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CritPt / Challenge_70_main / Put 4n qubits on a lattice of n rows and 4 columns. Let…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem description

# Problem setup: Put 4n4n qubits on a lattice of nn rows and 44 columns. Let N:=∫U(2)U⊗4(S⊗S)(U†)⊗4dUN:=\int_{U(2)}U^{\otimes 4}(S\otimes S)(U^\dagger)^{\otimes 4}dU act on the 44-qubit space of each row, where S=|00⟩⟨00|+|11⟩⟨11|S=|00\rangle\langle00|+|11\rangle\langle11|, and |ψ⟩|\psi\rangle is a pure state on the nn-qubit space of each column. # Main problem: Please compute tr(N⊗nψ⊗4)\text{tr}(N^{\otimes n}\psi^{\otimes 4}) when |ψ⟩|\psi\rangle is the nn-qubit GHZ state for n=3n=3.
Plain-text mathematical notation (without MathML)
# Problem setup:
Put 4n qubits on a lattice of n rows and 4 columns. Let N:=∫_(U(2))U^(⊗4)(S⊗S)(U^(†))^(⊗4)dU act on the 4-qubit space of each row, where S=|00⟩⟨00|+|11⟩⟨11|, and |ψ⟩ is a pure state on the n-qubit space of each column.

# Main problem:
Please compute tr(N^(⊗n)ψ^(⊗4)) when |ψ⟩ is the n-qubit GHZ state for n=3.
Original LaTeX notation
# Problem setup:
Put $4n$ qubits on a lattice of $n$ rows and $4$ columns. Let $N:=\int_{U(2)}U^{\otimes 4}(S\otimes S)(U^\dagger)^{\otimes 4}dU$ act on the $4$-qubit space of each row, where $S=|00\rangle\langle00|+|11\rangle\langle11|$, and $|\psi\rangle$ is a pure state on the $n$-qubit space of each column.

# Main problem:
Please compute $\text{tr}(N^{\otimes n}\psi^{\otimes 4})$ when $|\psi\rangle$ is the $n$-qubit GHZ state for $n=3$.

code template

Code

def answer():
    r"""
    Return the value of $\text{tr}(N^{\otimes n}\psi^{\otimes 4})$.

    Inputs
    ----------
    None

    Outputs
    ----------
    trace: float, $\text{tr}(N^{\otimes n}\psi^{\otimes 4})$ when $|\psi\rangle$ is the $n$-qubit GHZ state for $n=3$
    """

    # ------------------ FILL IN YOUR RESULTS BELOW ------------------
    trace = ...
    # ---------------------------------------------------------------

    return trace

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Source and history

upstream_id / Original problem ID
Challenge_70_main
task_id
aafd0ef3-cefb-527a-99d2-e82346e74ef8
task_key
train--Challenge~5f70~5fmain
task_revision_id
4
config / split
/ train

Official source

initial import