`simple`¶

Simple Circuit Case Library (:cls:`qurry.recipe.library.simple`)

`cat`¶

GHZ state (qurry.recipe.library.simple.cat)

The entangled circuit :cls:`GHZ` a.k.a. :cls:`Cat`.

Reference:

Note

Measurement of the Entanglement Spectrum of a Symmetry-Protected Topological State

Using the IBM Quantum Computer - Choo, Kenny and von Keyserlingk, Curt W. and Regnault, Nicolas and Neupert, Titus [doi:10.1103/PhysRevLett.121.086808](

https://doi.org/10.1103/PhysRevLett.121.086808)

}

class qurry.recipe.simple.cat.Cat(num_qubits: int, name: str = 'cat')[source]¶

:cls:`Cat`, the anthor name of entangled circuit :cls:`GHZ`.

# Open boundary at 8 qubits:
    ┌───┐
q0: ┤ H ├──■────────────────────────────────
    └───┘┌─┴─┐
q1: ─────┤ X ├──■───────────────────────────
         └───┘┌─┴─┐
q2: ──────────┤ X ├──■──────────────────────
              └───┘┌─┴─┐
q3: ───────────────┤ X ├──■─────────────────
                   └───┘┌─┴─┐
q4: ────────────────────┤ X ├──■────────────
                        └───┘┌─┴─┐
q5: ─────────────────────────┤ X ├──■───────
                             └───┘┌─┴─┐
q6: ──────────────────────────────┤ X ├──■──
                                  └───┘┌─┴─┐
q7: ───────────────────────────────────┤ X ├
                                       └───┘

Parameters:

num_qubits (int) – The number of qubits for constructing the example circuit.
name (str, optional) – Name of case. Defaults to “cat”.

class qurry.recipe.simple.cat.GHZ(num_qubits: int, name: str = 'ghz')[source]¶

The entangled circuit :cls:`GHZ`. Introduce in https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.086808 .

# Open boundary at 8 qubits:
    ┌───┐
q0: ┤ H ├──■────────────────────────────────
    └───┘┌─┴─┐
q1: ─────┤ X ├──■───────────────────────────
         └───┘┌─┴─┐
q2: ──────────┤ X ├──■──────────────────────
              └───┘┌─┴─┐
q3: ───────────────┤ X ├──■─────────────────
                   └───┘┌─┴─┐
q4: ────────────────────┤ X ├──■────────────
                        └───┘┌─┴─┐
q5: ─────────────────────────┤ X ├──■───────
                             └───┘┌─┴─┐
q6: ──────────────────────────────┤ X ├──■──
                                  └───┘┌─┴─┐
q7: ───────────────────────────────────┤ X ├
                                       └───┘

Parameters:

num_qubits (int) – The number of qubits for constructing the example circuit.
name (str, optional) – Name of case. Defaults to “ghz”.

`intracell`¶

Intracell (qurry.recipe.library.simple.intracell)

class qurry.recipe.simple.intracell.Intracell(num_qubits: int, state: Literal['singlet', 'minus', 'plus'] = 'singlet', name: str = 'intracell')[source]¶

The entangled circuit :cls:`Intracell`.

# At state `singlet`, `minus` a.k.a. `Singlet` with 8 qubits:
    ┌───┐┌───┐
q0: ┤ X ├┤ H ├──■──
    ├───┤└───┘┌─┴─┐
q1: ┤ X ├─────┤ X ├
    ├───┤┌───┐└───┘
q2: ┤ X ├┤ H ├──■──
    ├───┤└───┘┌─┴─┐
q3: ┤ X ├─────┤ X ├
    ├───┤┌───┐└───┘
q4: ┤ X ├┤ H ├──■──
    ├───┤└───┘┌─┴─┐
q5: ┤ X ├─────┤ X ├
    ├───┤┌───┐└───┘
q6: ┤ X ├┤ H ├──■──
    ├───┤└───┘┌─┴─┐
q7: ┤ X ├─────┤ X ├
    └───┘     └───┘

\[\frac{1}{\sqrt{2}} \left({|01\rangle} - {|10\rangle} \right)^{\otimes N/2}, N = 8\]

# At state `plus` with 8 qubits:
    ┌───┐
q0: ┤ H ├──■──
    ├───┤┌─┴─┐
q1: ┤ X ├┤ X ├
    ├───┤└───┘
q2: ┤ H ├──■──
    ├───┤┌─┴─┐
q3: ┤ X ├┤ X ├
    ├───┤└───┘
q4: ┤ H ├──■──
    ├───┤┌─┴─┐
q5: ┤ X ├┤ X ├
    ├───┤└───┘
q6: ┤ H ├──■──
    ├───┤┌─┴─┐
q7: ┤ X ├┤ X ├
    └───┘└───┘

\[\frac{1}{\sqrt{2}} \left({|01\rangle} + {|10\rangle} \right)^{\otimes N/2}, N = 8\]

Parameters:

num_qubits (int) – Number of qubits.
state (str, optional) – Choosing the state. There are ‘singlet’, ‘minus’, ‘plus’ which ‘minus’ is same as ‘singlet’. Defaults to “singlet”.
name (str, optional) – Name of case. Defaults to “intracell”.

property state: Literal['singlet', 'minus', 'plus']¶

The state of the circuit.

Returns:: The state of the circuit.

class qurry.recipe.simple.intracell.Singlet(num_qubits: int, name: str = 'singlet')[source]¶

:cls:`Siglet`, the entangled circuit :cls:`Intracell` with singlet state.

# At 8 qubits:
    ┌───┐┌───┐
q0: ┤ X ├┤ H ├──■──
    ├───┤└───┘┌─┴─┐
q1: ┤ X ├─────┤ X ├
    ├───┤┌───┐└───┘
q2: ┤ X ├┤ H ├──■──
    ├───┤└───┘┌─┴─┐
q3: ┤ X ├─────┤ X ├
    ├───┤┌───┐└───┘
q4: ┤ X ├┤ H ├──■──
    ├───┤└───┘┌─┴─┐
q5: ┤ X ├─────┤ X ├
    ├───┤┌───┐└───┘
q6: ┤ X ├┤ H ├──■──
    ├───┤└───┘┌─┴─┐
q7: ┤ X ├─────┤ X ├
    └───┘     └───┘

\[\frac{1}{\sqrt{2}} \left({|01\rangle} - {|10\rangle} \right)^{\otimes N/2}, N = 8\]

Parameters:

num_qubits (int) – Number of qubits.
name (str, optional) – Name of case. Defaults to “singlet”.

Raises:

ValueError – When given number of qubits is not even.

`paramagnet`¶

Paramagnet (qurry.recipe.library.simple.paramagnet)

The circuits :cls:`TrivialParamagnet` and :cls:`TopologicalParamagnet`.

Reference:

Note

Measurement of the Entanglement Spectrum of a Symmetry-Protected Topological State

Using the IBM Quantum Computer - Choo, Kenny and von Keyserlingk, Curt W. and Regnault, Nicolas and Neupert, Titus [doi:10.1103/PhysRevLett.121.086808](

https://doi.org/10.1103/PhysRevLett.121.086808)

}

class qurry.recipe.simple.paramagnet.Cluster(num_qubits: int, border_cond: Literal['open', 'period'] = 'period', name: str = 'cluster')[source]¶

:cls:`Cluster`, another name of The entangled circuit :cls:`Topological paramagnet`. Introduce in https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.086808 .

# With ACTUAL `CZGate`, Open boundary at 8 qubits:
    ┌───┐
q0: ┤ H ├─■────
    ├───┤ │
q1: ┤ H ├─■──■─
    ├───┤    │
q2: ┤ H ├─■──■─
    ├───┤ │
q3: ┤ H ├─■──■─
    ├───┤    │
q4: ┤ H ├─■──■─
    ├───┤ │
q5: ┤ H ├─■──■─
    ├───┤    │
q6: ┤ H ├─■──■─
    ├───┤ │
q7: ┤ H ├─■────
    └───┘

# With ACTUAL `CZGate`, Period boundary at 8 qubits:
    ┌───┐
q0: ┤ H ├─■─────■─
    ├───┤ │     │
q1: ┤ H ├─■──■──┼─
    ├───┤    │  │
q2: ┤ H ├─■──■──┼─
    ├───┤ │     │
q3: ┤ H ├─■──■──┼─
    ├───┤    │  │
q4: ┤ H ├─■──■──┼─
    ├───┤ │     │
q5: ┤ H ├─■──■──┼─
    ├───┤    │  │
q6: ┤ H ├─■──■──┼─
    ├───┤ │     │
q7: ┤ H ├─■─────■─
    └───┘

Parameters:

num_qubits (int) – Number of qubits.
border_cond (str, optional) – Boundary condition is open or period. Defaults to “period”.
name (str, optional) – Name of case. Defaults to “cluster”.

Raises:

ValueError – When given number of qubits is not even.

class qurry.recipe.simple.paramagnet.TopologicalParamagnet(num_qubits: int, border_cond: Literal['open', 'period'] = 'period', name: str = 'cluster')[source]¶

The entangled circuit :cls:`Topological paramagnet`. Introduce in https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.086808 .

# With ACTUAL CZGate, Open boundary at 8 qubits:
    ┌───┐
q0: ┤ H ├─■────
    ├───┤ │
q1: ┤ H ├─■──■─
    ├───┤    │
q2: ┤ H ├─■──■─
    ├───┤ │
q3: ┤ H ├─■──■─
    ├───┤    │
q4: ┤ H ├─■──■─
    ├───┤ │
q5: ┤ H ├─■──■─
    ├───┤    │
q6: ┤ H ├─■──■─
    ├───┤ │
q7: ┤ H ├─■────
    └───┘

# With ACTUAL CZGate, Open boundary at 5 qubits:
    ┌───┐
q0: ┤ H ├─■────
    ├───┤ │
q1: ┤ H ├─■──■─
    ├───┤    │
q2: ┤ H ├─■──■─
    ├───┤ │
q3: ┤ H ├─■──■─
    ├───┤    │
q4: ┤ H ├────■─
    └───┘

# With ACTUAL CZGate, Period boundary at 8 qubits:
    ┌───┐
q0: ┤ H ├─■─────■─
    ├───┤ │     │
q1: ┤ H ├─■──■──┼─
    ├───┤    │  │
q2: ┤ H ├─■──■──┼─
    ├───┤ │     │
q3: ┤ H ├─■──■──┼─
    ├───┤    │  │
q4: ┤ H ├─■──■──┼─
    ├───┤ │     │
q5: ┤ H ├─■──■──┼─
    ├───┤    │  │
q6: ┤ H ├─■──■──┼─
    ├───┤ │     │
q7: ┤ H ├─■─────■─
    └───┘

# With ACTUAL CZGate, Period boundary at 5 qubits:
    ┌───┐
q0: ┤ H ├─■──■────
    ├───┤ │  │
q1: ┤ H ├─■──┼──■─
    ├───┤    │  │
q2: ┤ H ├─■──┼──■─
    ├───┤ │  │
q3: ┤ H ├─■──┼──■─
    ├───┤    │  │
q4: ┤ H ├────■──■─
    └───┘

Parameters:

num_qubits (int) – Number of qubits.
border_cond (str, optional) – Boundary condition is open or period. Defaults to “period”.
name (str, optional) – Name of case. Defaults to “cluster”.

Raises:

ValueError – When given number of qubits is not even.

property border_cond: Literal['open', 'period']¶: The border condition.

class qurry.recipe.simple.paramagnet.TrivialParamagnet(num_qubits: int, name: str = 'trivial_paramagnet')[source]¶

The product state circuit :cls:`TrivialParamagnet`. Introduce in https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.086808 .

# At 8 qubits:
    ┌───┐
q0: ┤ H ├
    ├───┤
q1: ┤ H ├
    ├───┤
q2: ┤ H ├
    ├───┤
q3: ┤ H ├
    ├───┤
q4: ┤ H ├
    ├───┤
q5: ┤ H ├
    ├───┤
q6: ┤ H ├
    ├───┤
q7: ┤ H ├
    └───┘

\[{|+\rangle}^{\otimes N}, N = 8\]

Parameters:

num_qubits (int) – Number of qubits.
name (str, optional) – Name of case. Defaults to “trivial_paramagnet”.

simple¶

cat¶

intracell¶

paramagnet¶

`simple`¶

`cat`¶

`intracell`¶

`paramagnet`¶