Quantum Signal Research Articles

Deterministic construction of unimodular tight frames consisting orthogonal blocks via block preserving operators

A highly redundant incoherent unimodular tight frame (UMTF) finds desirability across various fields, including quantum communications and signal processing. Incorporating a larger number of orthogonal blocks into such a UMTF yields advantages, especially in domains like image compression and wireless communications. Despite their valuable utility, constructions of these frames are exceedingly rare. Moreover, in most of such existing UMTFs, the number of orthogonal blocks is in the order of the frame vectors dimension. This paper focuses on a deterministic construction of incoherent UMTFs consisting of a large number of orthogonal blocks using combinatorial design. Further, we illustrate that the computational complexity for constructing the stated frame is lower compared to the existing methods. Additionally, we show that our proposed construction yields comparable results in sparse and block sparse signal recovery compared to the existing methods and outperforms the partial discrete Fourier transform matrix. Furthermore, empirical findings highlight that images reconstructed using our construction exhibit higher structural similarity index measure values in comparison with other existing methods.

Efficient Cryogenic Nonlinear Conversion Processes in Periodically‐Poled Thin‐Film Lithium Niobate Waveguides

AbstractPeriodically poled thin‐film lithium niobate (TFLN) waveguides, which enable efficient quadratic nonlinear processes, serve as crucial foundation for classical and quantum signal processing. To expand their application scope, the first investigation of nonlinear conversion processes in periodically poled TFLN waveguides at cryogenic conditions (7 K) is provided. Through systematic experimental characterization, it is found that the periodically poled TFLN waveguide retains its high conversion efficiency at both cryogenic and room temperatures for both classical second‐harmonic generation and quantum photon‐pair generation processes. Particularly, the photon‐pair source at cryogenic conditions shows high brightness (≈8 MHz µW−1) and broad bandwidth (>100 THz). These results demonstrate the significant potential of TFLN wavelength conversion devices for cryogenic applications and foster future scalable quantum photonic systems.

Counting collisions in random circuit sampling for benchmarking quantum computers

We show that counting the number of collisions (re-sampled bitstrings) when measuring a random quantum circuit provides a practical benchmark for the quality of a quantum computer and a quantitative noise characterization method. We analytically estimate the difference in the expected number of collisions when sampling bitstrings from a pure random state and when sampling from the classical uniform distribution. We show that this quantity, if properly normalized, can be used as a collision anomaly benchmark or as a collision volume test, which is similar to the well-known quantum volume test, with advantages (no classical computing cost) and disadvantages (high sampling cost). We also propose to count the number of cross-collisions between two independent quantum computers running the same random circuit in order to obtain a cross-validation test of the two devices. Finally, we quantify the sampling cost of quantum collision experiments. We find that the sampling cost for running a collision volume test on state-of-the-art processors (e.g., 20 effective clean qubits) is quite small: less than 105 shots. For large-scale experiments in the quantum supremacy regime, the required number of shots for observing a quantum signal in the observed number of collisions is currently infeasible (>1012), but not completely out of reach for near-future technology.

Comment on "Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle"

Multivariable Quantum Signal Processing (M-QSP) \cite{Rossi2022multivariable} is expected to provide an efficient means to handle polynomial transformations of multiple variables simultaneously. However, we identified several inconsistencies in the main theorem, where necessary and sufficient conditions for achievable polynomials are provided, and its proof in Ref. \cite{Rossi2022multivariable}. Moreover, a counterexample to the conjecture in Ref. \cite{Rossi2022multivariable}, based on which the main theorem is constructed, is presented in Ref. \cite{n^^c3^^a9meth2023variants}, meaning the requirement of the conjecture should be included as a condition in the theorem. Here we note our observations and propose the revised necessary conditions for M-QSP. We also show that these necessary conditions cannot be sufficient conditions, and thus some additional condition on top of these revisions is essentially required for the complete M-QSP theorem.

Innovative Applications of Quantum Signal Processing in Network Security and Image Processing

Innovative Applications of Quantum Signal Processing in Network Security and Image Processing

Estimating the link budget of satellite-based Quantum Key Distribution (QKD) for uplink transmission through the atmosphere

Satellite-based quantum communications including quantum key distribution (QKD) represent one of the most promising approaches toward global-scale quantum communications. To determine the viability of transmitting quantum signals through the atmosphere, it is essential to conduct atmospheric simulations for both uplink and downlink quantum communications. In the case of the uplink scenario, the initial phase of the beam’s propagation involves interaction with the atmosphere, making simulation particularly critical. To analyze the atmosphere over the Indian subcontinent, we begin by validating our approach by utilizing atmospheric data obtained from the experiments carried out in the Canary Islands within the framework of Quantum Communication (QC). We also verify our simulation methodology by reproducing simulation outcomes from diverse Canadian locations, taking into account both uplink and downlink scenarios in Low Earth Orbit (LEO). In this manuscript, we explore the practicality of utilizing three different ground station locations in India for uplink-based QC, while also considering beacon signals for both uplink and downlink scenarios. The atmospheric conditions of various geographical regions in India are simulated, and a dedicated link budget analysis is performed for each location, specifically focusing on three renowned observatories: IAO Hanle, Aries Nainital, and Mount Abu. The analysis involves computing the overall losses of the signal and beacon beams. The findings indicate that the IAO Hanle site is a more suitable choice for uplink-based QC when compared to the other two sites.

Hybrid quantum key distribution: A novel approach for secure end-to-end communication in network infrastructure

The Quantum Key Distribution (QKD) network approach has emerged as a promising solution and has garnered significant interest across various domains. QKD networks can be broadly categorized into two main types: those based on measurement-device-dependent (MDD) protocols and those based on measurement-device-independent (MDI) protocols. A novel network scheme is proposed combining these two protocols to guarantee end-to-end secure communication. It comprises two interconnected networks — the first uses a measurement-device-dependent protocol to connect routers with nearby nodes, while the second employs a measurement-device-independent protocol to interconnect the routers. In the first network, the process begins with Alice (Router) generating two types of weak quantum signals — the first has intensity, frequency and polarization or phase randomly varied, while the second with different delay times. Alice randomly transmits either signal states carrying information or decoy states with varying properties to the receivers (Bobs) over the quantum channels. She also sends a synchronization signal along with the quantum signals. At the receiver end, the synchronization pulse timestamps the incoming quantum signals. Each Bob then randomly shifts the frequencies of the received signals and measures their phase/polarization of the first signal and measures the delay times of the second signal. The secret key is derived by combining the frequency, the delay time and the phase/polarization information of the quantum signals, resulting in longer key lengths. Encoding information across multiple degrees of freedom enables extended key generation for secure communication. However, between the routers, MDI-QKD protocols are used to securely share the keys. This hybrid approach aims to ensure secure end-to-end communication across the network.

Magnetic bilayer qubits: A bipartite quantum system

An exfoliated monolayer CrI3 possessing the ferromagnetic (FM) nature of out-of-plane Ising spin-up (or spin-down) electrons can be considered as a qubit with a quantum state of |ѱ>=|↑>=|0> (or |ѱ>=|↓>=|1>) due to the theory of the Bloch sphere. Therefore, here a bipartite quantum system of the antiferromagnetic (AFM) and FM bilayer CrI3 is proposed for four fundamental two-qubit (2Q) quantum states (≡|ѱѱ>) of |↑↓>=|01>, |↓↑>=|10>, |↑↑>=|00> and |↓↓>=|11>, respectively. Energy-resolved magnetic circular dichroism (MCD) spectropolarimetry was used to detect d-d transitions of the FM and AFM bilayer CrI3 for the four fundamental quantum states. The obtained MCD spectra of the d-d transitions with spin-frustration and spin-parallelism possess quantum signals of the four fundamental 2Q quantum states at θB = 0, where θB is the angle between the magnetic field and the surface normal. Hence, the bilayer CrI3 is a potential candidate for use in quatum computer.

Encoding of linear kinetic plasma problems in quantum circuits via data compression

We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation $\boldsymbol {A}{\boldsymbol{\psi} } = \boldsymbol {b}$ to be solved by using the quantum signal processing algorithm. The latter requires encoding of matrix $\boldsymbol {A}$ in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode $\boldsymbol {A}$ in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.

Single-shot Quantum Signal Processing Interferometry

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

Quantum and coherent signal transmission on a single-frequency channel via the electro-optic serrodyne technique.

Fiber-optical networks are well established to accommodate global data traffic via coherent information transmission. The next generation of telecommunications will require the integration of quantum information into fiber-optic networks, e.g., for quantum key distribution. A promising and scalable route to enable quantum networking is encoding quantum information into the frequency of photons. While the cointegration of frequency-entangled photons with coherent information transmission is achieved via spectral multiplexing, more resource-efficient approaches are required. In this work, we introduce and experimentally demonstrate a transceiver concept that enables the transmission of coherent and frequency-entangled photons over a single-frequency channel. Our concept leverages the serrodyne technique via electro-optic phase modulation leading to very different dynamics for entangled and coherent photons. This enables temporal multiplexing of the respective signals. We demonstrate the preservation of entanglement over the channel in the presence of coherent light. Our approach reveals a strong potential for efficient bandwidth use in hybrid networks.

The exact solutions for the fractional Riemann wave equation in quantum mechanics and optics

In this paper, the fractional Riemann wave equation with M-truncated derivative (FRWE-MTD) is considered. The Jacobi elliptic function method and the modified extended tanh function method are applied to acquire new elliptic, rational, hyperbolic, and trigonometric functions solutions. Moreover, we expand some earlier studies. The obtained solutions are important in explaining some exciting physical phenomena, since the Riemann wave equation is used in various fields, including quantum mechanics, optics, signal processing, and general relativity. Also, this equation is used to describe the propagation of waves in various dispersive systems, where wave motion is affected by the medium through which it travels. Several 3D and 2D graphs are shown to demonstrate how the M-truncated derivative affects the exact solutions of the FRWE-MTD.

Optical attenuator-oriented quantum hacking on continuous-variable quantum key distribution with local local oscillator

Continuous-variable quantum key distribution with local local oscillator (LLO-CVQKD) eliminates the security loophole caused by transmitting high power local oscillator (LO). However, in order to establish a common phase frame between the sender and receiver, a low power phase reference needs to be transmitted with quantum signals, which may bring in new security problems for eavesdroppers to obtain information illegally. Especially in trusted phase noise model, phase noise associated with detectors is regarded as trusted noise in order to obtain a higher secret key rate and transmission distance, which further provides opportunities for eavesdroppers. To this end, we propose an optical attenuator-oriented attack strategy against the LLO-CVQKD system under the trusted phase noise model, where Eve can inject suitable light into the optical attenuator in reference light path to reduce the attenuation level of it, thereby controlling the intensity of the reference pulses and resulting in an underestimated excess noise. Simulation results show that the proposed attack strategy can render the estimated secret key rate much higher than the actual values. When the transmission distance exceeds 25 km, the eavesdropper can obtain approximately 90% of the key information by adjusting the intensity of the reference pulses to twice the original value.

A chip-integrated homodyne detection system with enhanced bandwidth performance for quantum applications

The rapid development of quantum technology has driven the need for high-performance quantum signal processing modules. Balanced homodyne detector (BHD) is one of the most promising options for practical quantum state measurement, providing substantial advantages of cost-effectiveness, no cooling requirement, and system compactness. However, due to the stringent requirements in BHD design, it typically suffers from a relatively small operating bandwidth which limits the overall speed of a quantum system. In this study, we propose comprehensive modelling for the BHD in quantum applications and enhance the performance of BHDs based on our modelling. Specifically, we utilise a photonic chip approach and optimise the electronic design to create the integrated BHD, which significantly boosts the 3 dB bandwidth to 4.75 GHz and achieves a shot-noise-limited bandwidth of 23 GHz. We demonstrate the capability of this setup to generate quantum random numbers at a rate of 240 Gbit s−1, highlighting its potential for ultra-high-speed quantum communication and quantum cryptography applications.

Doubling the efficiency of Hamiltonian simulation via generalized quantum signal processing

Doubling the efficiency of Hamiltonian simulation via generalized quantum signal processing

100-km entanglement distribution with coexisting quantum and classical signals in a single fiber

The development of prototype metropolitan-scale quantum networks is underway and entails transmitting quantum information via single photons through deployed optical fibers spanning several tens of kilometers. The major challenges in building metropolitan-scale quantum networks are compensation for polarization fluctuation, high-precision clock synchronization, and compensation for cumulative transmission time fluctuations. One approach addressing these challenges is to copropagate classical probe signals in the same fiber as the quantum signal. Thus, both signals experience the same conditions, and the changes of the fiber can therefore be monitored and compensated. Here, we demonstrate the distribution of polarization-entangled quantum signals copropagating with the White Rabbit precision time protocol classical signals in the same single-core fiber strand at metropolitan-scale distances. Our results demonstrate the feasibility of this quantum-classical coexistence by achieving high-fidelity entanglement distribution between nodes separated by 100 km of optical fiber. This advancement is a significant step towards the practical implementation of robust and efficient metropolitan-scale quantum networks.

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that |P|≤1, a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 107. We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ-approximate fractional query problem that requires O((1/δ)+log(1/ϵ)) queries to perform where O(1/δ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O(dlogN+log2N) 1 and 2-qubit gates for a filter of lengths d. Published by the American Physical Society 2024

Quantum signal processing and nonlinear Fourier analysis

Elucidating a connection with nonlinear Fourier analysis (NLFA), we extend a well known algorithm in quantum signal processing (QSP) to represent measurable signals by square summable sequences. Each coefficient of the sequence is Lipschitz continuous as a function of the signal.

Analyzing Quantum Error Resilience for Quantum Communication in Guided and Unguided Media

AbstractThis research examines quantum key distribution and its applications in guided and unguided quantum communication. The importance of secure communication in the quantum era requires a thorough exploration of both guided and unguided quantum communication strategies. The research aims to address the challenges posed by guided channels, such as fiber optics, and unguided channels, such as free‐space quantum communication. This study addresses existing knowledge gaps in quantum error resilience management and signal processing techniques in unguided quantum communication. Advanced quantum gate analysis, environmental noise analysis, and quantum channel modeling techniques are employed. The research presents key findings on the impact of gate imperfections on quantum error resilience in guided media, the influence of noise‐induced errors in unguided media, and a unified metric for assessing various error sources in guided channels. Additionally, the study analyses stabilizer codes and surface codes for error mitigation through quantum error correction strategies. Simulation results provide a benchmark for theoretical predictions and guide the refinement of quantum communication protocols. In this context, machine learning‐based error prediction is introduced as a cutting‐edge approach to enhance the robustness of quantum communication systems.

Optimized Recovery of the Frequency of Repetition of a Satellite Quantum Signal

Optimized Recovery of the Frequency of Repetition of a Satellite Quantum Signal