Quantum Noise Correlations Research Articles

Practical Trainable Temporal Postprocessor for Multistate Quantum Measurement

We develop and demonstrate a trainable temporal postprocessor (TPP) harnessing a simple but versatile machine learning algorithm to provide optimal processing of quantum measurement data subject to arbitrary noise processes for the readout of an arbitrary number of quantum states. We demonstrate the TPP on the essential task of qubit state readout, which has historically relied on temporal processing via matched filters in spite of their applicability for only specific noise conditions. Our results show that the TPP can reliably outperform standard filtering approaches under complex readout conditions, such as high-power readout. Using simulations of quantum measurement noise sources, we show that this advantage relies on the TPP’s ability to learn optimal linear filters that account for general quantum noise correlations in data, such as those due to quantum jumps, or correlated noise added by a phase-preserving quantum amplifier. Furthermore, we derive an exact analytic form for the optimal TPP weights: this positions the TPP as a linearly scaling generalization of matched filtering, valid for an arbitrary number of states under the most general readout noise conditions, all while preserving a training complexity that is essentially negligible in comparison with that of training neural networks for processing temporal quantum measurement data. The TPP can be autonomously and reliably trained on measurement data and requires only linear operations, making it ideal for field-programmable gate array implementations in circuit QED for real-time processing of measurement data from general quantum systems. Published by the American Physical Society 2024

Finite-temperature quantum noise correlations as a probe for topological helical edge modes

Finite-temperature quantum noise correlations as a probe for topological helical edge modes

Coherent Ising machines—Quantum optics and neural network Perspectives

A coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs), in which the “strongest” collective mode of oscillation at well above threshold corresponds to an optimum solution of a given Ising problem. When a pump rate or network coupling rate is increased from below to above threshold, however, the eigenvectors with the smallest eigenvalue of the Ising coupling matrix [Jij] appear near threshold and impede the machine to relax to true ground states. Two complementary approaches to attack this problem are described here. One approach is to utilize the squeezed/anti-squeezed vacuum noise of OPOs below threshold to produce coherent spreading over numerous local minima via quantum noise correlation, which could enable the machine to access either true ground states or excited states with eigen-energies close enough to that of ground states above threshold. The other approach is to implement a real-time error correction feedback loop so that the machine migrates from one local minimum to another during an explorative search for ground states. Finally, a set of qualitative analogies connecting the CIM and traditional computer science techniques are pointed out. In particular, belief propagation and survey propagation used in combinatorial optimization are touched upon.

Quantum Noise Correlations of an Optical Parametric Oscillator Based on a Nondegenerate Four Wave Mixing Process in Hot Alkali Atoms.

We present the first measurement of two-mode squeezing between the twin beams produced by a doubly resonant optical parameter oscillator (OPO) in an above threshold operation based on parametric amplification by nondegenerate four wave mixing with rubidium (^{85}Rb). We demonstrate a maximum intensity difference squeezing of -2.7 dB (-3.5 dB corrected for losses) with a pump power of 285mW and an output power of 12mW for each beam, operating close to the D1 line of Rb atoms. The use of open cavities combined with the high gain media can provide a strong level of noise compression and the access to new operation regimes that could not be explored by crystal based OPOs. The spectral bandwidth of the squeezed light is broadened by the cavity dynamics, and the squeezing level is robust for strong pump powers. Stable operation was obtained up to 4 times above the threshold. Moreover, operation of the OPO close to the atomic resonances of alkali atoms allows a natural integration into quantum networks, including structures such as quantum memories.

Efficient learning of quantum noise

Noise is the central obstacle to building large-scale quantum computers. Quantum systems with sufficiently uncorrelated and weak noise could be used to solve computational problems that are intractable with current digital computers. There has been substantial progress towards engineering such systems1–8. However, continued progress depends on the ability to characterize quantum noise reliably and efficiently with high precision9. Here, we describe such a protocol and report its experimental implementation on a 14-qubit superconducting quantum architecture. The method returns an estimate of the effective noise and can detect correlations within arbitrary sets of qubits. We show how to construct a quantum noise correlation matrix allowing the easy visualization of correlations between all pairs of qubits, enabling the discovery of long-range two-qubit correlations in the 14-qubit device that had not previously been detected. Our results are the first implementation of a provably rigorous and comprehensive diagnostic protocol capable of being run on state-of-the-art devices and beyond. These results pave the way for noise metrology in next-generation quantum devices, calibration in the presence of crosstalk, bespoke quantum error-correcting codes10 and customized fault-tolerance protocols11 that can greatly reduce the overhead in a quantum computation. A protocol for the reliable, efficient and precise characterization of quantum noise is reported and implemented in an architecture consisting of 14 superconducting qubits. Correlated noise within arbitrary sets of qubits can be easily detected.

Transmission of Classical Information Over Noisy Quantum Channels–A Spectrum Approach

Based upon the Fluctuation-Dissipation Theorem of Nyquist-Callen-Welton and the spectrum balancing relationship of Kubo-Martin-Schwinger for operator-valued stochastic noise processes, a two-parameter Quantum Noise-Energy Spectral Density (QN-ESD) is constructed and Fourier-Laplace transformed to obtain its associated Quantum Noise-Autocorrelation Function (QN-ACF). By means of a Taylor series expansion, the quantum thermal noise correlations are linked to Number Theory's Reimann-Zeta function. From this perspective, a panoply of spectral components and their QN correlations are characterized for three disjoint regions located across the Electromagnetic Spectrum (EMS). The second-moment characterizations and frequency boundaries for each region are specified as a function of two frequency dependent design parameters, viz., a normalized temperature dependent frequency and a quantum receiver cutoff frequency. These boundaries define where the quadrature noise correlation projections of the QN-ESD become noticeably asymmetric-in-frequency. For the operator-valued white quantum noise region, various communication system performance metrics are characterized and their limits are presented and compared via interconnecting parameter relations to their classical communications (CC) counterparts. These metrics include Shannon's non-additive, but regularized, zero-error capacity in bits/photon-pair, bits/photon, bits/channel-use and bits/sec, the spectral efficiency in bits/sec/Hz and the error-correcting code rate. For long coded messages, Shannon's capacity quadrature approaches 2π√5/ ln(2) ≈ 20 bits/photon-pair or (10 bits/photon) while for single-photon per channel use transmission it approaches 3 bits/photon-pair. Results are graphically illustrated for the quantum noise spectral density, quantum noise correlations, Shannon's Î-Q̂ capacities and spectral efficiency.

The dynamics and prethermalization of one-dimensional quantum systems probed through the full distributions of quantum noise

Quantum noise correlations have been employed in several areas of physics, including condensed matter, quantum optics and ultracold atoms, to reveal the non-classical states of the systems. To date, such analyses have mostly focused on systems in equilibrium. In this paper, we show that quantum noise is also a useful tool for characterizing and studying the non-equilibrium dynamics of a one-dimensional (1D) system. We consider the Ramsey sequence of 1D, two-component bosons, and obtain simple, analytical expressions for time evolutions of the full distribution functions for this strongly correlated, many-body system. The analysis can also be directly applied to the evolution of interference patterns between two 1D quasi-coindensates created from a single condensate through splitting. Using the tools developed in this paper, we demonstrate that 1D dynamics in these systems exhibits the phenomenon known as ‘prethermalization’, where the observables of non-equilibrium, long-time transient states become indistinguishable from those of thermal equilibrium states.

An efficient source of continuous variable polarization entanglement

We have experimentally demonstrated the efficient creation of highly entangled bipartite continuous variable polarization states. Exploiting an optimized scheme for the production of squeezing using the Kerr non-linearity of a glass fibre we generated polarization squeezed pulses with a mean classical excitation in . Polarization entanglement was generated by interfering two independent polarization squeezed fields on a symmetric beam splitter. The resultant beams exhibit strong quantum noise correlations in the dark polarization plane. To verify entanglement generation, we characterized the quantum correlations of the system for two different sets of conjugate Stokes parameters. The quantum correlations along the squeezed and the anti-squeezed Stokes parameters were observed to be −4.1±0.3 and −2.6±0.3 dB below the shot noise level, respectively. The degree of correlations was found to depend critically on the beam-splitting ratio of the entangling beam splitter. Carrying out measurements on a different set of conjugate Stokes parameters, correlations of −3.6±0.3 and −3.4±0.3 dB have been observed. This result is more robust against asymmetries in the entangling beam splitter, even in the presence of excess noise.

A pulsed source of continuous variable polarization entanglement

We have experimentally demonstrated polarization entanglement using continuous variables in an ultra-short pulsed laser system at telecommunication wavelengths. Exploiting the Kerr-nonlinearity of a glass fibre we generated a polarization squeezed pulse with S2 the only non-zero Stokes parameter thus S1 and S3 being the conjugate pair. Polarization entanglement was generated by interference of the polarization squeezed field with a vacuum on a 50:50 beam splitter. The two resultant beams exhibit strong quantum noise correlations in S1 and S3. The sum noise signal of S3 was at the respective shot noise level and the difference noise signal of S1 fell 2.9dB below this value.

The extended phase space: a formalism for the study of quantum noise and quantum correlations

Extended Wigner and extended Weyl functions which are quartic functions of the wavefunction are introduced and their properties are studied. They provide an insight into the connection between quantum noise and quantum correlations. The general theory is applied to the examples of coherent states and thermal states. The construction of the extended Wigner function from quantum tomography experiments is also discussed and exemplified for the cases of superposition and also for a mixture of two coherent states.

Stochastic approach to inflation. II. Classicality, coarse graining, and noises

In this work we generalize a previously developed semiclassical approach to inflation, devoted to the analysis of the effective dynamics of coarse-grained fields, which are essential to the stochastic approach to inflation. We consider general non-trivial momentum distributions when defining these fields. The use of smooth cutoffs in momentum space avoids highly singular quantum noise correlations and allows us to consider the whole quantum noise sector when analyzing the conditions for the validity of an effective classical dynamical description of the coarse-grained field. We show that the weighting of modes has physical consequences, and thus cannot be considered as a mere mathematical artifact. In particular we discuss the exponential inflationary scenario and show that colored noises appear with cutoff dependent amplitudes.

Measurement of quantum-noise correlations in parametric image amplification

We demonstrate quantum-noise correlations between the spatial frequencies of a parametrically amplified signal image and the generated conjugate (idler) image. Test images were amplified by an optical parametric amplifier that can be operated either as a low-pass or a band-pass amplifier for spatial frequencies. Direct difference detection of the signal and idler spatial frequencies at +- 16 mm{;{-1}} resulted in noise that fell below the shot-noise level by approx. 5 dB. Parametric-gain and phase-mismatch dependence of the observed quantum-noise reduction is in good agreement with the theory of a spatially-broadband optical parametric amplifier.

Enhancement in quantum noise correlation between the two outputs of a nondegenerate optical amplifier with a non-vacuum state idler input

The theoretical limit of the noise correlation between the signal and idler outputs of a nondegenerate optical parametric amplifier (NOPA) with a coherent state signal and vacuum state idler input can be enhanced if a non-vacuum coherent state idler input is employed. By choosing a balanced signal and idler input, the noise correlation is $1/{({\root}g + {\root}{g-1})}^2$ , where g is the intensity gain of the NOPA, and that is superior to the prediced outputs with single signal input by approximately 3dB. The result is applicable to all the schemes that use the NOPA to produce a sub-shot noise light generation such as feed-back or feed-forward control.

Use of quantum-noise correlation for noise reduction in semiconductor lasers.

Both the junction voltage fluctuations and the frequency fluctuations of a semiconductor laser are highly correlated with its intensity noise. We analyze three schemes where the correlation information is used to reduce the intensity noise. In conventional semiconductor lasers, starting with intensity noise at the standard quantum limit, ideally 3-dB amplitude squeezing is possible. The influence of nonideal factors such as parasitics for junction voltage feedforward and the linewidth floor for frequency noise feedforward are discussed. It is shown that under certain conditions the number-phase uncertainty can reach the ultimate limit set by Heisenberg's uncertainty principle. These conditions are clarified, and examples are given for both conventional semiconductor lasers and microcavity lasers.

Squeezing and quantum noise correlations in dispersive two-photon optical bistability

Presents an analysis of a two-photon double-beam bistable device, in the dispersive and high-finesse limits. The expressions for the mean fields inside the cavity are given above the destabilization thresholds, and quantum fluctuations of the outcoming fields are analyzed below these thresholds. It appears that this device yields several new quantum noise reduction schemes, which are closely related to the mean fields behaviour.

Local calculation of black hole radiance

We show that, by calculating the quantum noise correlation function with a point splitting technique, one can obtain the Planck spectrum of black hole radiation.