qutip_qip.algorithms

Classes

`BitFlipCode`()	Implementation of the 3-qubit bit-flip quantum error correction code using projective measurements and classically controlled correction gates.
`PhaseFlipCode`()	Implementation of the 3-qubit phase-flip quantum error correction code.
`ShorCode`()	Constructs the 9-qubit Shor code encoding circuit using BitFlipCode and PhaseFlipCode.

Functions

`qft`([N])	Quantum Fourier Transform operator on N qubits.
`qpe`(U, num_counting_qubits[, target_qubits, ...])	Quantum Phase Estimation circuit implementation for QuTiP.
`grover`(oracle, search_qubits, num_solutions)	Construct the Grover search algorithm's circuit.
`grover_oracle`(search_qubits, marked_states)	Constructs a Phase Oracle circuit for Grover's algorithm.

class qutip_qip.algorithms.BitFlipCode[source]

Bases: object

Implementation of the 3-qubit bit-flip quantum error correction code using projective measurements and classically controlled correction gates.

This code detects and corrects a single bit-flip (X) error on any of the three qubits using two syndrome (ancilla) qubits.

decode_circuit(data_qubits: list[int | integer] | tuple[int | integer, ...] | ndarray[tuple[Any, ...], dtype[integer]]) → QubitCircuit[source]

Constructs the decoding circuit which is the inverse of the encoding operation, used to recover the original logical qubit. TOFFOLI gate verifies parity.

Parameters:

data_qubitssequence of int: Indices of 3 data qubits.

Returns:

qcQubitCircuit: The decoding quantum circuit.

Raises:

ValueError: If the number of data qubits is not 3.

encode_circuit(data_qubits: list[int | integer] | tuple[int | integer, ...] | ndarray[tuple[Any, ...], dtype[integer]]) → QubitCircuit[source]

Constructs the encoding circuit for the bit-flip code. The first qubit is the control, and CNOT gates are applied from it to the other data qubits to encode logical states \(|0\rangle\) or \(|1\rangle\).

Parameters:

data_qubitssequence of int: Indices of 3 data qubits.

Returns:

qcQubitCircuit: The encoding quantum circuit.

Raises:

ValueError: If the number of data qubits is not 3.

property n_data: int

Returns:

int: Number of data qubits (always 3 for bit-flip code).

property n_syndrome: int

Returns:

int: Number of syndrome qubits used for error detection (2 for this code).

Constructs the circuit for syndrome extraction and classical error correction. The circuit measures parity between qubit pairs and applies X gates conditionally.

Parameters:

data_qubitssequence of int: Indices of 3 data qubits.
syndrome_qubitssequence of int: Indices of 2 syndrome qubits.

Returns:

qcQubitCircuit: Circuit for syndrome measurement and X correction.

Raises:

ValueError: If the number of data or syndrome qubits is incorrect.

class qutip_qip.algorithms.PhaseFlipCode[source]

Bases: object

Implementation of the 3-qubit phase-flip quantum error correction code.

This code protects against a single Z (phase) error by encoding the logical qubit into a 3-qubit entangled state using Hadamard transformations and CNOT gates, then measuring parity between pairs of qubits using ancilla qubits. Conditional Z corrections are applied based on classical measurement outcomes.

decode_circuit(data_qubits: list[int | integer] | tuple[int | integer, ...] | ndarray[tuple[Any, ...], dtype[integer]]) → QubitCircuit[source]

Constructs the decoding circuit that reverses the encoding operation.

It first applies the Hadamard (H) gates to convert the qubits back from the X-basis to the Z-basis, then applies the inverse of the CX encoding to decode the qubits. A Toffoli gate is applied in the end to verify parity.

Parameters:

data_qubitssequence of int: Indices of 3 data qubits.

Returns:

qcQubitCircuit: The decoding circuit.

Raises:

ValueError: If the number of data qubits is not 3.

encode_circuit(data_qubits: list[int | integer] | tuple[int | integer, ...] | ndarray[tuple[Any, ...], dtype[integer]]) → QubitCircuit[source]

Constructs the encoding circuit for the phase-flip code.

The logical qubit is first encoded by two CX gates and then converted to the X-basis using Hadamard (H). This creates redundancy to detect and correct a single phase error.

Parameters:

data_qubitssequence of int: Indices of 3 data qubits.

Returns:

qcQubitCircuit: The encoding quantum circuit.

Raises:

ValueError: If the number of data qubits is not 3.

property n_data: int

Returns:

int: Number of data qubits (3).

property n_syndrome: int

Returns:

int: Number of syndrome qubits (2).

Builds the circuit for syndrome extraction and correction.

The data qubits are temporarily converted back to the Z-basis so parity can be measured between pairs using ancillas and CNOT gates. Measurements are stored in classical bits, and Z corrections are applied conditionally based on the measured syndrome.

Parameters:

data_qubitssequence of int: Indices of 3 data qubits.
syndrome_qubitssequence of int: Indices of 2 syndrome qubits.

Returns:

qcQubitCircuit: Circuit for syndrome measurement and Z correction.

Raises:

ValueError: If there are not exactly 3 data qubits and 2 syndrome qubits.

class qutip_qip.algorithms.ShorCode[source]

Bases: object

Constructs the 9-qubit Shor code encoding circuit using BitFlipCode and PhaseFlipCode.

The Shor code protects against arbitrary single-qubit errors by combining bit-flip and phase-flip redundancy encoding.

encode_circuit() → QubitCircuit[source]

Construct the 9-qubit Shor code encoding circuit.

Returns:

qcQubitCircuit: Circuit that encodes one logical qubit into the Shor code.

Construct the Grover search algorithm’s circuit.

Parameters:

oracleQubitCircuit or Gate: The oracle that flips the phase of marked states.
search_qubitsint or sequence of int: The qubits to run the search on.
num_solutionsint: The number of expected solutions M.
num_iterationsint, optional: Number of iterations. Defaults to optimal for M solutions.
num_qubitsint, optional: Total number of qubits in the system.

Returns:

qcQubitCircuit: Quantum Circuit implementing Grover’s search algorithm.

Raises:

ValueError: If the oracle gate targets do not match the algorithm qubits.

Notes

The algorithm performs the following steps:

Apply Hadamard gates to all qubits to create superposition.
For each iteration:
1. Apply the oracle (phase flip on marked states).
2. Apply the diffusion operator (inversion about the mean):
  
  Hadamard gates
  
  X gates
  
  Multi-controlled Z gate
  
  X gates
  
  Hadamard gates

References

[1]

L. K. Grover, “A fast quantum mechanical algorithm for database search,” Proceedings of the 28th Annual ACM Symposium on Theory of Computing (1996).

Examples

Search for state \(|01\rangle\) using 2 qubits:

>>> from qutip_qip.algorithms.grover import grover, grover_oracle
>>> oracle = grover_oracle([0, 1], marked_states=1)
>>> qc = grover(oracle, search_qubits=[0, 1], num_solutions=1)

Constructs a Phase Oracle circuit for Grover’s algorithm.

Parameters:

search_qubitsint or sequence of int: The specific qubit indices the oracle acts on.
marked_statesint or sequence of int: The states to mark (integer representation).

Returns:

qcQubitCircuit: The oracle circuit.

qutip_qip.algorithms.qft(N: int = 1) → Qobj[source]

Quantum Fourier Transform operator on N qubits.

Parameters:

Nint: Number of qubits. (default = 1)

Returns:

QFTQobj: Quantum Fourier transform operator.

qutip_qip.algorithms.qft_gate_sequence(N: int = 1, swapping: bool = True, to_cnot: bool = False) → QubitCircuit[source]

Quantum Fourier Transform operator on N qubits returning the gate sequence.

Parameters:

Nint: Number of qubits.
swappingbool, optional: Flag indicating sequence of swap gates to be applied at the end or not (default: True).
to_cnotbool, optional: Flag to decompose controlled phase gates to CNOT gates (default: False).

Returns:

qcQubitCircuit: Gate sequence of Hadamard and controlled rotation gates implementing QFT.

qutip_qip.algorithms.qft_steps(N: int = 1, swapping: bool = True) → list[Qobj][source]

Quantum Fourier Transform operator on N qubits returning the individual steps as unitary matrices operating from left to right.

Parameters:

Nint: Number of qubits.
swappingbool, optional: Flag indicating sequence of swap gates to be applied at the end or not.

Returns:

U_step_listlist of Qobj: List of Hadamard and controlled rotation gates implementing QFT.

Quantum Phase Estimation circuit implementation for QuTiP.

Parameters:

UQobj: Unitary operator whose eigenvalue we want to estimate. Should be a unitary quantum operator.
num_counting_qubitsint: Number of counting qubits to use for the phase estimation. More qubits provide higher precision.
target_qubitsint or sequence of int, optional: Index or indices of the target qubit(s) where the eigenstate is prepared. If None, target_qubits is set automatically based on U’s dimension.
to_cnotbool, optional: Flag to decompose controlled phase gates to CNOT gates (default: False)

Returns:

qcQubitCircuit: Gate sequence implementing Quantum Phase Estimation.