Quantum_Measurement_Protocols

Code accompanying the manuscript Quantum and Classical Memory for Storage and Retrieval of Quantum Measurements by F. Turoboś, L. Marcinkowska and Z. Puchała.

The code computes every register size and success probability quoted in the manuscript: Tables 1, 2 and 4, Figure 1, and the numerical values in the text.

Reproduce the tables and the figure

pip install -r requirements.txt
python numerical_supplement/make_tables.py       # prints the rows of Tables 2 and 4 as LaTeX
python numerical_supplement/make_fig_qubits.py   # writes figures/fig_qubits_vs_N.pdf (Figure 1)

Tested in clean environments with Python 3.9 (numpy 1.24, pandas 2.0, matplotlib 3.7) and Python 3.12 (numpy 2.5, pandas 3.0, matplotlib 3.11).

Table 1 is the row $d=2$, $n=4$, $N=50$ of Table 2; Table 3 is symbolic. SciPy is not required. All combinatorics use exact integer arithmetic, and the maximum over outcome types is computed exactly by dynamic programming, without assuming log-concavity.

What calculations.py computes

function	quantity	manuscript
dim_direct, qubits_direct, classical_direct	uncompressed direct program	Proposition 14
K_D, K_D_littlewood	retained dimension $K_D(m)$, via the Weyl sum and via Littlewood's identity	Lemma 11, Eq. (14)
max_type_product, max_type_product_all	exact maximum over outcome types	—
qubits_direct_cq, classical_direct_cq	compressed direct program	Proposition 16
qubits_direct_rank1, qubits_direct_rank1_quantum	rank-one refinement, type kept classical / type in the quantum register	Proposition 18
dim_naimark_D, qubits_naimark	Naimark register for dilation dimension $D$	Theorem 36
dim_branch, qubits_branch_ppbt, classical_branch_table	branch program with a finite classical table	Theorem 41, Proposition 42
qubits_measured_branch, classical_measured_branch	measured-branch program, type kept classical	Proposition 43
qubits_measured_branch_quantum	measured-branch program, type in the quantum register	Corollary 44
success_*	heralded success probabilities	—

The remaining functions in calculations.py (generate_memory_sweep, comparison_summary, log_memory_*, …) come from earlier drafts. They compare uncompressed program dimensions and are not used for any result in the manuscript.

License

MIT (see LICENSE).