# Glossary

A comprehensive glossary of terms used in QubitOS and quantum computing.

---

## Quantum Computing Terms

### Anharmonicity

The difference between the 0→1 and 1→2 transition frequencies in a multi-level quantum
system. For transmons, anharmonicity is typically negative (around -200 to -300 MHz),
which allows selective addressing of the qubit transition.

$$\alpha = \omega_{12} - \omega_{01}$$

### Bloch Sphere

A geometrical representation of the pure state space of a two-level quantum system
(qubit). Any pure qubit state can be represented as a point on the surface of a
unit sphere.

### Coherence Time

The timescale over which a qubit maintains its quantum properties:

- **T1 (Relaxation time)**: Time for energy decay from |1⟩ to |0⟩
- **T2 (Dephasing time)**: Time for phase coherence loss
- **T2* (Echo time)**: Coherence time measured with spin echo

### Control Hamiltonian

The part of the system Hamiltonian that can be externally modulated to control
the qubit. In QubitOS, typically σx and σy terms driven by I and Q quadratures.

### Detuning

The difference between the qubit frequency and the drive frequency:

$$\Delta = \omega_q - \omega_d$$

Operating at a small detuning can be intentional (for AC Stark shift) or
unintentional (calibration error).

### Drift Hamiltonian

The always-on part of the system Hamiltonian that evolves the system even
without external control. Includes qubit frequencies, coupling terms, and
unwanted interactions.

### DRAG (Derivative Removal by Adiabatic Gate)

A pulse shaping technique that adds a derivative component to reduce leakage
to non-computational states. Particularly useful for transmons with finite
anharmonicity.

### Fidelity

A measure of how close an implemented quantum operation is to the ideal target.
QubitOS uses the average gate fidelity (Nielsen formula):

$$F = \frac{|\text{Tr}(U_\text{target}^\dagger U)|^2 + d}{d^2 + d}$$

where d is the Hilbert space dimension.

### Gate

A unitary operation on one or more qubits. Common gates include:

| Gate | Matrix | Description |
|------|--------|-------------|
| X (Pauli-X) | `[[0,1],[1,0]]` | Bit flip |
| Y (Pauli-Y) | `[[0,-i],[i,0]]` | Bit+phase flip |
| Z (Pauli-Z) | `[[1,0],[0,-1]]` | Phase flip |
| H (Hadamard) | `[[1,1],[1,-1]]/√2` | Superposition |
| CZ | diag(1,1,1,-1) | Controlled-Z |
| CNOT | Controlled-X | Entangling |

### Hamiltonian

The operator representing the total energy of a quantum system. Evolution
is governed by the Schrödinger equation:

$$i\hbar \frac{d|\psi\rangle}{dt} = H |\psi\rangle$$

### Infidelity

The complement of fidelity: 1 - F. Often used in log-scale plots where
lower is better.

### Leakage

Population transfer to non-computational states (e.g., |2⟩ in a transmon).
Leakage reduces gate fidelity and can accumulate over circuits.

### Pauli Matrices

The fundamental 2×2 Hermitian matrices for qubit operations:

$$\sigma_x = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \quad
\sigma_y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}, \quad
\sigma_z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$$

### Propagator

The unitary operator describing time evolution:

$$U(t) = \exp(-i H t / \hbar)$$

### Qubit

A two-level quantum system used as the basic unit of quantum information.
Physical implementations include superconducting circuits, trapped ions,
and quantum dots.

### Rabi Frequency

The frequency of oscillations between |0⟩ and |1⟩ when a qubit is driven
on resonance. Proportional to the drive amplitude.

### Rotating Frame

A reference frame that rotates at the drive frequency, simplifying the
time-dependent Hamiltonian to a time-independent one (in the rotating
wave approximation).

### Rotating Wave Approximation (RWA)

An approximation that neglects rapidly oscillating counter-rotating terms
in the Hamiltonian. Valid when drive frequency is close to qubit frequency.

### Tensor Product

The mathematical operation combining quantum systems:

$$|\psi_{AB}\rangle = |\psi_A\rangle \otimes |\psi_B\rangle$$

For operators: H_total = H_A ⊗ I_B + I_A ⊗ H_B

### Transmon

A type of superconducting qubit with reduced sensitivity to charge noise.
Characterized by large E_J/E_C ratio and negative anharmonicity.

### Unitary

A matrix U satisfying U†U = UU† = I. All quantum gates are unitary
(reversible).

---

## QubitOS-Specific Terms

### AgentBible

A configuration file defining safety constraints and validation rules.
Used to prevent parameter values that could damage hardware or produce
unphysical results.

### Backend

A hardware-specific implementation in the HAL server. Examples:
- `opx3`: Quantum Machines OPX3
- `zurich`: Zurich Instruments
- `mock`: Simulated hardware for testing

### Calibration

The measured parameters of a quantum device, including qubit frequencies,
coupling strengths, and coherence times. Stored in JSON/YAML format.

### Envelope

The time-dependent amplitude shape of a control pulse. QubitOS generates
I (in-phase) and Q (quadrature) envelopes.

### GRAPE (GRadient Ascent Pulse Engineering)

The primary optimization algorithm in QubitOS for pulse synthesis.
Iteratively improves pulses by computing analytical gradients of fidelity.

### GrapeConfig

The configuration dataclass for GRAPE optimization:

```python
@dataclass
class GrapeConfig:
    num_time_steps: int = 100
    duration_ns: float = 20.0
    target_fidelity: float = 0.999
    max_iterations: int = 1000
    learning_rate: float = 1.0
    max_amplitude: float = 100.0  # MHz
    regularization: float = 0.0
    random_seed: int | None = None
```

### GrapeResult

The result dataclass from GRAPE optimization containing:

- `i_envelope`: In-phase pulse amplitudes
- `q_envelope`: Quadrature pulse amplitudes
- `fidelity`: Achieved gate fidelity
- `iterations`: Number of optimization iterations
- `converged`: Whether target fidelity was reached
- `fidelity_history`: Fidelity at each iteration
- `final_unitary`: The implemented unitary matrix

### HAL (Hardware Abstraction Layer)

The interface between QubitOS core and quantum hardware. Provides a
uniform API regardless of the underlying hardware platform.

### HALClient

The Python client for communicating with the HAL server. Available in
async (`HALClient`) and sync (`HALClientSync`) versions.

### Pauli String

A string representation of Hamiltonian terms:

```
"0.5 * X0 + 0.3 * Z0 Z1"
```

Parsed by `parse_pauli_string()` into a matrix.

### Protocol Buffers (protobuf)

The serialization format for gRPC communication between QubitOS core
and the HAL server. Defined in `qubit-os-proto`.

### Pulse

A time-dependent control signal applied to a qubit. Characterized by:
- Duration (typically 10-100 ns for single-qubit gates)
- Amplitude envelope (I and Q quadratures)
- Carrier frequency (at or near qubit frequency)

### Validation

The process of checking parameters against physical constraints before
execution. Prevents invalid or dangerous configurations.

---

## Abbreviations

| Abbreviation | Full Form |
|--------------|-----------|
| AWG | Arbitrary Waveform Generator |
| CLI | Command Line Interface |
| CW | Continuous Wave |
| DAC | Digital-to-Analog Converter |
| DRAG | Derivative Removal by Adiabatic Gate |
| gRPC | gRPC Remote Procedure Call |
| HAL | Hardware Abstraction Layer |
| I/Q | In-phase / Quadrature |
| OPX | Quantum Machines' pulse processor |
| QND | Quantum Non-Demolition |
| RF | Radio Frequency |
| RWA | Rotating Wave Approximation |
| SNR | Signal-to-Noise Ratio |
| TLS | Transport Layer Security |

---

## Mathematical Notation

| Symbol | Meaning |
|--------|---------|
| \|ψ⟩ | Quantum state (ket) |
| ⟨ψ\| | Dual state (bra) |
| ⟨ψ\|φ⟩ | Inner product |
| ⊗ | Tensor product |
| † | Hermitian conjugate (dagger) |
| Tr(A) | Matrix trace |
| exp(A) | Matrix exponential |
| ℏ | Reduced Planck constant |
| ω | Angular frequency |
| σ | Pauli matrix |

---

## See Also

- [Architecture](architecture.md) - System architecture overview
- [API Reference](../api/index.md) - Detailed API documentation
- [Tutorials](../tutorials/pulse-generation.md) - Step-by-step guides
