Quantum Advantage Tracker - Loschmidt Echo – Quantum Computing Dataset

aqora / Quantum Advantage Tracker - Loschmidt Echo

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About dataset version

Loschmidt Echo Quantum Circuits (OLE) — Observable Estimation & Operator Hydrodynamics Benchmarks (Parquet)

Short Description

This Parquet dataset packages the OpenQASM circuits used to evaluate Operator Loschmidt Echo (OLE) protocols for observable estimation, operator hydrodynamics, and OTOC-style diagnostics. The circuits originate from the Quantum Advantage Tracker’s classically verifiable observable estimation problems and are described in Algorithmiq’s 2025 report “Loschmidt echo for probing operator hydrodynamics in heterogeneous structures.” By preserving raw QASM and structured metadata in a columnar format, the dataset supports scalable analytics, ML workflows, and benchmarking across classical simulators and NISQ-era hardware.

Scientific Background

The Operator Loschmidt Echo is defined as

f_\delta(O) = \frac{1}{2^n} \mathrm{Tr}\left(U O U^\dagger V_\delta^\dagger U O U^\dagger V_\delta\right)

, where

O \in {I, Z}^{\otimes n}

satisfies

\mathrm{Tr}(O^2) = 1

U

is a unitary generated by Trotterized Ising-like dynamics, and

V_\delta = e^{-i \delta G}

is a local perturbation with generator

G = \sum_{u \in \mathcal{P}} X_u

. The encoded unitary follows

U = (U_{-b}^\dagger)^L U_b^L

, so

2L

is the number of Trotter steps, and site-dependent fields ( b_u ) split the lattice into disjoint subsets ( F ) and ( S ) (e.g., heavy-hex vs. square sites). In the small-(\delta) regime, the OLE reduces to an out-of-time-ordered-correlator-like expression that probes operator spreading and hydrodynamics. The circuits implement random computational-basis sampling of

f_\delta^z(O)

, and the estimator variance scales as

O(1 / \sqrt{N_{\text{init}}})

. All circuits were produced by Algorithmiq, IBM, and the Flatiron Institute as part of the observable estimations tracker.

Circuit Instances

operator_loschmidt_echo_49x648: 49 qubits, $L = 3$ , $\delta = 0.15$ , observable $O = Z_{52} Z_{59} Z_{72}$ .
operator_loschmidt_echo_49x1296: 49 qubits, $L = 6$ , $\delta = 0.15$ , same observable $O = Z_{52} Z_{59} Z_{72}$ .
operator_loschmidt_echo_70x1872: 70 qubits, $L = 6$ , $\delta = 0.15$ , observable $O = Z_{52} Z_{59} Z_{72}$ .
Each circuit mirrors the protocol $U^\dagger_2 U_1$ with a perturbation ( V_\delta ) inserted between scrambling and unscrambling phases, yielding an operator-sensitive echo readout.

Dataset Contents

Every Parquet row corresponds to one complete OLE circuit instance stored as verbatim OpenQASM. Metadata such as qubit count, Floquet depth

L

, perturbation strength

\delta

, gate counts, and observable structure are parsed from filenames and circuit text whenever the information is encoded. No recompilation, transpilation, or scientific modification has been applied; the conversion solely repackages .qasm sources into a columnar layout.

Schema

Column	Type	Description
`circuit_id`	String	Filename stem uniquely identifying the OLE instance.
`family`	String	Constant label `operator_loschmidt_echo`.
`num_qubits`	Int32	Number of qubits declared in the circuit.
`num_gates`	Int32	Total instruction count (excludes qreg/creg/gate definitions).
`num_two_qubit_gates`	Int32	Count of instructions acting on exactly two distinct qubits.
`gate_types`	List<String>	Sorted, deduplicated gate mnemonics (parameters stripped).
`L`	Int32 (nullable)	Floquet layer count parsed from filenames.
`delta`	Float64 (nullable)	Perturbation strength parsed from filenames.
`observable`	String	Target observable (e.g., `Z52 Z59 Z72`).
`qasm`	String	Raw OpenQASM text preserved verbatim.

Loading Examples

Polars

import polars as pl
from aqora_cli.pyarrow import dataset

df = pl.scan_pyarrow_dataset(
    dataset("aqora/quantum-advantage-tracker-loschmidt-echo", "v0.0.0")
).collect()

print(df.head())

Pandas

import pandas as pd

df = pd.read_parquet(
    "aqora://aqora/quantum-advantage-tracker-loschmidt-echo/v0.0.0"
)

print(df.head())

Use Cases

Observable estimation benchmarks and mirror-circuit calibration.
Operator hydrodynamics and operator-spreading diagnostics in heterogeneous lattices.
OTOC-like protocol evaluation and perturbation-response studies.
Hardware calibration stress tests for NISQ processors.
Classical simulation benchmarking (tensor-network solvers, sampling-based, hybrid methods).
Circuit analytics and ML cost prediction workflows that require structured metadata and raw QASM.

Observable estimations tracker (Quantum Advantage Tracker): https://quantum-advantage-tracker.github.io/trackers/observable-estimations
Algorithmiq technical report: https://algorithmiq.fi/wp-content/uploads/2025/11/model-information-flow-complex-material-document.pdf

Notes

Circuits are unchanged; Parquet packaging only affects storage and accessibility.
Metadata extraction is best-effort and may expand in future releases while maintaining reproducibility.
Raw QASM remains the canonical source for any downstream compilation.