvard and MIT with 51 Rydberg atoms, and Maryland with 53 trapped ions, run programmable simulators of many-body physics, in back-to-back Nature papers.

2016

  1. Jul

    Atom arrays assembled one by one Experiment

    Groups at Institut d'Optique and Harvard use movable laser tweezers to sort atoms into gap-free arrays, the foundation of today's neutral-atom quantum computers.

  2. May

    A quantum computer on the cloud Experiment

    IBM puts a five-qubit superconducting processor online as the IBM Quantum Experience, letting anyone run experiments on real quantum hardware.

  3. Feb

    Error correction reaches break-even Experiment

    Ofek, Schoelkopf and colleagues at Yale store a qubit in “cat” states of microwave light and correct it in real time, so it outlives the best uncorrected encoding in the same system.

2015

  1. Dec

    Two-qubit gates reach 99.9% Experiment

    Ion-trap groups at Oxford and NIST push two-qubit gates to about 99.9% fidelity, an error rate roughly ten times below what surface-code error correction requires.

2014

  1. Nov

    Repeated error detection on a chip Experiment

    Kelly, Martinis and colleagues at Google and UC Santa Barbara protect stored states with a repetition code of up to nine superconducting qubits; the larger code suppresses errors more.

  2. Nov

    First two-qubit gate in silicon Experiment

    Veldhorst, Dzurak and colleagues at UNSW perform a controlled-NOT between two electron spins in a silicon device much like an ordinary transistor.

  3. Mar

    A color code on seven ions Experiment

    Nigg, Blatt and colleagues at Innsbruck spread one logical qubit over seven trapped ions with the smallest color code, a topological code, and compute with it.

  4. Feb

    Gates at the surface-code threshold Experiment

    Barends, Martinis and colleagues at UC Santa Barbara reach 99.4% two-qubit gate fidelity across five superconducting qubits, good enough for surface-code error correction.

2013

  1. Oct

    Constant overhead is possible Theory

    Gottesman shows that qLDPC codes could make fault tolerance cost only a constant factor more qubits.

2012

  1. Aug

    The surface-code blueprint Theory

    Fowler et al. lay out how to build a surface-code quantum computer, and estimate about a billion qubits for RSA-2048.

  2. Feb

    Topological error correction with photons Experiment

    Pan Jian-Wei's group at USTC entangles photons into a cluster state and demonstrates topological error correction, a measurement-based relative of the surface code.

2011

  1. Nov

    Lattice surgery Theory

    Horsman, Fowler, Devitt and Van Meter compute between surface-code patches by merging and splitting their edges; this cut overhead and became the standard way to compute with surface codes.

  2. Sep

    Error correction on a superconducting chip Experiment

    Reed, Schoelkopf and colleagues at Yale run a three-qubit code on superconducting transmons, correcting single bit-flip or phase-flip errors, the first error correction on a superconducting chip.

2009

  1. Sep

    Flat codes hit a limit Theory

    Bravyi, Poulin and Terhal prove that codes with only local checks in a plane face a strict trade-off between logical qubits and distance, so beating the surface code needs long-range connections.

  2. Jul

    Atoms linked by Rydberg blockade Experiment

    Groups in Wisconsin and at Institut d'Optique near Paris use the Rydberg blockade, where one highly excited atom blocks its neighbor, to make a CNOT gate and entangle two atoms.

  3. Mar

    Hypergraph product codes Theory

    Tillich and Zémor turn any two classical LDPC codes into a quantum LDPC code with constant rate and distance growing like √n, seeding modern qLDPC constructions such as lifted-product codes.

2007

  1. Feb

    The transmon qubit Theory

    Koch, Schoelkopf, Girvin and colleagues at Yale design the transmon, a superconducting qubit insensitive to stray electric charge; it became the standard qubit of IBM, Google and others.

2006

  1. Oct

    A surface-code threshold near one percent Theory

    Raussendorf and Harrington show fault-tolerant computing with only nearest-neighbor gates on a 2D lattice, tolerating about 0.75% error per operation; this made surface-code architectures the leading plan.

  2. May

    Color codes Theory

    Bombin and Martin-Delgado introduce color codes, topological codes in which all Clifford gates act qubit by qubit, which makes many logical operations simple.

2004

  1. Dec

    Error correction with trapped ions Experiment

    Chiaverini, Wineland and colleagues at NIST use three beryllium ions to protect one qubit against spin-flip errors, the first quantum error correction with trapped ions.

  2. Jul

    Circuit QED: qubit meets photon Experiment

    Wallraff, Schoelkopf and colleagues at Yale couple a superconducting qubit strongly to a single microwave photon on a chip, the wiring and readout scheme of today's superconducting processors.

  3. Mar

    Magic state distillation Theory

    Bravyi and Kitaev show how noisy “magic” states can be purified to complete a universal set of fault-tolerant gates.

2001

  1. Dec

    Shor's algorithm factors 15 Experiment

    Vandersypen, Chuang and colleagues at IBM Almaden and Stanford use Shor's algorithm to factor 15 into 3 × 5 with nuclear spins in a custom-made molecule.

  2. Oct

    Thresholds as phase transitions Theory

    Dennis, Kitaev, Landahl and Preskill map the surface code's threshold onto a random-bond Ising model, an idea at the heart of our threshold work.

2000

  1. Oct

    Computing by measurement alone Theory

    Raussendorf and Briegel show that a computation can run as single-qubit measurements on a pre-made entangled “cluster state”, the model behind photonic fault-tolerant architectures.

  2. Aug

    A qubit inside an oscillator Theory

    Gottesman, Kitaev and Preskill encode a qubit in an oscillator, such as a microwave cavity mode, so that small shifts can be detected and corrected, founding bosonic error correction.

  3. Jun

    Quantum computing with linear optics Theory

    Knill, Laflamme and Milburn show that single photons, beam splitters and detectors suffice for scalable quantum computing when measurement results steer later steps, founding photonic quantum computing.

1999

  1. Apr

    A circuit behaves like a qubit Experiment

    Nakamura, Pashkin and Tsai at NEC make a tiny superconducting island oscillate coherently between two charge states, the first sign that an electrical circuit can serve as a qubit.

1998

  1. Nov

    The planar surface code Theory

    Bravyi and Kitaev cut the toric code down to a flat patch with boundaries; this “surface code” needs only neighboring checks on a chip and is what most hardware teams pursue.

  2. Feb

    First quantum error correction experiment Experiment

    Cory and colleagues at MIT and Los Alamos use three nuclear spins in a molecule to encode one qubit and undo phase errors on it.

  3. Jan

    First quantum algorithms on hardware Experiment

    Groups at Oxford and at IBM, Berkeley and MIT solve Deutsch's problem with nuclear spins in liquid molecules; Grover search follows in April.

1997

  1. Jul

    Topological codes Theory

    Kitaev's toric code stores information in the global topology of a lattice, where local errors cannot read or change it unless they pile up.

  2. Jan

    Qubits from single electron spins Theory

    Loss and DiVincenzo propose using the spin of one electron trapped in a semiconductor quantum dot as a qubit, with gates made by letting neighboring electrons interact.

1996

  1. Oct

    The threshold theorem Theory

    If each operation fails rarely enough, arbitrarily long quantum computations are possible (Knill, Laflamme and Zurek; Aharonov and Ben-Or; Kitaev).

  2. Aug

    Universal quantum simulators Theory

    Lloyd proves Feynman's conjecture: a quantum computer can efficiently simulate any quantum system with local interactions, still a leading use for error-corrected machines.

  3. May

    Grover's search algorithm Theory

    Grover shows how to search N unsorted items in about √N steps instead of N, a quadratic speedup that applies to a huge range of problems.

  4. Apr

    When errors can be undone Theory

    Knill and Laflamme give the exact conditions under which a code can reverse a set of errors, the test that every quantum code must pass.

  5. Apr

    Stabilizer codes Theory

    Gottesman, and independently Calderbank, Rains, Shor and Sloane, describe codes by the set of checks they satisfy, the common language of nearly all codes used today.

1995

  1. Dec

    The first quantum logic gate Experiment

    Monroe, Wineland and colleagues at NIST run a controlled-NOT, the basic two-qubit gate, on two qubits stored in a single trapped beryllium ion.

  2. Dec

    Quantum codes from classical ones Theory

    Calderbank and Shor, and independently Steane, build quantum codes from pairs of classical codes, including Steane's seven-qubit code, and show that good quantum codes exist.

  3. Oct

    The first quantum code Theory

    Shor protects one qubit from any single error by spreading it over nine.

  4. May

    Blueprint for a trapped-ion computer Theory

    Cirac and Zoller show how a row of laser-cooled ions, linked through their shared vibration, could run any quantum computation, launching experimental quantum computing.

1994

  1. Nov

    Shor's factoring algorithm Theory

    Shor shows that a quantum computer could factor large numbers and compute discrete logarithms exponentially faster than known classical methods, threatening RSA and turning quantum computing into a major field.

1985

  1. Jul

    The universal quantum computer Theory

    Deutsch defines a universal quantum computer that can simulate any physical process, and gives the first task where quantum parallelism helps.

1982

  1. Jun

    Simulating physics with quantum computers Theory

    Feynman argues that ordinary computers cannot efficiently simulate quantum physics but computers made of quantum parts could, the founding motivation of the field (from his 1981 MIT talk).

1980

  1. May

    A quantum model of a computer Theory

    Benioff describes a Turing machine that runs entirely by quantum mechanics, the first model of a computer built from quantum parts.

Key terms

Physical qubit
One quantum bit in hardware: an atom, an ion or a superconducting circuit. Each one makes errors.
Logical qubit
One qubit's worth of information spread over many physical qubits, so that errors can be detected and undone.
Code distance d
The smallest number of single-qubit errors that can change the stored information without being detected. A code of distance d corrects any (d − 1)/2 errors, rounded down.
[[n, k, d]]
Shorthand for a code that stores k logical qubits in n physical qubits at distance d. A surface-code patch is [[d², 1, d]].
Encoding rate
Logical qubits per data qubit, k/n: 1/121 for a distance-11 surface code, 21/90 for our [[90,21,11]] code.
qLDPC code
Quantum low-density parity-check code. Each check involves only a few qubits and each qubit only a few checks, but checks may connect distant qubits.
Check weight
How many qubits one check involves: 4 in the surface code, 6 to 10 in the high-rate codes on this page.
Threshold
For a family of codes, the physical error rate below which making the code bigger makes it better.
Decoder
The classical algorithm that reads the check results and infers a correction. In a real machine it has to keep up with the stream of results.
Code surgery
Measuring logical qubits by temporarily attaching extra qubits and checks to a code; a leading way to compute with qLDPC codes.
Magic state
A special resource state that, combined with the easy operations, makes a quantum computer universal.
Toffoli gate and CCZ state
The Toffoli gate flips a target qubit only when two control qubits are both 1, the basic step of quantum arithmetic. Error-corrected machines usually run it by consuming a CCZ magic state.

Get involved

Talks from QID 2026: qLDPC Theory and Application, the workshop we co-organized at KIAS in Seoul in July 2026, are on the KIAS School of Physics YouTube channel. Students and postdocs who want to work on these questions can start at the Join page.