Software = projected resource estimates for a target application.
Hardware = metrics measured on a physical device. Papers can appear on both tabs.
About & methodology →
Cost Metric
Toffoli
Number of Toffoli (CCX) gates — the dominant fault-tolerant cost in most estimates
Pauli rotations
Number of arbitrary-angle Pauli rotations — used by Trotter-based estimates
Active volume
Spacetime blocks in a photonic fusion-based architecture
These units are not interconvertible — only compare Cost Count and
Spacetime Volume between rows that share the same Cost Metric.
Quantum Computing Benchmarks
Quantum Software — resource estimates from published papers. Click any blue value to open the source PDF with the data highlighted.
How to read this table
Every row answers the same question: what size quantum computer would it take to
break this encryption or simulate this molecule? Compare answers with
Logical Qubits (how wide a machine the algorithm needs) and
Cost Count (how deep — how many operations it has to get through). Before
trusting Physical Qubits or Runtime, check
Assumed Phys. Error Rate / QEC Code: those headline numbers depend entirely
on each paper's assumptions, and rows with different assumptions aren't comparable.
Blue values are cited — click one to open the paper at the highlighted sentence. Orange
values are derived by us (hover for the formula). Greyed rows have been superseded by newer
papers. Any ⓘ gives a column's definition.
Full methodology →
Cited — click to open PDF Calculated — derived from paper n.r. — not reported
Tip: Blue underlined values link directly to the highlighted PDF page.
Sort columns by clicking headers.
Sharing: Zip this file + the pdfs/ folder — links work on any machine.
Gate Type
None
No logical qubits demonstrated — pre-fault-tolerant / utility regime
Memory
Logical qubit storage: QEC rounds applied, no logical gate operations
Logical Cliffords
Fault-tolerant Clifford gates (H, CNOT, S) — not universal alone
Universal gate set
Includes a non-Clifford gate (CCZ or T) enabling universal fault-tolerant computation
Check QEC Mode alongside: the same Gate Type is a stronger claim under
active error correction than under detection/post-selection.
QEC Mode
Detection
Errors are flagged via syndromes and flagged runs are discarded (post-selection) — no active correction
Correction
Errors are actively corrected via a decoder; results are kept, not discarded
None
No encoded qubits — physical-qubit operation only
Detection-based logical qubit counts are not directly comparable to
corrected ones: post-selection discards shots and does not scale to deep circuits.
Below Threshold
Yes
Logical error rate demonstrably decreases as code distance grows
Partial
Distance scaling shown only for some operations or bases
No
No distance-scaling demonstration
The quantitative version is the Suppression Factor Λ — the factor by
which logical error falls per +2 code distance (Λ > 1 ⇔ below threshold).
Quantum Hardware
Physical quantum systems — resource metrics from published papers. Click any blue value to open the source PDF.
How to read this table
Every row is one real machine's best published result. Judge a machine by Gate
Type and QEC Mode together: "Universal gate set" under Correction
(errors found and fixed) is a far stronger claim than under Detection (bad
runs thrown away — which makes large logical-qubit counts cheap).
Logical Error Rate is how good it is today; Suppression Factor
Λ is whether it gets better as it grows — the property the whole field hinges on.
Physical Qubits is raw size — the number headlines quote, and the least
meaningful on its own: 105 physical qubits protecting one logical qubit well beats 97
protecting seventy thinly.
Three frontiers are currently held by different machines: largest encoded computation
(Detection), largest error-corrected computation, and proven error suppression at scale.
Blue values open the paper at the highlighted sentence; any ⓘ gives a column's definition.
Full methodology →
Tip: Blue underlined values link directly to the highlighted PDF page.
Sort columns by clicking headers. Cells without PDF links are from papers without an arXiv preprint.
About this benchmark
Why the tables look the way they do, and how to read them honestly.
What this is
This site tracks two questions side by side. Quantum Software: what would it
take for a quantum computer to break real cryptography or simulate industrially important
molecules? Those answers come from resource-estimate papers — careful paper-and-pencil
engineering studies of algorithms nobody can run yet. Quantum Hardware: how far
along are real machines? Those answers come from lab demonstrations. Every number on both tabs
is traceable to a specific sentence in a published paper.
Why two tabs
Estimates and demonstrations are different kinds of claims and should never share a table.
A software row says "a machine with these specs could do this." A hardware row says
"this machine did this." The same paper can appear on both tabs when it does both.
The distance between the two tabs is the honest state of quantum computing.
Why these columns
Each column answers one question. On the Software tab:
Width — Logical Qubits. How big a machine (in error-protected qubits) the
algorithm needs.
Depth — Cost Count & Cost Metric. How many operations the computation
must survive. The metric names the unit — Toffoli gates, Pauli rotations, and active volume are
not interchangeable, so only compare counts within one metric.
Spacetime Volume. Width × depth. Exposes the common trade where a paper
cuts qubits by paying more gates — a smaller machine isn't automatically a cheaper computation.
The fine print — Assumed Phys. Error Rate & QEC Code. Physical Qubits
and Runtime depend entirely on these assumptions. Two rows with different assumptions are
answering different questions; sorting by Physical Qubits across them is a category error.
On the Hardware tab:
Capability — Gate Type × QEC Mode, read together. Gate Type says which
logical operations ran; QEC Mode says how protected they were. Correction means errors
were found and fixed. Detection means bad runs were simply thrown away — which makes
big logical-qubit counts cheap, but stops working as circuits grow. The same Gate Type is a far
stronger claim under Correction.
Quality — Logical Error Rate. How often an encoded operation fails today.
Trajectory — Suppression Factor Λ and Below Threshold. Whether quality
improves as the code grows. This is the property the entire field depends on: without
it, adding qubits makes things worse, not better.
Scale — Physical Qubits. Raw size. Meaningful only alongside the other
three — 105 physical qubits protecting one logical qubit well is further ahead than 97
protecting seventy thinly.
How the evidence works
Blue values are cited. Click one and the
source PDF opens at the exact page, with the supporting sentence highlighted in yellow.
Orange values are calculated by us from
cited numbers — hover to see the formula and inputs. n.r. means the paper doesn't
report it; we never guess or interpolate. Dates are arXiv v1 submission dates. When a newer
paper supersedes an estimate, the old row is greyed and linked — never deleted, so the record
of progress stays visible.
The current picture
The frontier software estimate needs 835 logical qubits to break
256-bit elliptic-curve cryptography — and roughly a billion operations through them, each
failing less than one time in a billion. The largest number of logical qubits that has ever run
a universal gate set under real error correction: 1. The best
demonstrated logical error rates are about 10⁻⁴–10⁻⁵ per operation; the estimates assume
10⁻⁹ or better. That is the gap, measured — a few thousand-fold in size, and about five orders
of magnitude in quality. (These numbers are computed from the tables and update automatically.)
How it stays current
An automated reviewer sweeps new papers weekly against a written bar: only results that move
a frontier cell get added — a new capability record, a new below-threshold demonstration, a
lower resource estimate. Incremental results are deliberately skipped. Every addition carries
the same evidence standard: no verbatim sentence in the paper, no number in the table.