Quantum random number generation (QRNG) harnesses the inherent indeterminacy of quantum processes to produce truly unpredictable random sequences. True randomness, not the pseudo-random approximations that deterministic algorithms afford, is a non-negotiable requirement in cryptographic key generation, secure protocol design, and Monte Carlo simulation. Quantum random number generators (QRNGs) address this directly, tracing randomness back to quantum measurement outcomes of quantum systems rather than computational hardness assumptions. We report here on a Michelson interferometer QRNG realised as an 8-qubit circuit simulation within the Qiskit/Aer environment, where bit values are sampled from the interferometric output distribution rather than inferred indirectly from hardware counters. Operating at the quadrature point — the phase condition under which <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$P(|1\rangle ) = \sin ^{2}(\varphi _{\textrm{eff}}/2) \approx 0.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi>P</mi> <mrow> <mo stretchy="false">(</mo> <mo stretchy="false">|</mo> <mn>1</mn> <mo stretchy="false">⟩</mo> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> </mrow> <msup> <mo>sin</mo> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msub> <mi>φ</mi> <mtext>eff</mtext> </msub> <mo stretchy="false">/</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mo>≈</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation> — each qubit contributes maximally to the output entropy. Phase noise, inevitable in any real laser source, was incorporated as a Wiener process with 1 MHz linewidth; a power-variance sweep then fixed the working point at the peak quantum signal-to-noise ratio (QSNR), above which classical noise begins to erode the entropy budget. The raw bit stream is biased by residual phase drift, and Von Neumann unbiasing corrects this at a cost of roughly half the bits — an acceptable trade given the generation rate. Randomness extraction against the Leftover Hash Lemma bound was carried out using a Toeplitz matrix applied via FFT convolution, keeping both time (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$O(n \log n)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>log</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>) and memory (O(n)) costs modest even at scale. Against the NIST SP 800-22 battery — 50 sequences, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$10^{6}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mn>6</mn> </msup> </math></EquationSource> </InlineEquation> bits each — the generator returned clean passes across all 15 tests, with the weakest category still clearing the threshold at 48/50. At <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\varepsilon = 10^{-6}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, the Leftover Hash Lemma safety margin sits above <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$3.9 \times 10^{6}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.9</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> bits, a figure that is not merely reassuring on paper but places the system within the formal security definitions relevant to real deployment. That the system passes at this level without dedicated hardware points to something worth noting — physical realism in the model matters more than implementation complexity.

Interferometric Quantum Random Number Generation via Michelson Configuration

期刊论文
发表日期：

2026年6月2日

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Ram Soorat,
Aakash Chilakamarri,
Priyanka,
Barath Sai Kumar Jakkuva,
Syed Areebuddin

摘要

Quantum random number generation (QRNG) harnesses the inherent indeterminacy of quantum processes to produce truly unpredictable random sequences. True randomness, not the pseudo-random approximations that deterministic algorithms afford, is a non-negotiable requirement in cryptographic key generation, secure protocol design, and Monte Carlo simulation. Quantum random number generators (QRNGs) address this directly, tracing randomness back to quantum measurement outcomes of quantum systems rather than computational hardness assumptions. We report here on a Michelson interferometer QRNG realised as an 8-qubit circuit simulation within the Qiskit/Aer environment, where bit values are sampled from the interferometric output distribution rather than inferred indirectly from hardware counters. Operating at the quadrature point — the phase condition under which $P(|1\rangle ) = \sin ^{2}(\varphi _{\textrm{eff}}/2) \approx 0.5$ $P (| 1 ⟩) = {sin}^{2} (φ_{eff} / 2) \approx 0.5$ — each qubit contributes maximally to the output entropy. Phase noise, inevitable in any real laser source, was incorporated as a Wiener process with 1 MHz linewidth; a power-variance sweep then fixed the working point at the peak quantum signal-to-noise ratio (QSNR), above which classical noise begins to erode the entropy budget. The raw bit stream is biased by residual phase drift, and Von Neumann unbiasing corrects this at a cost of roughly half the bits — an acceptable trade given the generation rate. Randomness extraction against the Leftover Hash Lemma bound was carried out using a Toeplitz matrix applied via FFT convolution, keeping both time ( $O(n \log n)$ $O (n log n)$ ) and memory (O(n)) costs modest even at scale. Against the NIST SP 800-22 battery — 50 sequences, $10^{6}$ $10^{6}$ bits each — the generator returned clean passes across all 15 tests, with the weakest category still clearing the threshold at 48/50. At $\varepsilon = 10^{-6}$ $ε = 10^{- 6}$ , the Leftover Hash Lemma safety margin sits above $3.9 \times 10^{6}$ $3.9 \times 10^{6}$ bits, a figure that is not merely reassuring on paper but places the system within the formal security definitions relevant to real deployment. That the system passes at this level without dedicated hardware points to something worth noting — physical realism in the model matters more than implementation complexity.