In this paper, we consider the photoelectron counting distribution when the wave field incident on the detector is a mixture of harmonic signal and thermal noise. An expression for the factorial moment-generating function of the number of counts is obtained in terms of the eigenvalues of an associated integral equation. This expression is then used to evaluate the factorial cumulants of the number of counts. The results are valid for an arbitrary counting interval. The extension to photoelectron counting with several detectors is considered in paper II of the present investigation.In this paper, we consider the photoelectron counting distribution when the wave field incident on the detector is a mixture of harmonic signal and thermal noise. An expression for the factorial moment-generating function of the number of counts is obtained in terms of the eigenvalues of an associated integral equation. This expression is then used to evaluate the factorial cumulants of the number of counts. The results are valid for an arbitrary counting interval. The extension to photoelectron counting with several detectors is considered in paper II of the present investigation.

Physical Review AJul 1, 197042 citations

Dark counts of superconducting nanowire single-photon detector under illumination

Sijing Chen, Lixing You, Weijun Zhang +5 more

An abnormal increase in the SDE was observed for superconducting nanowire single-photon detectors (SNSPDs) when the bias current (I(b)) was close to the switching current (I(sw)). By introducing the time-correlated single-photon counting technique, we investigated the temporal histogram of the detection counts of an SNSPD under illumination. The temporal information helps us to distinguish photon counts from dark counts in the time domain. In this manner, the dark count rate (DCR) under illumination and the accurate SDE can be determined. The DCR under moderate illumination may be significantly larger than the conventional DCR measured without illumination under a high I(b), which causes the abnormal increase in the SDE. The increased DCR may be explained by the suppression of I(sw) under illumination.An abnormal increase in the SDE was observed for superconducting nanowire single-photon detectors (SNSPDs) when the bias current (I(b)) was close to the switching current (I(sw)). By introducing the time-correlated single-photon counting technique, we investigated the temporal histogram of the detection counts of an SNSPD under illumination. The temporal information helps us to distinguish photon counts from dark counts in the time domain. In this manner, the dark count rate (DCR) under illumination and the accurate SDE can be determined. The DCR under moderate illumination may be significantly larger than the conventional DCR measured without illumination under a high I(b), which causes the abnormal increase in the SDE. The increased DCR may be explained by the suppression of I(sw) under illumination.

arXiv:1504.04713Optics ExpressApr 17, 201530 citations

Tensor Decomposition for Non-Clifford Gate Minimization

Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta

Fault-tolerant quantum computation requires substantial resources for non-Clifford gates. Their count also enters exponentially into the runtime of several classical simulation methods. We present algebraic methods for minimizing the non-Clifford CCZ (Toffoli) count in {CNOT,CCZ} phase circuits using tensor decomposition over $\mathbb{F}_2$ . On standard cubic benchmarks, these methods match or improve prior automated Toffoli counts, with most instances optimized in under a minute on a single CPU. With additional computation, the decompositions provide effective initializations for existing T-count methods, improving T counts on several circuits. We also present algebraic methods for CNOT-count optimization at fixed Toffoli count. This gives competitive ancilla-free finite-field multiplication circuits and reduces the CNOT count of XOR AES S-box circuits.Fault-tolerant quantum computation requires substantial resources for non-Clifford gates. Their count also enters exponentially into the runtime of several classical simulation methods. We present algebraic methods for minimizing the non-Clifford CCZ (Toffoli) count in {CNOT,CCZ} phase circuits using tensor decomposition over $\mathbb{F}_2$. On standard cubic benchmarks, these methods match or improve prior automated Toffoli counts, with most instances optimized in under a minute on a single CPU. With additional computation, the decompositions provide effective initializations for existing T-count methods, improving T counts on several circuits. We also present algebraic methods for CNOT-count optimization at fixed Toffoli count. This gives competitive ancilla-free finite-field multiplication circuits and reduces the CNOT count of XOR AES S-box circuits.

quant-pharXiv:2602.15285Feb 18, 20260 citations

Two in one

Anonymous

PhysicsJan 31, 20110 citations

Neural Counting and Photon Counting in the Presence of Dead Time

Malvin Carl Teich, William J. McGill

The usual stimulus-based neural counting model for audition is found to be mathematically identical to the well-know semiclassical formalism for photon counting. In particular, we explicitly demonstrate the equivalence of McGill's noncentral negative binomial distribution and Pe\ifmmode \check{r}\else \v{r}\fi{}ina's multimode confluent hypergeometric distribution for a coherent signal imbedded in chaotic noise. Dead-time corrections, important both in neural counting and in photon counting, are incorporated in a generalized form of this distribution. Some specific implications of these results are discussed.The usual stimulus-based neural counting model for audition is found to be mathematically identical to the well-know semiclassical formalism for photon counting. In particular, we explicitly demonstrate the equivalence of McGill's noncentral negative binomial distribution and Pe\ifmmode \check{r}\else \v{r}\fi{}ina's multimode confluent hypergeometric distribution for a coherent signal imbedded in chaotic noise. Dead-time corrections, important both in neural counting and in photon counting, are incorporated in a generalized form of this distribution. Some specific implications of these results are discussed.

Physical Review LettersMar 29, 197634 citations

\mathbb{F}_2

. On standard cubic benchmarks, these methods match or improve prior automated Toffoli counts, with most instances optimized in under a minute on a single CPU. With additional computation, the decompositions provide effective initializations for existing T-count methods, improving T counts on several circuits. We also present algebraic methods for CNOT-count optimization at fixed Toffoli count. This gives competitive ancilla-free finite-field multiplication circuits and reduces the CNOT count of XOR AES S-box circuits.