Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

Primary Navigation

    • Cloud & Deployment
    • Core Language & Structure
    • Data Manipulation & Analysis
    • Engineering Data & Computation
    • External Interfaces & Connections
    • Financial Data & Computation
    • Geographic Data & Computation
    • Geometry
    • Graphs & Networks
    • Higher Mathematical Computation
    • Images
    • Knowledge Representation & Natural Language
    • Machine Learning
    • Notebook Documents & Presentation
    • Scientific and Medical Data & Computation
    • Social, Cultural & Linguistic Data
    • Strings & Text
    • Symbolic & Numeric Computation
    • System Operation & Setup
    • Time-Related Computation
    • User Interface Construction
    • Visualization & Graphics
    • Random Paclet
    • Alphabetical List
  • Using Paclets
    • Get Started
    • Download Definition Notebook
  • Learn More about Wolfram Language

QuantumFramework

Tutorials

  • Getting Started
  • Quantum Object Composition

Guides

  • Wolfram Quantum Computation Framework

Tech Notes

  • Bell's Theorem: CHSH inequality
  • Circuit Diagram
  • Exploring Fundamentals of Quantum Theory
  • An IBM Quantum Error Map
  • QPU Service Connection
  • Quantum object abstraction
  • Quantum Optimization
  • Second Quantization Functions
  • Sending Queries to IBM QPUs
  • Tensor Network
  • Quantum Computation

Symbols

  • CliffordChannel
  • EinsteinSummation
  • GraphState
  • IBMJob
  • IBMJobSubmit
  • LocalComplement
  • PauliStabilizer
  • QiskitCircuit
  • QiskitTarget
  • QuantumBasis
  • QuantumChannel
  • QuantumCircuitMultiwayGraph [EXPERIMENTAL]
  • QuantumCircuitOperator
  • QuantumDistance
  • QuantumEntangledQ
  • QuantumEntanglementMonotone
  • QuantumEvolve
  • QuantumMeasurement
  • QuantumMeasurementOperator
  • QuantumMeasurementSimulation
  • QuantumMPS [EXPERIMENTAL]
  • QuantumOperator
  • QuantumPartialTrace
  • QuantumPhaseSpaceTransform
  • QuantumQASM
  • QuantumShortcut [EXPERIMENTAL]
  • QuantumSimilarity
  • QuantumStateEstimate [EXPERIMENTAL]
  • QuantumState
  • QuantumTensorProduct
  • QuantumWignerMICTransform [EXPERIMENTAL]
  • QuantumWignerTransform [EXPERIMENTAL]
  • QuditBasis
  • QuditName
  • StabilizerFrame
  • StabilizerStateQ
An IBM Quantum Error Map
A quantum processor is only as good as its current calibration, and that calibration drifts from hour to hour. This note draws a single picture of an IBM device's instantaneous health: the qubit connectivity graph with the live per-qubit and per-bond calibration painted onto it. It is the IBM analogue of QUALink's
QUAConnect[backend]["ErrorMap"]
, and it reads only the free metadata endpoints, so it runs no circuit and spends no quantum time.
The example below is
ibm_fez
, a 156-qubit Heron r2 device.
What IBM actually exposes
Two read-only endpoints carry everything the map needs. The device's
ServiceConnect
connection to
"IBMQuantumPlatform"
already defines both as raw requests.
◼
  • configuration
    gives the static layout: the coupling map (the list of physically connected qubit pairs), a per-qubit grid coordinate, and the native gate set (
    {cz,id,rx,rz,rzz,sx,x}
    on Heron).
  • ◼
  • properties
    gives the live calibration, each value time-stamped: per qubit the relaxation time
    T
    1
    , the dephasing time
    T
    2
    , the single-shot readout error, and the asymmetric state-preparation-and-measurement probabilities; per gate the error and duration; and, in a
    general
    block, the static
    ZZ
    crosstalk for every coupled pair.
  • One thing is worth stating plainly, because it differs from QUALink: IBM publishes no Bell-state fidelity. There is no two-qubit fidelity number beyond the
    cz
    gate error itself. So the
    cz
    error becomes the bond color, and the natural second per-bond channel is the static
    ZZ
    crosstalk: the always-on residual coupling a pair carries even while idle, an error source independent of the gate error.
    Building the map
    The error map is a property of the
    "IBMQuantumPlatform"
    ServiceConnect
    connection. It needs IBM credentials for the read-only metadata fetch: an API key, and the IBM Cloud resource name stored as
    LocalSymbol["ibm_crn"]
    .
    LocalSymbol["ibm_crn"]="crn:v1:bluemix:public:quantum-computing:us-east:...";​​ibm=ServiceConnect["IBMQuantumPlatform","New",Authentication{"apikey"api}]
    Draw the map. A bare call uses the curated default styling shown above and the first available device:
    ibm["ErrorMap"]
    Pick a device by name with the
    "Backend"
    parameter:
    ibm["ErrorMap","Backend""ibm_fez"]
    The connection also exposes the underlying error model and its projections, each keyed by the sorted qubit pair, so the map's numbers are independently queryable (still no circuit, no quantum time):
    ibm["DeviceModel","Backend""ibm_fez"]
    The accessor family is
    "DeviceModel"
    ,
    "CouplingMap"
    ,
    "CZErrors"
    ,
    "ZZ"
    ,
    "GateErrors"
    (which takes a
    "GateName"
    parameter, default
    "cz"
    ),
    "ReadoutErrors"
    ,
    "Coherence"
    , and
    "Qubits"
    .
    "DeviceModel"
    fetches once and carries every projection as a key, so it is the efficient path when you need several at once; nothing device-specific is hardcoded, so a metric the device adds later is ingested with no change.
    Reading the map
    The drawing carries four calibration channels at once, plus the qubit labels and the defect markers.
    ◼
  • Bond color is the
    log
    10
    of the
    cz
    gate error, on a temperature scale: blue is a clean coupler, red a lossy one.
  • ◼
  • Bond thickness is the static
    ZZ
    crosstalk (0 to about 26 kHz on
    ibm_fez
    ): a thick bond leaks more always-on coupling.
  • ◼
  • Vertex color is
    T
    1
    on an avocado scale. Larger
    T
    1
    is better, so a long-lived qubit is dark green and a short-lived one glows yellow.
  • ◼
  • Vertex size is the readout error, but inverted so that a big disk is a good (low-readout) qubit. The single worst qubit is therefore the smallest dot.
  • ◼
  • Vertex label is the physical qubit index, so a problem qubit can be named, not just pointed at.
  • A coupler IBM currently flags as uncalibrated (gate error reported as exactly 1, the analogue of QUALink's 0 sentinel) is drawn as a dashed gray defect bond, and a qubit with no readout number as a dashed defect site, so the full physical lattice is always visible. The bonds carry double-headed arrows; the next section says why.
    Options
    Every channel is a parameter of the
    "ErrorMap"
    request, so the look is fully steerable; the defaults are the curated dark look above. Pass one override directly after the request name, or several wrapped in a list (the standard
    ServiceConnect
    parameter form).
    Parameter
    Default
    Meaning
    "EdgeColorScheme"
    "TemperatureMap"
    gradient for the
    cz
    -error bond color
    "VertexColorScheme"
    "AvocadoColors"
    gradient for the
    T
    1
    vertex color
    "VertexColorReversed"
    True
    map low
    T
    1
    to the gradient's bright end
    "VertexSizeReversed"
    True
    big disk = low readout error (good); set
    False
    for big = bad
    "EdgeThicknessMetric"
    "ZZ"
    bond thickness source:
    "ZZ"
    crosstalk,
    "Duration"
    (
    cz
    length), or
    None
    "EdgeThicknessRange"
    {4.,12.}
    thinnest-to-thickest bond width in points
    "EdgeArrows"
    True
    double-headed arrows on the bonds
    "ShowQubitLabels"
    True
    print the qubit index in each disk
    "BackgroundColor"
    Black
    canvas; the title, legends, and outlines follow its luminance
    A single override goes right after the request name:
    ibm["ErrorMap","BackgroundColor"White]
    Several overrides are passed as one list of rules:
    ibm["ErrorMap",{"Backend""ibm_fez","BackgroundColor"White,"EdgeThicknessMetric""Duration"}]
    Why the bonds are bidirectional
    IBM's native two-qubit gate is the controlled-
    Z
    ,
    CZ=diag(1,1,1,-1)
    , which is symmetric: swapping the two qubits leaves the gate unchanged, and the hardware calibrates both orderings to identical numbers. There is therefore no control or target for a
    cz
    , which is why the bonds are undirected and the arrows are drawn double-headed (bidirectional) rather than one-way.
    A directional
    CNOT
    is synthesized from a
    cz
    and single-qubit gates, with the basis-change Hadamards placed on whichever qubit you choose. So a
    CNOT
    can be realized in either orientation on the same physical bond: either qubit can serve as control or target.
    How it works
    The map lives entirely on the
    "IBMQuantumPlatform"
    connection. The
    "ErrorMap"
    request reads
    "RawBackendConfiguration"
    and
    "RawBackendProperties"
    (the same IAM-token and service-CRN authentication the connection already carries), folds them into one normalized, provider-neutral device model, and draws it. The drawing uses only built-in graphics, so the feature adds no dependency on the quantum paclet. This mirrors QUALink's
    QUAConnect[backend]["ErrorMap"]
    , with the per-pair
    ZZ
    crosstalk standing in for the Bell-state fidelity that QUA exposes and IBM does not.
    RelatedGuides
    ▪
    WolframQuantumComputationFramework
    RelatedTechNotes
    ▪
    QPUServiceConnect
    ▪
    SendingQueriesToIBMQPUs
    ""

    © 2026 Wolfram. All rights reserved.

    • Legal & Privacy Policy
    • Contact Us
    • WolframAlpha.com
    • WolframCloud.com