classical_shadow

Post Processing - Classical Shadow - Classical Shadow (qurry.process.classical_shadow.classical_shadow)

qurry.process.classical_shadow.classical_shadow.classical_shadow_complex(shots: int, counts: list[dict[str, int]], random_unitary_um: dict[int, dict[int, Literal[0, 1, 2] | int]], selected_classical_registers: Iterable[int], given_operators: list[ndarray[tuple[int, int], dtype[complex128]]] | None = None, accuracy_prob_comp_delta: float = 0.01, max_shadow_norm: float | None = None, rho_method: Literal['numpy', 'numpy_precomputed'] | str | Literal['numpy_flatten', 'jax_flatten'] = 'numpy_precomputed', trace_method: Literal['trace_of_matmul', 'quick_trace_of_matmul', 'einsum_ij_ji'] | str | Literal['einsum_aij_bji_to_ab_numpy', 'einsum_aij_bji_to_ab_jax'] = 'einsum_aij_bji_to_ab_jax', estimate_trace_method: Literal['einsum_aij_bji_to_ab_numpy', 'einsum_aij_bji_to_ab_jax'] | str = 'einsum_aij_bji_to_ab_jax', pbar: tqdm | None = None) → ClassicalShadowComplex

Calculate the expectation value of Rho and the purity by classical shadow.

Reference:

Note

• Predicting many properties of a quantum system from very few measurements -

Huang, Hsin-Yuan and Kueng, Richard and Preskill, John [doi:10.1038/s41567-020-0932-7](

https://doi.org/10.1038/s41567-020-0932-7)

• The randomized measurement toolbox -

Elben, Andreas and Flammia, Steven T. and Huang, Hsin-Yuan and Kueng, Richard and Preskill, John and Vermersch, Benoît and Zoller, Peter [doi:10.1038/s42254-022-00535-2](

https://doi.org/10.1038/s42254-022-00535-2)

Parameters:

• shots (int) – The number of shots.

• counts (list[dict[str, int]]) – The list of the counts.

• random_unitary_um (dict[int, dict[int, Union[Literal[0, 1, 2], int]]]) – The shadow direction of the unitary operators.

• selected_classical_registers (Iterable[int]) – The list of the index of the selected_classical_registers.

• given_operators (list[np.ndarray[tuple[int, int], np.dtype[np.complex128]]]) – The list of the operators to estimate. Defaults to None.

• accuracy_prob_comp_delta (float, optional) – The accuracy probability component delta. Defaults to 0.01.

• max_shadow_norm (Optional[float], optional) – The maximum shadow norm. Defaults to None. If it is None, it will be calculated by the largest shadow norm upper bound. If it is not None, it must be a positive float number. It is \(|| O_i - \frac{\text{tr}(O_i)}{2^n} ||_{\text{shadow}}^2\) in equation.

• rho_method (RhoMCoreMethod, optional) – The method to use for the calculation. Defaults to “numpy_precomputed”. It can be either “numpy”, “numpy_precomputed”, “jax_flatten”, or “numpy_flatten”. - “numpy”: Use Numpy to calculate the rho_m. - “numpy_precomputed”: Use Numpy to calculate the rho_m with precomputed values. - “numpy_flatten”: Use Numpy to calculate the rho_m with a flattening workflow. Currently, “numpy_precomputed” is the best option for performance.

• trace_method (TraceRhoMethod, optional) –

  The method to calculate the trace of Rho square. - “trace_of_matmul”:

  Use np.trace(np.matmul(rho_m1, rho_m2)) to calculate the each summation item in rho_m_list.

  • ”quick_trace_of_matmul” or “einsum_ij_ji”:

    Use np.einsum(“ij,ji”, rho_m1, rho_m2) to calculate the each summation item in rho_m_list.

  • ”einsum_aij_bji_to_ab_numpy”:

    Use np.einsum(“aij,bji->ab”, rho_m_list, rho_m_list) to calculate the trace.

  • ”einsum_aij_bji_to_ab_jax”:

    Use jnp.einsum(“aij,bji->ab”, rho_m_list, rho_m_list) to calculate the trace.

• estimate_trace_method (AllTraceRhoMethod, optional) –

  The method to calculate the trace for searching esitmator. - “einsum_aij_bji_to_ab_numpy”:

  Use np.einsum(“aij,bji->ab”, rho_m_list, rho_m_list) to calculate the trace.

  • ”einsum_aij_bji_to_ab_jax”:

    Use jnp.einsum(“aij,bji->ab”, rho_m_list, rho_m_list) to calculate the trace.

• pbar (Optional[tqdm.tqdm], optional) – The progress bar. Defaults to None.

Returns:

The expectation value of Rho and the purity calculated by classical shadow.

Return type:

ClassicalShadowComplex

qurry.process.classical_shadow.classical_shadow.esitimation_of_given_operators(shots: int, counts: list[dict[str, int]], random_unitary_um: dict[int, dict[int, Literal[0, 1, 2] | int]], selected_classical_registers: Iterable[int], given_operators: list[ndarray[tuple[int, int], dtype[complex128]]], accuracy_prob_comp_delta: float = 0.01, max_shadow_norm: float | None = None, rho_method: Literal['numpy', 'numpy_precomputed'] | str | Literal['numpy_flatten', 'jax_flatten'] = 'numpy_precomputed', estimate_trace_method: Literal['einsum_aij_bji_to_ab_numpy', 'einsum_aij_bji_to_ab_jax'] | str = 'einsum_aij_bji_to_ab_jax', pbar: tqdm | None = None) → ClassicalShadowEstimation

Calculate the expectation value of given operators.

Reference:

Note

• Predicting many properties of a quantum system from very few measurements -

Huang, Hsin-Yuan and Kueng, Richard and Preskill, John [doi:10.1038/s41567-020-0932-7](

https://doi.org/10.1038/s41567-020-0932-7)

• The randomized measurement toolbox -

Elben, Andreas and Flammia, Steven T. and Huang, Hsin-Yuan and Kueng, Richard and Preskill, John and Vermersch, Benoît and Zoller, Peter [doi:10.1038/s42254-022-00535-2](

https://doi.org/10.1038/s42254-022-00535-2)

Parameters:

• shots (int) – The number of shots.

• counts (list[dict[str, int]]) – The list of the counts.

• random_unitary_um (dict[int, dict[int, Union[Literal[0, 1, 2], int]]]) – The shadow direction of the unitary operators.

• selected_classical_registers (Iterable[int]) – The list of the index of the selected_classical_registers.

• given_operators (list[np.ndarray[tuple[int, int], np.dtype[np.complex128]]]) – The list of the operators to estimate.

• accuracy_prob_comp_delta (float, optional) – The accuracy probability component delta. Defaults to 0.01.

• max_shadow_norm (Optional[float], optional) – The maximum shadow norm. Defaults to None. If it is None, it will be calculated by the largest shadow norm upper bound. If it is not None, it must be a positive float number. It is \(|| O_i - \frac{\text{tr}(O_i)}{2^n} ||_{\text{shadow}}^2\) in equation.

• rho_method (RhoMCoreMethod, optional) – The method to use for the calculation. Defaults to “numpy_precomputed”. It can be either “numpy”, “numpy_precomputed”, “jax_flatten”, or “numpy_flatten”. - “numpy”: Use Numpy to calculate the rho_m. - “numpy_precomputed”: Use Numpy to calculate the rho_m with precomputed values. - “numpy_flatten”: Use Numpy to calculate the rho_m with a flattening workflow. Currently, “numpy_precomputed” is the best option for performance.

• estimate_trace_method (AllTraceRhoMethod, optional) –

  The method to calculate the trace for searching esitmator. - “einsum_aij_bji_to_ab_numpy”:

  Use np.einsum(“aij,bji->ab”, rho_m_list, rho_m_list) to calculate the trace.

  • ”einsum_aij_bji_to_ab_jax”:

    Use jnp.einsum(“aij,bji->ab”, rho_m_list, rho_m_list) to calculate the trace.

• pbar (Optional[tqdm.tqdm], optional) – The progress bar. Defaults to None.

Returns:

The estimation of the given operators.

Return type:

ClassicalShadowEstimation

qurry.process.classical_shadow.classical_shadow.mean_of_rho(shots: int, counts: list[dict[str, int]], random_unitary_um: dict[int, dict[int, Literal[0, 1, 2] | int]], selected_classical_registers: Iterable[int], rho_method: Literal['numpy', 'numpy_precomputed'] | str | Literal['numpy_flatten', 'jax_flatten'] = 'numpy_precomputed', pbar: tqdm | None = None) → ClassicalShadowMeanRho

Calculate the mean of Rho.

Reference:

Note

• Predicting many properties of a quantum system from very few measurements -

Huang, Hsin-Yuan and Kueng, Richard and Preskill, John [doi:10.1038/s41567-020-0932-7](

https://doi.org/10.1038/s41567-020-0932-7)

• The randomized measurement toolbox -

Elben, Andreas and Flammia, Steven T. and Huang, Hsin-Yuan and Kueng, Richard and Preskill, John and Vermersch, Benoît and Zoller, Peter [doi:10.1038/s42254-022-00535-2](

https://doi.org/10.1038/s42254-022-00535-2)

Parameters:

• shots (int) – The number of shots.

• counts (list[dict[str, int]]) – The list of the counts.

• random_unitary_um (dict[int, dict[int, Union[Literal[0, 1, 2], int]]]) – The shadow direction of the unitary operators.

• selected_classical_registers (list[int]) – The list of the index of the selected_classical_registers.

• rho_method (RhoMCoreMethod, optional) – The method to use for the calculation. Defaults to “numpy_precomputed”. It can be either “numpy”, “numpy_precomputed”, “jax_flatten”, or “numpy_flatten”. - “numpy”: Use Numpy to calculate the rho_m. - “numpy_precomputed”: Use Numpy to calculate the rho_m with precomputed values. - “numpy_flatten”: Use Numpy to calculate the rho_m with a flattening workflow. Currently, “numpy_precomputed” is the best option for performance.

• backend (PostProcessingBackendLabel, optional) – The backend for the postprocessing. Defaults to DEFAULT_PROCESS_BACKEND.

• pbar (Optional[tqdm.tqdm], optional) – The progress bar. Defaults to None.

Returns:

The expectation value of Rho.

Return type:

ClassicalShadowMeanRho

qurry.process.classical_shadow.classical_shadow.trace_rho_square(shots: int, counts: list[dict[str, int]], random_unitary_um: dict[int, dict[int, Literal[0, 1, 2] | int]], selected_classical_registers: Iterable[int], rho_method: Literal['numpy', 'numpy_precomputed'] | str | Literal['numpy_flatten', 'jax_flatten'] = 'numpy_precomputed', trace_method: Literal['trace_of_matmul', 'quick_trace_of_matmul', 'einsum_ij_ji'] | str | Literal['einsum_aij_bji_to_ab_numpy', 'einsum_aij_bji_to_ab_jax'] = 'einsum_aij_bji_to_ab_jax', pbar: tqdm | None = None) → ClassicalShadowPurity

Trace of Rho square.

Parameters:

• shots (int) – The number of shots.

• counts (list[dict[str, int]]) – The list of the counts.

• random_unitary_um (dict[int, dict[int, Union[Literal[0, 1, 2], int]]]) – The shadow direction of the unitary operators.

• selected_classical_registers (Iterable[int]) – The list of the index of the selected_classical_registers.

• rho_method (RhoMCoreMethod, optional) – The method to use for the calculation. Defaults to “numpy_precomputed”. It can be either “numpy”, “numpy_precomputed”, “jax_flatten”, or “numpy_flatten”. - “numpy”: Use Numpy to calculate the rho_m. - “numpy_precomputed”: Use Numpy to calculate the rho_m with precomputed values. - “numpy_flatten”: Use Numpy to calculate the rho_m with a flattening workflow. Currently, “numpy_precomputed” is the best option for performance.

• trace_method (TraceRhoMethod, optional) –

  The method to calculate the trace of Rho square. - “trace_of_matmul”:

  Use np.trace(np.matmul(rho_m1, rho_m2)) to calculate the each summation item in rho_m_list.

  • ”quick_trace_of_matmul” or “einsum_ij_ji”:

    Use np.einsum(“ij,ji”, rho_m1, rho_m2) to calculate the each summation item in rho_m_list.

  • ”einsum_aij_bji_to_ab_numpy”:

    Use np.einsum(“aij,bji->ab”, rho_m_list, rho_m_list) to calculate the trace.

• pbar (Optional[tqdm.tqdm], optional) – The progress bar. Defaults to None.

Returns:

The trace of Rho.

Return type:

float