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:

@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