Quantum Systems Research Articles

A General Strategy for Improving the Performance of PINNs -- Analytical Gradients and Advanced Optimizers in the NeuralSchrödinger Framework

In this work, the previously introduced NeuralSchrödinger PINN is extended towards the use of analytical gradient expressions of the loss function. It is shown that the analytical gradients derived in this work increase the convergence properties for both the BFGS and ADAM optimizers compared to the previously employed numerical gradient implementation. In addition, the use of parallelised GPU computations via CUDA greatly increased the computational performance over the previous implementation using single-core CPU computations. As a consequence, an extension of the NeuralSchrödinger PINN towards two-dimensional quantum systems became feasible as also demonstrated in this work.

Quantitative Analogue Simulation of Planar Molecules.

Synthetic quantum systems provide a pathway for exploring the physics of complex quantum matter in a programmable fashion. This approach becomes particularly advantageous when it comes to systems that are thermodynamically unfavorable. By sculpting the potential landscape of Cu(111) surfaces with carbon monoxide quantum corrals in a cryogenic scanning tunneling microscope, we created analogue simulators of planar organic molecules, including antiaromatic and non-Kekulé species that are generally reactive or unstable. Spectroscopic imaging of such synthetic molecules reveals close replications of molecular orbitals obtained from ab initio calculations of the organic molecules. We further illustrate the quantitative nature of such analogue simulators by faithful extraction of bond orders and global aromaticity indices, which are otherwise technically daunting using real molecules. Our approach therefore sets the stage for new research frontiers pertaining to the quantum physics and chemistry of designer nanostructures.

Efficiency of neural-network state representations of one-dimensional quantum spin systems

Neural-network state representations of quantum many-body systems are attracting great attention and more rigorous quantitative analysis of their expressibility and complexity is warranted. Our analysis of the restricted Boltzmann machine (RBM) state representation of one-dimensional (1D) quantum spin systems provides new insight into their computational complexity. We define a class of long-range-fast-decay (LRFD) RBM states with quantifiable upper bounds on truncation errors and provide numerical evidence for a large class of 1D quantum systems that may be approximated by LRFD RBMs of at most polynomial complexities. These results lead us to conjecture that the ground states of a wide range of quantum systems may be exactly represented by LRFD RBMs or a variant of them, even in cases where other state representations become less efficient. At last, we provide the relations between multiple typical state manifolds. Our work proposes a paradigm for doing complexity analysis for generic long-range RBMs which naturally yields a further classification of this manifold. This paradigm and our characterization of their nonlocal structures may pave the way for understanding the natural measure of complexity for quantum many-body states described by RBMs and are generalizable for higher-dimensional systems and deep neural-network quantum states. Published by the American Physical Society 2024

Principle of Information Increase: An Operational Perspective on Information Gain in the Foundations of Quantum Theory

A measurement performed on a quantum system is an act of gaining information about its state. However, in the foundations of quantum theory, the concept of information is multiply defined, particularly in the area of quantum reconstruction, and its conceptual foundations remain surprisingly under-explored. In this paper, we investigate the gain of information in quantum measurements from an operational viewpoint in the special case of a two-outcome probabilistic source. We show that the continuous extension of the Shannon entropy naturally admits two distinct measures of information gain, differential information gain and relative information gain, and that these have radically different characteristics. In particular, while differential information gain can increase or decrease as additional data are acquired, relative information gain consistently grows and, moreover, exhibits asymptotic indifference to the data or choice of Bayesian prior. In order to make a principled choice between these measures, we articulate a Principle of Information Increase, which incorporates a proposal due to Summhammer that more data from measurements leads to more knowledge about the system, and also takes into consideration black swan events. This principle favours differential information gain as the more relevant metric and guides the selection of priors for these information measures. Finally, we show that, of the symmetric beta distribution priors, the Jeffreys binomial prior is the prior that ensures maximal robustness of information gain for the particular data sequence obtained in a run of experiments.

A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems

We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate Γ of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues {λα}α=1n of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size n→∞ it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of λ’s at each time t and for each size n. Two relevant regimes emerge: at short times tΓ=O(1), the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the n→∞ limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times tΓ=O(n), one enters instead a regime in which the eigenvalues are exponentially separated log(λα/λβ)=O(Γt/n), but fluctuations ∼O(Γt/n) play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime.

Non‐Markovian Cost Function for Quantum Error Mitigation

Non‐Markovian Cost Function for Quantum Error Mitigation

Multiparameter critical quantum metrology with impurity probes

Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin- 12 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular—even though the parameters to be estimated are independent—resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters.

Generation of true quantum random numbers with on-demand probability distributions via single-photon quantum walks

Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required “coin” parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.

Measurement-induced transitions beyond Gaussianity: A single particle description

Repeated measurements can induce entanglement phase transitions in the dynamics of quantum systems. Interacting models, both chaotic and integrable, generically show a stable volume-law entangled phase at low measurement rates that disappears for free, Gaussian fermions. Interactions break the Gaussianity of a dynamical map in its unitary part, but non-Gaussianity can be introduced through measurements as well. By comparing the entanglement and non-Gaussianity structure of different protocols, we propose a single particle indicator of the measurement-induced phase transition, and we use it to argue in favor of the stability of the transition when non-Gaussianity is purely provided by measurements. Published by the American Physical Society 2024

Efficient multimode Wigner tomography.

Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales exponentially with the number of modes in both computational and experimental measurement requirement, which becomes prohibitive as the system size increases. Here, we implement a state reconstruction method whose sampling requirement instead scales polynomially with system size, and thus mode number, for states that can be represented within such a polynomial subspace. We demonstrate this improved scaling with Wigner tomography of multimode entangled W states of up to 4 modes on a 3D circuit quantum electrodynamics (cQED) system. This approach performs similarly in efficiency to existing matrix inversion methods for 2 modes, and demonstrates a noticeable improvement for 3 and 4 modes, with even greater theoretical gains at higher mode numbers.

Entangled states dynamics of moving two-level atoms in a thermal field bath

Abstract We consider a two-level atom that follows a wordline of constant velocity, while interacting with a massless scalar field in a thermal state through: (i) an Unruh-DeWitt coupling, and (ii) a coupling that involves the time derivative of the field. We treat the atom as an open quantum system, with the field playing the role of the environment, and employ a master equation to describe its time evolution. We study the dynamics of entanglement between the moving atom and a (auxiliary) qubit at rest and isolated from the thermal field. We find that in the case of the standard Unruh-DeWitt coupling and for high temperatures of the environment the decay of entanglement is delayed due to the atom's motion. Instead, in the derivative coupling case, the atom's motion always causes the rapid death of entanglement.

All-optical spin access via a cavity-broadened optical transition in on-chip hybrid quantum photonics

Hybrid quantum photonic systems connect classical photonics to the quantum world and promise to deliver efficient light-matter quantum interfaces while leveraging the advantages of both, the classical and the quantum, subsystems. However, combining efficient, scalable photonics and solid-state quantum systems with desirable optical and spin properties remains a formidable challenge. In particular, the access to individual spin states and coherent mapping to photons remains unsolved for hybrid systems. In this paper, we demonstrate all-optical initialization and readout of the electron spin of a negatively charged silicon-vacancy center in a nanodiamond coupled to a silicon nitride photonic crystal cavity. We characterize relevant parameters of the coupled emitter-cavity system and determine the silicon-vacancy center’s spin-relaxation and spin-decoherence rate. Our results mark a key step towards the realization of a hybrid spin-photon interface based on silicon nitride photonics and the silicon-vacancy center’s electron spin in nanodiamonds with potential use for quantum networks, quantum communication, and distributed quantum computation. Published by the American Physical Society 2024

Valuation of a financial claim contingent on the outcome of a quantum measurement

Abstract We consider a rational agent who at time 0 enters into a financial contract for which the payout is determined by a quantum measurement at some time T > 0. The state of the quantum system is given in the Heisenberg representation by a known density matrix p. How much will the agent be willing to pay at time 0 to enter into such a contract? In the case of a finite dimensional Hilbert space H, each such claim is represented by an observable X where the eigenvalues of X determine the amount paid if the corresponding outcome is obtained in the measurement. We prove, under reasonable axioms, that there exists a pricing state q which is equivalent to the physical state p such that the pricing function Π takes the linear form Π (X) = P_0T tr(q X) for any claim X, where P_0T is the one-period discount factor. By “equivalent” we mean that p and q share the same null space: thus, for any |ξ〉∈ H one has p|ξ〉 = 0 if and only if q|ξ〉 = 0. We introduce a class of optimization problems and solve for the optimal contract payout structure for a claim based on a given measurement. Then we consider the implications of the Kochen-Specker theorem in this setting and we look at the problem of forming portfolios of such contracts. Finally, we consider multi-period contracts.

Coherent Microwave, Optical, and Mechanical Quantum Control of Spin Qubits in Diamond

AbstractDiamond has emerged as a highly promising platform for quantum network applications. Color centers in diamond fulfill the fundamental requirements for quantum nodes: they constitute optically accessible quantum systems with long‐lived spin qubits. Furthermore, they provide access to a quantum register of electronic and nuclear spin qubits and they mediate entanglement between spins and photons. All these operations require coherent control of the color center's spin state. This review provides a comprehensive overview of the state‐of‐the‐art, challenges, and prospects of such schemes, including high‐fidelity initialization, coherent manipulation, and readout of spin states. Established microwave and optical control techniques are reviewed, and moreover, emerging methods such as cavity‐mediated spin–photon interactions and mechanical control based on spin–phonon interactions are summarized. For different types of color centers, namely, nitrogen–vacancy and group‐IV color centers, distinct challenges persist that are subject of ongoing research. Beyond fundamental coherent spin qubit control techniques, advanced demonstrations in quantum network applications are outlined, for example, the integration of individual color centers for accessing (nuclear) multiqubit registers. Finally, the role of diamond spin qubits in the realization of future quantum information applications is described.

A unifying quantum speed limit for time-independent Hamiltonian evolution

Abstract Quantum speed limit (QSL) is the study of fundamental limits on the evolution time of quantum systems. For instance, under the action of a time-independent Hamiltonian, the evolution time between an initial and a final quantum state obeys various mutually complementary lower bounds. They include the Mandelstam-Tamm bound, the Margolus-Levitin bound, the Luo-Zhang
 bound, the Lee-Chau bound together with the dualML bound introduced by Ness and coworkers. Here we show that the Mandelstam-Tamm bound can be obtained by optimizing the Lee-Chau bound over a certain parameter. More importantly, we report a QSL that includes all the above bounds as special cases before optimizing over the physically meaningless reference energy level of a quantum system. This unifying bound depends on a certain parameter $p$. For any fixed $p$, we find all pairs of time-independent Hamiltonian and initial pure quantum state that saturate this unifying bound. More importantly, these pairs allow us to compute this bound accurately and efficiently using an oracle that returns certain $p$th moments related to the absolute value of
 energy of the quantum state. Moreover, this oracle can be simulated by a computationally efficient and accurate algorithm for finite-dimensional quantum systems as well as for certain infinite-dimensional quantum states with bounded and continuous energy spectra. This makes our computational method feasible in a lot of practical situations. We find that if the dimension of
 the underlying Hilbert space is $\lesssim 2000$, our unifying bound optimized over $p$ can be computed accurately in a few minutes using Mathematica code with just-in-time compilation in a typical desktop. Besides, this optimized unifying QSL is at least as good as all the existing ones combined and can occasionally be a few percent to a few times better.

Testing Bell–CHSH inequalities using topological Aharonov–Casher and He–McKellar–Wilkens phases

The effects of Aharonov–Casher (AC) and He–McKellar–Wilkens (HMW) phases on entangled spin-1/2 quantum systems are investigated. We use linear charge distributions positioned at the center of resulting closed orbits, capitalizing on Mach Zender-type interferometers modified with phase retarders to unveil the topological effects. We analyze how AC-HMW phases influence the Bell angles and maximal violation of Bell–CHSH inequalities (BI) without any classical interaction. We incorporate the spin and path of particles in the interferometers as observables to test noncontextual hidden variable theories against quantum mechanics, leveraging the non-local features of AC-HMW effects. Furthermore, we discuss potential implementations of our scheme in physical systems.

Dynamics of the nonlinear optical second, and third harmonic generation in GaAs/Ga0.7Al0.3As quantum well due to hydrostatic pressure and temperature

Abstract We studied the effects of hydrostatic pressure and temperature on the second and third harmonic generation (SHG and THG) of nonlinear optics semi-parabolic GaAs/Al0.3Ga0.7As quantum well. By solving the Schrödinger equation numerically, we can determine the system's subband energy levels and propagation wave functions, and then calculate its optical gain. The numerical simulation results show that both temperature and hydrostatic pressure can effectively improve the nonlinear optical performance of the system. As an interesting observation, we studied the mechanism of the two in this process. These findings highlight a feasible method to adjust the nonlinear optical performance of GaAs/Al0.3Ga0.7As quantum system through the subtle interaction between hydrostatic pressure, temperature and structural parameters.

Landauer Bound in the Context of Minimal Physical Principles: Meaning, Experimental Verification, Controversies and Perspectives

The physical roots, interpretation, controversies, and precise meaning of the Landauer principle are surveyed. The Landauer principle is a physical principle defining the lower theoretical limit of energy consumption necessary for computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surroundings. The Landauer principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus–Levitin limit, and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus–Levitin, and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decreasing the temperature of a thermal bath will decrease the energy consumption of a single computation, but in parallel, it will slow the computation. The Landauer principle bridges John Archibald Wheeler’s “it from bit” paradigm and thermodynamics. Experimental verifications of the Landauer principle are surveyed. The interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to quantum and non-equilibrium systems is addressed. The Landauer principle represents the powerful heuristic principle bridging physics, information theory, and computer engineering.

Evidence for Magnetic Crystallization Waves at the Surface of $$^3$$He Crystal

AbstractUltralow temperature crystals of the helium isotopes $$^3$$ 3 He and $$^4$$ 4 He are intriguing quantum systems. Deciphering the complex features of these unusual materials has been made possible in large part by Alexander Andreev’s groundbreaking research. In 1978, Andreev and Alexander Parshin predicted the existence of melting/freezing waves at the surface of a solid $$^4$$ 4 He crystal, which was subsequently promptly detected. Successively, for the fermionic $$^3$$ 3 He superfluid/solid interface, even more intricate crystallization waves were anticipated, although they have not been observed experimentally so far. In this work, we provide preliminary results on $$^3$$ 3 He crystals at the temperature $$T = 0.41$$ T = 0.41 mK, supporting the existence of spin supercurrents in the melting/freezing waves on the crystal surface below the antiferromagnetic ordering temperature $$T_N= 0.93$$ T N = 0.93 mK, as predicted by Andreev. The spin currents that accompany such a melting-freezing wave make it a unique object, in which the inertial mass is distinctly different from the gravitational mass.

Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space.

Recent progress on the constraint coordinate-momentum phase space (CPS) formulation of finite-state quantum systems has revealed that the triangle window function approach is an isomorphic representation of the exact population-population correlation function of the two-state system. We use the triangle window (TW) function and the CPS mapping kernel element to formulate a novel useful representation of discrete electronic degrees of freedom (DOFs). When it is employed with nonadiabatic field (NaF) dynamics, a new variant of the NaF approach (i.e., NaF-TW) is proposed. The NaF-TW expression of the population of any adiabatic state is always positive semidefinite. Extensive benchmark tests of model systems in both the condensed phase and gas phase demonstrate that the NaF-TW approach is able to faithfully capture the dynamical interplay between electronic and nuclear DOFs in a broad region, including where the states remain coupled all the time, as well as where the bifurcation characteristic of nuclear motion is important.