SIA — Simplified Integrated Architecture

sia-script is the Python library of Sia Software Innovations Private Limited. It provides an offline quantum simulator, a client for the HDQS quantum server, a declarative entity module, and an ABAP-style enterprise logic interpreter, all behind short, chainable APIs.

from sia import hdqs

q = hdqs(2).h(0).cx(0, 1)
print(q.sample(1000))          # {'00': ~500, '11': ~500}

One import is all a program needs.

Contents

• Installation
• Components
• Quantum simulation: hdqs
• HDQS server client
• Entities: ntt
• Enterprise logic: els
• Optional dependencies
• Conventions
• Licensing
• Citation
• Support

Installation

pip install sia-script

Requires Python 3.9 or newer. The install brings NumPy, Requests, Matplotlib and openqasm3, so figures, animations, paper figures, worksheets and QASM work straight away. Heavier features are extras:

pip install "sia-script[torch]"     # trainable quantum layers, CUDA acceleration
pip install "sia-script[full]"      # torch and SciPy
pip install "sia-script[all]"       # everything, including Qiskit/Aer/PennyLane adapters

Components

The simulator runs entirely on your machine. Importing sia makes no network call; only the server client contacts the HDQS server, and only when you create a client.

Quantum simulation: hdqs

Chainable circuits

Every gate returns the register, so programs stay short:

from sia import hdqs

q = hdqs(3).h(0).cx(0, 1).cx(1, 2)          # GHZ state
q.show_state()                                    # amplitude table
print(q.sample(1000))                             # measurement counts
print(q.estimator("ZZI")["value"])                # <ZZI> = 1.0
print(q.resources()["depth"])                     # 3

Gates: h x y z s sdg t tdg rx ry rz p u3 cx cy cz cp crx cry crz swap ccx cswap mcx (cnot and toffoli are aliases), the cx_chain() ladder, plus barrier, reset_qubit, measure and custom unitary.

Noise

Density-matrix mode supports CPTP-verified channels:

from sia import hdqs

q = hdqs.dm(2).h(0).cx(0, 1).depolarizing(0, 0.05).amplitude_damping(1, 0.1)
print(q.purity(), q.concurrence())

noisy = hdqs(2).h(0).cx(0, 1).with_noise("depolarizing", 0.01)   # replay with noise

Channels: bit flip, phase flip, depolarizing, amplitude damping, phase damping, generalized amplitude damping, thermal relaxation, coherent over-rotation, amplitude–phase coupling, correlated two-qubit noise, and classical readout error.

Programs: replay, feed-forward, undo

The register remembers its own program, so the same object can be rerun, drawn, optimized, exported or undone:

from sia import hdqs

q = hdqs(3).h(0).cx(0, 1).ry(2, 0.4)
print(q.run(500).counts)                               # rerun as a program
print(q.copy().compose(q.inverse()).probability_of("000"))   # undo: 1.0

ff = hdqs(2).h(0).measure(0, key="m").if_x("m", 1)    # mid-circuit feed-forward
print(ff.records, ff.run(1000).counts)

measure(qubit, key="m") keeps the chain going and stores the outcome in q.records["m"]; if_x, if_z and if_gate record their condition, so run(), draw() and to_qasm3() reproduce the program exactly. Branch with these, not with a Python if. Plain measure(qubit) still returns the outcome as a string.

Large registers and simulation modes

A register too large for a full state (above the 1 GiB default budget) records its program instead of failing, and can run on the stabilizer or MPS simulator:

from sia import hdqs

print(hdqs(200).h(0).cx_chain().stabilizer().sample(5))       # 200-qubit GHZ
print(hdqs(40).h(0).cx_chain().mps().summary()["max_bond_dimension"])   # 2

For parameterized templates reused with different values, use hdqs.Circuit with hdqs.Parameter and run(bindings=...) or sweep(...).

Algorithms and protocols

from sia import hdqs

print(hdqs.grover(3, ["101"])["best"])          # '101'
print(hdqs.simon("110")["recovered"])           # '110'
print(sorted(hdqs.shor_demo(15)["factors"]))    # [3, 5]
print(hdqs.teleport()["fidelity"])              # 1.0
print(hdqs.bb84(256, eavesdrop=True)["eavesdropping_suspected"])   # True

Included: Deutsch, Deutsch–Jozsa, Bernstein–Vazirani, Grover, Simon, QFT (qft_demo), phase estimation, order finding and a small Shor demonstration, teleportation, superdense coding, VQE, QAOA, a repetition code, and the BB84, E91 and QSS protocols (educational simulations, not production key distribution). Every result can animate itself with .draw() (see Algorithm visuals).

Analysis and mitigation

Observables and Pauli sums, sampled estimates with standard errors, Trotter evolution, entropy, concurrence, negativity, mutual information, state tomography, readout-error mitigation, zero-noise extrapolation, and CRIA interference accessibility (interference_report, interference_profile, recover_interference).

Machine learning (requires [torch])

import torch
from sia import hdqs

layer = hdqs.quantum_layer(4, layers=2)                 # an ordinary torch.nn.Module
out = layer(torch.rand(8, 4, dtype=torch.float64))     # (8, 4) Pauli-Z expectations

hdqs.quantum_layer(..., diff="parameter_shift") gives hardware-style gradients instead. The underlying classes are BackpropQuantumLayer, QuantumLayer, MidCircuitQuantumLayer, QASMQuantumLayer, and CircuitQuantumLayer (any Circuit, including exact gradients through mid-circuit measurement).

Visuals: one call, letter codes

from sia import hdqs

q = hdqs(3).h(0).cx(0, 1).ry(2, 0.7).cx(1, 2)
q.draw("b")                          # Bloch spheres, shown inline or in a window
q.draw("b,a,e", "state.png")         # several views in one figure
q.draw("all", "lesson.html")         # offline interactive page with a gate-by-gate slider
q.draw("a,b", "steps.gif")           # animation over the gates
q.draw("b,q,d", "model.glb")         # 3D for Blender
q.draw("b", "bloch.3mf")             # colour 3D print, with a print report
q.draw("c,b,a", "fig.pdf", preset="paper")   # journal figure + caption
q.draw("c", "circuit.tex")           # LaTeX (quantikz)
q.export_bundle("experiment.zip")    # everything needed to publish or reproduce it
q.code()                             # the hdqs chain that rebuilds q

New to the mathematics? hdqs.cnum, hdqs.vec, hdqs.mat and hdqs.practice cover complex numbers, vectors, matrices, eigenvalues and tensor products, with practice problems (see Quantum maths).

Codes combine with commas ("b,a,e"), and several outputs can be written at once ("x.png,x.html,x.glb"). The file extension picks the output:

The e view also tests every split of the register, so a GHZ state is reported as entangled as a whole, not in pairs. In the .html page, stepping animates between states, each Bloch sphere shows its qubit's 2×2 reduced density matrix, and the density matrix can be shown as |ρ| with phase colour or as real and imaginary parts.

3D files are produced only when a 3D extension is named, so "all" never writes one by accident. The 3D views are b, q and d. q.draw("bell.png") still draws the circuit, and q.plot(...) still returns a Matplotlib figure.

3D printing

q = hdqs(2).h(0).cx(0, 1).ry(1, 0.4)
q.draw("b", "bell.3mf", diameter=60)                  # 60 mm spheres, FDM settings
q.draw("b", "bell.stl", preset="resin", wall=0.6)     # finer resin print
q.last_print_report["min_feature_mm"]

3D print report — bell.3mf  (3MF, preset fdm)
  ✓ watertight / manifold
  ✓ minimum feature: 1.2 mm  (target wall 1.2 mm)
  • size: 153 × 66 × 76.4 mm
  • volume: ≤ 32.71 cm³ (overlapping parts are merged by the slicer)
  • 34 parts, 49,456 triangles, 6 colours
  • overhangs: 6.5% of surface — supports recommended

3MF keeps units, colours and part names (bloch_q0_equator, bloch_q0_state_arrow, …), so multi-colour slicers can assign a filament per part. The report checks each part for closed, consistently oriented edges and measures the thinnest feature, size, volume and overhang share.

Publication figures

q.draw("c,b,a,e", "figure.pdf", preset="paper")                        # double column (7.16 in)
q.draw("a", "amps.png", preset="paper", column="single")               # 3.5 in, 600 dpi
q.draw("a,d", "bw.pdf", preset="paper", palette="grayscale")           # prints in black and white
print(q.last_caption)                                                    # also in figure.caption.txt

The paper preset uses serif (STIX) type, removes the dashboard header, scales lines and fonts to the real page size (never below 6 pt), uses a colour-blind-safe palette by default and writes a caption generated from the run: what is shown, the gates, exact versus sampled data and the version.

Research bundles

q = hdqs(2, seed=42).h(0).cx(0, 1)
q.export_bundle("bell_experiment")          # a folder, or "bell.zip"
hdqs.grover(3, ["101"], seed=3).export_bundle("grover.zip")

The two kinds of bundle differ, because an algorithm is told in stages rather than one figure:

metadata.json holds the engine version, seed, shots, mode, inputs, circuit hash and the provenance of every file.

In notebooks

In Jupyter and VS Code a register or algorithm result shows itself: a summary card with the interactive explorer (or live player) embedded, no .draw() needed. hdqs.rich_display(False) switches it off.

Browser playground

hdqs.playground("playground.html")          # an empty playground with examples
hdqs.playground("mine.html", q)             # starts from q.code()

One offline HTML file with an editor that runs hdqs chains in the browser: gates, measure, if_x/if_z, unitary, load_state, for loops, lists, complex numbers and print, up to 10 qubits. The circuit, amplitudes, Bloch spheres, Q-sphere and entanglement update with a gate-by-gate slider, and errors point at the line. The same code runs unchanged in Python. Algorithm players have a Playground tab too: Edit & run in the playground loads r.code().

Algorithm visuals: how it works, not just the circuit

Every algorithm returns its usual result dictionary, which now also has .draw(), .code() and .circuit. The animation explains the idea behind the algorithm using the states recorded during that very run, so every picture matches the returned numbers, and it changes with whatever inputs you give it.

from sia import hdqs

r = hdqs.grover(3, ["101"])
r.draw("grover.gif")              # the circuit, then inversion about the mean and the rotation picture
r.draw("grover.html")             # live player: change the inputs and re-run, right in the browser
r.draw("grover.png", summary=True)   # one slide with the answer
r.code()                          # the hdqs chain that builds this run's circuit
r.draw("grover.tex")              # the circuit in LaTeX, sections boxed (standalone=False: bare environment)
r.lesson("grover.html")           # predict, then reveal: a question before each key stage
r.worksheet("grover.pdf")         # printable worksheet with a solutions page
r.export_frames("frames", "svg")  # every stage as a numbered image

Each animation opens with the circuit built for your input, with the oracle and other parts labelled. Grover, Deutsch–Jozsa and Simon use real gate-level oracles (X gates around a multi-controlled Z; one Z per bit when f is linear; CNOT copies for Simon). r.code() prints that circuit as a runnable one-import chain (repeated Grover iterations become a loop), and r.circuit is the program itself.

The last frame carries a result banner (FOUND 101, 15 = 3 × 5, ABORT · QBER 25%) and every panel says where its numbers come from: EXACT (from the state), SAMPLED (measurement shots), CLASSICAL (ordinary computation) or THEORY (a formula).

Teaching. r.lesson("x.html") turns the live player into a lesson: before each key stage the student predicts what happens (multiple choice, built from this run's numbers), reads why, and only then sees the stage; the inputs tab unlocks at the end. r.worksheet("x.pdf") prints the same questions on A4 with the stage before each one, answer space and a solutions section (solutions=False for the student copy).

The recording costs only a few numbers per stage; the pictures are made when .draw() is called. In the browser player, a seed gives a repeatable run, but sampled results use the browser's own random numbers, not Python's.

Quantum maths: numbers, vectors, matrices and practice

The mathematics underneath quantum computing, with the same one import:

from sia import hdqs

z = hdqs.cnum(1, 1)
(z * 1j).draw()                     # both arrows on the complex plane; the angles add
z.explain()                         # modulus √2, argument π/4, polar form √2·e^(iπ/4), conjugate
hdqs.vec([1, 1j]).normalize()       # vec(1/√2, i/√2)
hdqs.mat([[2, 1], [1, 2]]).draw()   # the grid, unit circle and square it transforms; eigen directions
hdqs.mat([[0, -1j], [1j, 0]]).eig() # eigenvalues ±1 with their eigenvectors

Values are shown exactly ((1+i)/√2, 3√13, 3π/4), inner products follow the physics convention ⟨u|v⟩ = Σ ūₖvₖ, and every object has .draw() and .explain().

Practice problems with exact answers and worked solutions:

ps = hdqs.practice("complex", n=10, level=2, seed=7)
print(ps)                           # the problems
ps.check(1, "(1+i)/√2")             # Correct ✓ / Not yet
ps.solution(1)                      # the worked steps
ps.draw("complex.html")             # interactive page: type answers, check, see solutions, print
hdqs.practice("matrices", n=8, students=40, seed=1).draw("class.pdf,key.csv")   # one set per student + keys

topic="mixed" draws from all of them. Problems never repeat within a set and are new across a class while the pool allows; only clean values are used, so no answer is a long decimal. Students may type 1+2i, (1+i)/√2, sqrt(2), 3π/4 or 3pi/4, e^(iπ/4), or a decimal such as 0.707; eigenvectors are accepted as any non-zero multiple and eigenvalues in any order. The same seed always gives the same set, so a key can be regenerated at any time.

Hindi and Telugu. English is the default. lang="hi" or lang="te" (on practice(), .draw() of a problem set, and .explain()) uses the terms of the school and intermediate textbooks (NCERT Hindi medium; Telugu Akademi), keeping the English term in brackets where a quantum term has no settled form; hdqs.glossary("te") lists them. PDF worksheets are English; for Hindi or Telugu, print the HTML page.

Dirac notation and quantum mechanics

Kets, bras and operators use the same exact display and .draw() / .explain() as the maths objects. Units: ħ = 1; hdqs.pauli("X") is σx, and hdqs.spin("x") is the spin observable along x, measured as ±1.

from sia import hdqs

plus, minus = hdqs.ket("+"), hdqs.ket("-")     # also "0", "1", "+i", "-i", "01+", "phi+", "psi-", "ghz", "w"
plus.dag() @ minus                              # ⟨+|−⟩ = 0
hdqs.ket("0") @ hdqs.bra("1")                   # outer product |0⟩⟨1|, a matrix
hdqs.HDQS(2).h(0).cx(0, 1).ket()                # '(1/√2)|00⟩ + (1/√2)|11⟩'   (latex=True for \ket{})

Z = hdqs.pauli("Z")
Z.expect("+"), Z.variance("+")                  # 0, 1
hdqs.spin("x").measure("0").explain().draw()    # outcomes, Born probabilities, states after
hdqs.evolve("X", "0", times=hdqs.np.linspace(0, 3.14, 60)).draw()   # Rabi curve and Bloch path
hdqs.uncertainty("X", "Y", "0")                 # ΔA·ΔB ≥ ½|⟨[A, B]⟩|, checked
hdqs.stern_gerlach(["z", "x", "z"]).draw()      # sequential analysers, every path and its probability

Checking and research tools

q = hdqs.HDQS(2).h(0).cx(0, 1)
q.matrix()                                      # the circuit's unitary, column j = result on |j⟩
hdqs.equivalent(hdqs.HDQS(1).h(0).z(0).h(0), hdqs.HDQS(1).x(0))   # True (global phase ignored)
hdqs.compare(q, "phi+").explain().draw()        # fidelity, trace distance, probabilities, Bloch vectors
hdqs.sweep(lambda t: hdqs.HDQS(2).ry(0, t).cx(0, 1),
           hdqs.np.linspace(0, 6.28, 41), observables=["ZI", "ZZ", "XX"]).draw().save("sweep.csv")
hdqs.selfcheck(q)                               # same program through every engine: they must agree

selfcheck replays one chain with the density-matrix, MPS and (for Clifford circuits) stabilizer engines, checks that optimize() keeps the matrix, that the inverse returns |0…0⟩, the OpenQASM 3 round trip, and agreement with Qiskit when it is installed. Checks that do not apply, or need a package you do not have, are listed as skipped.

Practice beyond maths, and a whole course

hdqs.practice also takes "dirac" (inner and outer products of named kets, Born probabilities, change of basis, density matrices, partial trace) and "physics" (expectation values, variance, measurement on unnormalised states, relative phase, spin at an angle, Rabi evolution, uncertainty products), at levels 1-3, with the same checking, class sets and languages.

hdqs.course("my_course")                  # open my_course/index.html
hdqs.course("my_course_te", lang="te")

course() writes one offline folder: an index page that walks from quantum maths (5 topics × 3 levels) through Dirac notation and quantum mechanics to quantum computing, the eleven explorers, the circuit playground, eleven algorithm lessons and a three-language glossary. Each practice page links back to the index, and the index shows your best score on each page (kept in the browser).

Explorers: touch, drag and rotate

Each explorer is one offline HTML page. 3D views turn with a drag or a finger, zoom with a pinch or the wheel, and reset with a double tap; they work on phones.

hdqs.explore()                                  # the list
hdqs.explore("phasor")                          # rotating e^(iωt) draws cosine and sine waves; two phasors: beats, cancelling
hdqs.explore("phasor", state="square")          # Fourier series: phasors at 1, 3, 5… × ω, head to tail, build a square wave (Gibbs ripple)
hdqs.explore("complex")                         # drag z and w: add, multiply (angles add), divide, conjugate, powers
hdqs.explore("matrix")                          # drag the columns of M: grid, determinant as area, eigen directions
hdqs.explore("double_slit")                     # a 2D Schrödinger wave through two slits: ripples, phase, |ψ|², 3D surface
hdqs.explore("bloch", state="+")                # gates as rotations, U·ψ = ψ′ as matrices, ρ = |ψ⟩⟨ψ|, measurement and collapse
hdqs.explore("entanglement")                    # product → Bell, 4×4 ρ and both partial traces, Alice then Bob, CHSH
hdqs.explore("hilbert")                         # 1–4 qubits: gates acting on the state vector and the density matrix
hdqs.explore("wavepacket")                      # 1D Schrödinger: free spreading, tunnelling, particle in a box, oscillator
hdqs.explore("fourier")                         # the QFT as sums of phasors; period finding peaks at multiples of N/r
hdqs.explore("rabi")                            # a spin in a field: Larmor precession, Rabi oscillation, Ramsey fringes
hdqs.explore("stern_gerlach")                   # one atom at a time through 1–3 magnets; z → x → z forgets the first result
hdqs(2).h(0).cx(0, 1).explore()                 # any 1–4 qubit register opens in the Hilbert-space explorer
hdqs.mat([[0, 1], [1, 0]]).explore()            # also hdqs.cnum(...).explore()

Hilbert space ("hilbert"): choose a qubit and press a gate. The page shows the full 2ⁿ×2ⁿ matrix multiplying the state vector, one output amplitude built from its contributions (arrows head to tail, so cancellation is visible), the amplitudes as phase wheels or waves, each qubit's reduced Bloch vector, the Q-sphere, the state-vector table and the density matrix (whole register or one qubit) with purity and entropies. Gates include H, X, Y, Z, S, T, √X, Rx/Ry/Rz/P(θ), controlled versions and SWAP; noise channels (dephasing, depolarizing, amplitude damping) and measurement act on ρ. Every step can be undone, examples load in one tap (Bell, GHZ, Grover, QFT, decoherence…), and "copy as code" gives the hdqs chain that rebuilds the circuit.

Double slit: the wave is a real solution of the 2D Schrödinger equation (Visscher's staggered leapfrog, absorbing edges), shown as ripples (crest and trough), as brightness and phase, as |ψ|², or as a lit 3D surface. One slit, both, or a which-path detector: the path qubit's coherence γ sets the fringe visibility, and the predicted and measured visibility are shown side by side. Particles arrive one at a time and build the pattern.

Every explorer has a toolbar: light/dark, undo, copy link (the link restores the exact settings), picture (PNG of all panels) and record video (WebM). lang="hi" or "te" translates the title, guidance and every control label, using the standard scientific terms (with the English term in brackets where it helps); symbols and formulas stay as they are. hdqs.course() includes all eleven explorers, each placed with the step it belongs to.

Interoperability

OpenQASM 3 via hdqs.from_qasm3(source) and q.to_qasm3(). Optional adapters: hdqs.to_qiskit, hdqs.run_aer, hdqs.to_pennylane.

HDQS server client

The same hdqs name reaches the HDQS quantum server. A whole number builds the local simulator; any other call connects to the server:

from sia import hdqs

client = hdqs(api_key="YOUR_TOKEN")
client.qbt_create(num_qubits=2)
client.qbt_run(["h 0", "cnot 0 1"])
print(client.qbt_measure([0, 1]))

An API token is issued by Sia Software Innovations. The server address can be changed without reinstalling, using the SIA_HDQS_HOST and SIA_HDQS_PORT environment variables. If the server is unreachable, client calls raise hdqs.HDQSError; the offline simulator is unaffected.

Entities: ntt

from sia import ntt

Person = ntt("name", "age").computed("group", "if (1) > 17: adult | else: minor")
p = Person("Ravi", 20)
print(p.name, p.group)          # Ravi adult

Templates refer to attributes by position, (0), (1), and so on. Conditions and validators are evaluated through a restricted expression checker, never eval.

Enterprise logic: els

from sia import els

program = """
*sia
  DATA total TYPE I.
  total = 40 + 2.
  WRITE total.
sia*
"""
print(els(program))             # 42

For multi-block programs, share state with env = els.make_env() and call els(block, env). An interactive prompt is available through els.repl().

Optional dependencies

Matplotlib and openqasm3 are regular dependencies since 1.5.4; the old [plot] and [qasm] extras still install without error.

A feature whose dependency is missing raises an ImportError naming the package to install. hdqs.capabilities() reports what is available.

Conventions

• Qubit 0 is the most significant bit: in '01', qubit 0 is 0. Qiskit uses the opposite order; the adapters convert automatically.
• measure() collapses the state; sample() and probabilities() do not.
• Memory grows exponentially with qubit count in the statevector and density-matrix modes. Above the 1 GiB default budget a register becomes program-only (q.is_lazy): use q.stabilizer() or q.mps(), or pass max_memory_mb= to allow a larger full state.

Licensing

sia-script is proprietary software of Sia Software Innovations Private Limited, with one exception: the quantum simulator, sia/hdqs_engine.py, is released under the MIT License. See LICENSE.md for the full terms of both.

Citation

If you use the CRIA interference-accessibility tools in research, please cite:

Seshabattara Venkata, N. S. D. N. Cardinality-Resolved Interference Accessibility in Multipartite Quantum Systems. Zenodo (2026). https://doi.org/10.5281/zenodo.23180889

Support

Sia Software Innovations Private Limited
Email: info@siasoftwareinnovations.com
Website: https://www.siasoftwareinnovations.com