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Quantum Computing

A quantum-computing record keeps logical representation, logical-to-physical mapping, control, measurement, and error evidence distinct. Circuit execution and annealing are treated as different operating models rather than interchangeable diagrams.

logical statecontrol pulse

Problem

Logical representation

  • variable
  • Hamiltonian
  • circuit
  • constraint

Mapping

Logical-to-physical translation

  • topology
  • embedding
  • compiler
  • schedule

Hardware

Physical execution

  • qubit
  • pulse
  • control unit
  • cryogenic stage

Evidence

Measurement and comparison

  • syndrome
  • sample
  • probability
  • scaling
  • discrepancy
ObjectStructureRecordForm
Qubit topologyNodes, connectivity, logical variables, embedding and limitsPhysical graph, mapping, coupling and constraintTopology / embedding map
Quantum circuitQubits, gates, stages, depth and measurementGate order, qubit relation, preparation and readoutCircuit diagram
Pulse and waveformGenerator, amplitude, phase, duration, target and responseControl parameter, timing, physical target and measured responseWaveform / calibration plot
Annealing scheduleInitial and problem Hamiltonians, control curve, duration and encodingSchedule parameter, physical-qubit mapping and scaling relationSchedule curve
Hybrid architectureClassical processor, quantum processor, interface, parameter loopRequest, parameter transfer, sample, metric and convergenceHybrid loop
Control hardwareControl unit, electrode grid, cryogenic stage and qubit arraySignal path, temperature stage, physical connection and calibrationHardware stack
Error correctionLogical qubits, physical qubits, stabilizers, syndrome and correctionCode relation, measurement, detected error and applied correctionCode / syndrome map
Scaling evidenceSuccess probability, nesting level, rescaled data and scaling lawDevice condition, sample set, metric and fitted relationProbability / scaling plot
Simulation comparisonHardware result, numerical result, margin and discrepancyShared system parameters, tolerance and attributed causeComparison chart
Programming and secure systemsProblem builder, embedding tool, job, QKD nodes and shared keyCompilation path, execution job, channel and key establishmentUI flow / secure network

logical → physical

Mapping record

The topology, constraint, and operation used to place a problem on hardware.

parameter → pulse → response

Control record

Amplitude, phase, duration, target, and calibration measurement.

classical ↔ quantum

Hybrid record

Parameters sent to the QPU, returned samples, metric, and convergence condition.

hardware ↔ simulation

Validation record

Comparable settings, tolerance, discrepancy, and stated noise or decoherence source.

Encode

One or more logical qubits are represented by a defined arrangement of physical data and ancillary qubits.

Measure

A syndrome circuit repeatedly measures stabilizer operators using ancillary qubits.

Decode

The syndrome is mapped to an error estimate by a stated decoder procedure.

Correct

A correction operation or tracked frame update is selected from the estimate.

Scale

Logical error rate is compared across code distance, physical error rate, or device condition.

The cycle connects an abstract code relation to a physical measurement protocol and a quantitative scaling record.

Logical qubit ≠ physical qubitCircuit ≠ annealing scheduleSyndrome measurement ≠ logical-state measurementSimulation agreement requires shared settings

Is the computation a gate sequence or a continuous schedule?

A circuit records discrete gates, qubit relations, order, depth, and measurement. An annealing record follows an initial Hamiltonian, a problem Hamiltonian, a control schedule, duration, and final readout.

  • state preparation
  • gate or Hamiltonian
  • ordering or schedule
  • measurement basis

Where does a logical problem meet physical hardware?

Variables or logical qubits are mapped to physical qubits and couplers subject to connectivity and parameter bounds. Control pulses then connect compiled operations to a physical drive and measured response.

  • logical variable
  • embedding or compiler mapping
  • physical topology
  • control parameter and calibration

What does error-correction evidence actually connect?

A code maps a logical qubit to physical qubits; stabilizer measurements yield a syndrome without directly measuring the logical state; a decoder maps that syndrome to a correction and a resulting logical error rate.

  • code and qubit relation
  • syndrome circuit
  • decoder rule
  • logical error rate versus code distance

The useful conclusion concerns the relation among an abstract problem, its physical realization, and measured device behavior. It does not follow from the label ‘quantum’ or from a circuit diagram alone.

  1. Connectivity and control bounds constrain the logical-to-physical mapping.

  2. Syndrome measurement, decoding, correction, and logical-error scaling are separate operations.

  3. Scaling and hardware-simulation comparisons require shared settings, parameter ranges, and quantified discrepancy.

  • The execution model and measurement basis are unambiguous.
  • Logical and physical objects remain separately identified through compilation or encoding.
  • Device settings, sample range, tolerance, and noise conditions accompany the reported result.