Quantum Physics (quant-ph)

Abstract: We model and experimentally demonstrate the full time-dependent counting statistics of photons emitted by a single nitrogen-vacancy (NV) center in diamond under non-resonant laser excitation and resonant microwave control. A generalization of the quantum jump formalism for the seven electronic states involved in the fast intrinsic dynamics of an NV center provides a self-contained model that allows for the characterization of its emission and clarifies the relation between the quantum system internal states and the measurable detected photon counts. The model allows the elaboration of detection protocols to optimize the energy and time resources while maximizing the system sensitivity to magnetic-field measurements.

Abstract: Precision experimental determination of photon correlation requires the massive amounts of data and extensive measurement time. We present a technique to monitor second-order photon correlation $g^{(2)}(0)$ of amplified quantum noise based on wideband balanced homodyne detection and deep-learning acceleration. The quantum noise is effectively amplified by an injection of weak chaotic laser and the $g^{(2)}(0)$ of the amplified quantum noise is measured with a real-time sample rate of 1.4 GHz. We also exploit a photon correlation convolutional neural network accelerating correlation data using a few quadrature fluctuations to perform a parallel processing of the $g^{(2)}(0)$ for various chaos injection intensities and effective bandwidths. The deep-learning method accelerates the $g^{(2)}(0)$ experimental acquisition with a high accuracy, estimating 6107 sets of photon correlation data with a mean square error of 0.002 in 22 seconds and achieving a three orders of magnitude acceleration in data acquisition time. This technique contributes to a high-speed and precision coherence evaluation of entropy source in secure communication and quantum imaging.

Abstract: We develop a new method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of its logical states. It is not always possible to achieve low error rates during the readout of the quantum states of ion qubits due to the finite lifetime of excited levels, photon scattering, dark noise, low numerical aperture, etc. However, the model of fuzzy quantum measurements makes it possible to ensure precise tomography of quantum states. To do this, we developed a fuzzy measurement model based on counting the number of fluorescent photons. A statistically adequate algorithm for the reconstruction of quantum states of ion qubit registers based on fuzzy measurement operators is proposed. The algorithm uses the complete information available in the experiment and makes it possible to account for systematic measurement errors associated with the limited distinguishability of the logical states of ion qubits. We show that the developed model, although computationally more complex, contains significantly more information about the state of the qubit and provides a higher accuracy of state reconstruction compared to the model based on the threshold algorithm.

Abstract: This experimental study aims to investigate the convex combinations of Pauli semigroups with arbitrary mixing parameters to determine whether the resulting dynamical map exhibits Markovian or non-Markovian behavior. Specifically, we consider the cases of equal as well as unequal mixing of two Pauli semigroups, and demonstrate that the resulting map is always non-Markovian. Additionally, we study three cases of three-way mixing of the three Pauli semigroups and determine the Markovianity or non-Markovianity of the resulting maps by experimentally determining the decay rates. To simulate the non-unitary dynamics of a single qubit system with different mixing combinations of Pauli semigroups on an NMR quantum processor, we use an algorithm involving two ancillary qubits. The experimental results align with the theoretical predictions.

Abstract: MIP*=RE implies that C_{qa} (the closure of the set of tensor product correlations) and C_{qc} (the set of commuting correlations) can be separated by a hyperplane (i.e., a Bell-like inequality) and that there are correlations produced by commuting measurements (a finite number of them and with a finite number of outcomes) on an infinite-dimensional quantum system which cannot be approximated by sequences of finite-dimensional tensor product correlations. We point out that there are four logically possible universes after this result. Each possibility is interesting because it reveals either limitations in accepted physical theories or opportunities to test crucial aspects of nature. We list some open problems that may help us to design a road map to learn in which of these universes we are.

Abstract: We investigate a discrete non-linear Schr\"odinger equation with dynamical, density-difference-dependent, gauge fields. We find a ground-state transition from a plane wave condensate to a localized soliton state as the gauge coupling is varied. Interestingly we find a regime in which the condensate and soliton are both stable. We identify an emergent chiral symmetry, which leads to the existence of a symmetry protected zero energy edge mode. The emergent chiral symmetry relates low and high energy solitons. These states indicate that the interaction acts both repulsively and attractively.

Abstract: The unavoidable presence of noise is a crucial roadblock for the development of large-scale quantum computers and the ability to characterize quantum noise reliably and efficiently with high precision is essential to scale quantum technologies further. Although estimating an arbitrary quantum channel requires exponential resources, it is expected that physically relevant noise has some underlying local structure, for instance that errors across different qubits have a conditional independence structure. Previous works showed how it is possible to estimate Pauli noise channels with an efficient number of samples in a way that is robust to state preparation and measurement errors, albeit departing from a known conditional independence structure. We present a novel approach for learning Pauli noise channels over n qubits that addresses this shortcoming. Unlike previous works that focused on learning coefficients with a known conditional independence structure, our method learns both the coefficients and the underlying structure. We achieve our results by leveraging a groundbreaking result by Bresler for efficiently learning Gibbs measures and obtain an optimal sample complexity of O(log(n)) to learn the unknown structure of the noise acting on n qubits. This information can then be leveraged to obtain a description of the channel that is close in diamond distance from O(poly(n)) samples. Furthermore, our method is efficient both in the number of samples and postprocessing without giving up on other desirable features such as SPAM-robustness, and only requires the implementation of single qubit Cliffords. In light of this, our novel approach enables the large-scale characterization of Pauli noise in quantum devices under minimal experimental requirements and assumptions.

Abstract: By using biorthogonal bases, we construct a complete framework for biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help of associated state which is overlooked previously, we define the automatically normalized biorthogonal Loschmidt echo. This approach is capable of handling arbitrary non-Hermitian systems with complex eigenvalues, which naturally eliminates the negative value of Loschmidt rate obtained without the biorthogonal bases. Taking the non-Hermitian Su-Schrieffer-Heeger model as a concrete example, a peculiar $1/2$ change in biorthogonal dynamical topological order parameter, which is beyond the traditional dynamical quantum phase transitions is observed. We also find the periodicity of biorthogonal dynamical quantum phase transitions depend on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state.

Abstract: We consider the nonequilibrium dispersion force acting on nanoparticles on the source side of gapped graphene sheet. Nanoparticles are kept at the environmental temperature, whereas the graphene sheet may be either cooler or hotter than the environment. Calculation of the dispersion force as a function of separation at different values of the mass-gap parameter is performed using the generalization of the fundamental Lifshitz theory to the out-of-thermal-equilibrium conditions. The response of gapped graphene to quantum and thermal fluctuations of the electromagnetic field is described by the polarization tensor in (2+1)-dimensional space-time in the framework of the Dirac model. The explicit expressions for the components of this tensor in the area of evanescent waves are presented. The nontrivial impact of the mass-gap parameter of graphene on the nonequilibrium dispersion force, as compared to the equilibrium one, is determined. It is shown that, unlike the case of a pristine graphene, the nonequilibrium force preserves an attractive character. The possibilities of using the obtained results in the design of micro- and nanodevices incorporating nanoparticles and graphene sheets for their functionality are discussed.

Abstract: This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group encoding. We establish a generic model of quantum computation for group-theoretic problems, which we call the quantum generic group model. Shor's algorithm for the DL problem and related algorithms can be described in this model. We show the quantum complexity lower bounds and almost matching algorithms of the DL and related problems in this model. More precisely, we prove the following results for a cyclic group $G$ of prime order. - Any generic quantum DL algorithm must make $\Omega(\log |G|)$ depth of group operations. This shows that Shor's algorithm is asymptotically optimal among the generic quantum algorithms, even considering parallel algorithms. - We observe that variations of Shor's algorithm can take advantage of classical computations to reduce the number of quantum group operations. We introduce a model for generic hybrid quantum-classical algorithms and show that these algorithms are almost optimal in this model. Any generic hybrid algorithm for the DL problem with a total number of group operations $Q$ must make $\Omega(\log |G|/\log Q)$ quantum group operations of depth $\Omega(\log\log |G| - \log\log Q)$. - When the quantum memory can only store $t$ group elements and use quantum random access memory of $r$ group elements, any generic hybrid algorithm must make either $\Omega(\sqrt{|G|})$ group operations in total or $\Omega(\log |G|/\log (tr))$ quantum group operations. As a side contribution, we show a multiple DL problem admits a better algorithm than solving each instance one by one, refuting a strong form of the quantum annoying property suggested in the context of password-authenticated key exchange protocol.

Abstract: Path calculus, or graphical linear algebra, is a string diagram calculus for the category of matrices over a base ring. It is the usual string diagram calculus for a symmetric monoidal category, where the monoidal product is the direct sum of matrices. We categorify this story to develop a surface diagram calculus for the bicategory of matrices over a base bimonoidal category. This yields a surface diagram calculus for any bimonoidal category by restricting to diagrams for 1x1 matrices. We show how additional structure on the base category, such as biproducts, duals and the dagger, adds structure to the resulting calculus. Applied to categorical quantum mechanics this yields a new graphical proof of the teleportation protocol.

Abstract: Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian systems, while the possible non-Hermitian solution remains outstanding. In this work, we generalize the quantum covariance matrix method to the cases that are applicable to non-Hermitian systems, through which we are able to explicitly reconstruct the non-Hermitian parent Hamiltonian from an arbitrary pair of biorthogonal eigenstates. As concrete examples, we successfully apply our approach in spin chain with Lee-Yang singularity and a non-Hermitian interacting fermion model. Some generalization and further application of our approach are also discussed. Our work provides a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates and shed light on future exploration on non-Hermitian physics.

Abstract: In this work, we propose a novel architecture (and several variants thereof) based on quantum cryptographic primitives with provable privacy and security guarantees regarding membership inference attacks on generative models. Our architecture can be used on top of any existing classical or quantum generative models. We argue that the use of quantum gates associated with unitary operators provides inherent advantages compared to standard Differential Privacy based techniques for establishing guaranteed security from all polynomial-time adversaries.

Abstract: We propose an annealing scheme for crystal structures prediction (CSP) by taking into account the general n-body atomic interactions, and in particular three-body interactions which are necessary to simulate covalent bonds. The crystal structure is represented by discretizing the real space by mesh and placing binary variables which express the existence or non-existence of an atom on every grid point. We implement n-body atomic interaction in quadratic unconstrained binary optimization (QUBO) or higher-order unconstrained binary optimization (HUBO) problems and perform CSP by simulated annealing. In this study we successfully reduce the number of bits necessary to implement three-body interactions within the HUBO formulation of MoS2 crystals. Further, we find that grand canonical simulation is possible by showing that we can simultaneously optimize for the particle density as well as the crystal structure using simulated annealing. In particular, we apply CSP to noble gasses, i.e. Lennard-Jones(LJ) solids, and show that the grand canonical calculation has a better time to solution scaling than its microcanonical counterpart.

Abstract: Quantum measurements generally introduce perturbations into the subsequent evolution of the measured system. Furthermore, a projective measurement cannot decrease the uncertainty on the system if the outcome is ignored; that is, the von Neumann entropy cannot decrease. However, under certain sound assumptions and using the quantum violation of Leggett-Garg inequalities, we demonstrate that this property is not inherited by a faithful classical causal simulation of a measurement process. In the simulation, a measurement erases previous information by performing a partial reset on the system. Thus, the measuring device acts as a low-temperature bath absorbing entropy from the measured system. Information erasure is a form of Spekkens' preparation contextuality. Our proof is straightforward if one assumes that maximal ignorance of the quantum state is compatible with maximal ignorance of the classical state. We also employ a weaker hypothesis. Information erasure is related to a theorem of Leifer and Pusey, which states that time symmetry implies retrocausality. In light of our findings, we discuss Spekkens' preparation contextuality, as well as a weakness in the hypothesis of time symmetry as defined by Leifer and Pusey.

Abstract: Quantum dynamics with local interactions in lattice models display rich physics, but is notoriously hard to study. Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered one- and higher-dimensional quantum systems. However, this family of models shows some non-universal features, like vanishing correlations inside the light-cone and instantaneous thermalization of local observables. In this work we propose a generalization of dual-unitary circuits where the exactly calculable spatial-temporal correlation functions display richer behavior, and have non-trivial thermalization of local observables. This is achieved by generalizing the single-gate condition to a hierarchy of multi-gate conditions, where the first level recovers dual-unitary models, and the second level exhibits these new interesting features. We also extend the discussion and provide exact solutions to correlators with few-site observables and discuss higher-orders, including the ones after a quantum quench. In addition, we provide exhaustive parametrizations for qubit cases, and propose a new family of models for local dimensions larger than two, which also provides a new family of dual-unitary models.

Abstract: A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is to design a system where errors can be detected and converted into erasures. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. In this work, we implement such a dual-rail cavity qubit and use it to demonstrate a projective logical measurement with erasure detection. We measure logical state preparation and measurement errors at the $0.01\%$-level and detect over $99\%$ of cavity decay events as erasures. We use the precision of this new measurement protocol to distinguish different types of errors in this system, finding that while decay errors occur with probability $\sim 0.2\%$ per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 170 times less frequently. These findings represent the first confirmation of the expected error hierarchy necessary to concatenate dual-rail erasure qubits into a highly efficient erasure code.

Abstract: We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected Variational Quantum Dynamics (pVQD) algorithm, that performs a global optimization with linear scaling in the number of variational parameters. Instead of fixing a variational ansatz at the beginning of the simulation, the circuit is grown systematically during the time evolution. Moreover, the adaptive step does not require auxiliary qubits and the gate search can be performed in parallel on different quantum devices. We apply the new algorithm, named Adaptive pVQD, to the simulation of driven spin models and fermionic systems, where it shows an advantage when compared to both Trotterized circuits and non-adaptive variational methods. Finally, we use the shallower circuits prepared using the Adaptive pVQD algorithm to obtain more accurate measurements of physical properties of quantum systems on hardware.

Abstract: We experimentally demonstrate a virtual two-qubit gate and characterize it using quantum process tomography (QPT). The virtual two-qubit gate decomposes an actual two-qubit gate into single-qubit operations and projective measurements in quantum circuits for expectation-value estimation. We implement projective measurements via mid-circuit dispersive readout. The deterministic sampling scheme reduces the number of experimental circuit evaluations required for decomposing a virtual two-qubit gate. We also apply measurement error mitigation to suppress the effect of readout errors and improve the average gate fidelity of a virtual controlled-$Z$ (CZ) gate to $f_{\rm av} = 0.9975 \pm 0.0028$. Our results highlight a practical approach to implement virtual two-qubit gates with high fidelities, which are useful for simulating quantum circuits using fewer qubits and implementing two-qubit gates on a distant pair of qubits.

Abstract: A number of exciting recent results have been seen in the field of quantum error correction. These include initial demonstrations of error correction on current quantum hardware, and resource estimates which improve understanding of the requirements to run large-scale quantum algorithms for real-world applications. In this work, we bridge the gap between these two developments by performing careful estimation of the resources required to fault-tolerantly perform quantum phase estimation (QPE) on a minimal chemical example. Specifically, we describe a detailed compilation of the QPE circuit to lattice surgery operations for the rotated surface code, for a hydrogen molecule in a minimal basis set. We describe a number of optimisations at both the algorithmic and error correction levels. We find that implementing even a simple chemistry circuit requires 900 qubits and 2,300 quantum error correction rounds, emphasising the need for improved error correction techniques specifically targeting the early fault-tolerant regime.

Abstract: Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage, namely a significant (in some cases exponential) speed-up of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models which are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this roadmap paper, led by CERN, DESY and IBM, we provide the status of high-energy physics quantum computations and give examples for theoretical and experimental target benchmark applications, which can be addressed in the near future. Having the IBM 100 x 100 challenge in mind, where possible, we also provide resource estimates for the examples given using error mitigated quantum computing.

Abstract: In this article, we present a hybrid quantum-classical generative adversarial network (GAN) for near-term quantum processors. The hybrid GAN comprises a generator and a discriminator quantum neural network (QNN). The generator network is realized using an angle encoding quantum circuit and a variational quantum ansatz. The discriminator network is realized using multi-stage trainable encoding quantum circuits. A modular design approach is proposed for the QNNs which enables control on their depth to compromise between accuracy and circuit complexity. Gradient of the loss functions for the generator and discriminator networks are derived using the same quantum circuits used for their implementation. This prevents the need for extra quantum circuits or auxiliary qubits. The quantum simulations are performed using the IBM Qiskit open-source software development kit (SDK), while the training of the hybrid quantum-classical GAN is conducted using the mini-batch stochastic gradient descent (SGD) optimization on a classic computer. The hybrid quantum-classical GAN is implemented using a two-qubit system with different discriminator network structures. The hybrid GAN realized using a five-stage discriminator network, comprises 63 quantum gates and 31 trainable parameters, and achieves the Kullback-Leibler (KL) and the Jensen-Shannon (JS) divergence scores of 0.39 and 4.16, respectively, for similarity between the real and generated data distributions.

Abstract: Neural-network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the physical error rates, making them highly adaptable. In this study, we investigate the performance of such a decoder using both simulated and experimental data obtained from a transmon-qubit processor, focusing on small-distance surface codes. We first show that the neural network typically outperforms the matching decoder due to better handling errors leading to multiple correlated syndrome defects, such as $Y$ errors. When applied to the experimental data of [Google Quantum AI, Nature 614, 676 (2023)], the neural network decoder achieves logical error rates approximately $25\%$ lower than minimum-weight perfect matching, approaching the performance of a maximum-likelihood decoder. To demonstrate the flexibility of this decoder, we incorporate the soft information available in the analog readout of transmon qubits and evaluate the performance of this decoder in simulation using a symmetric Gaussian-noise model. Considering the soft information leads to an approximately $10\%$ lower logical error rate, depending on the probability of a measurement error. The good logical performance, flexibility, and computational efficiency make neural network decoders well-suited for near-term demonstrations of quantum memories.

Abstract: For quantum error-correcting codes to be realizable, it is important that the qubits subject to the code constraints exhibit some form of limited connectivity. The works of Bravyi & Terhal (BT) and Bravyi, Poulin & Terhal (BPT) established that geometric locality constrains code properties -- for instance $[[n,k,d]]$ quantum codes defined by local checks on the $D$-dimensional lattice must obey $k d^{2/(D-1)} \le O(n)$. Baspin and Krishna studied the more general question of how the connectivity graph associated with a quantum code constrains the code parameters. These trade-offs apply to a richer class of codes compared to the BPT and BT bounds, which only capture geometrically-local codes. We extend and improve this work, establishing a tighter dimension-distance trade-off as a function of the size of separators in the connectivity graph. We also obtain a distance bound that covers all stabilizer codes with a particular separation profile, rather than only LDPC codes.

Abstract: In machine learning, overparameterization is associated with qualitative changes in the empirical risk landscape, which can lead to more efficient training dynamics. For many parameterized models used in statistical learning, there exists a critical number of parameters, or model size, above which the model is constructed and trained in the overparameterized regime. There are many characteristics of overparameterized loss landscapes. The most significant is the convergence of standard gradient descent to global or local minima of low loss. In this work, we study the onset of overparameterization transitions for quantum circuit Born machines, generative models that are trained using non-adversarial gradient-based methods. We observe that bounds based on numerical analysis are in general good lower bounds on the overparameterization transition. However, bounds based on the quantum circuit's algebraic structure are very loose upper bounds. Our results indicate that fully understanding the trainability of these models remains an open question.

Abstract: The pursuit of room temperature quantum optomechanics with tethered nanomechanical resonators faces stringent challenges owing to extraneous mechanical degrees of freedom. An important example is thermal intermodulation noise (TIN), a form of excess optical noise produced by mixing of thermal noise peaks. While TIN can be decoupled from the phase of the optical field, it remains indirectly coupled via radiation pressure, implying a hidden source of backaction that might overwhelm shot noise. Here we report observation of TIN backaction in a high-cooperativity, room temperature cavity optomechanical system consisting of an acoustic-frequency Si$_3$N$_4$ trampoline coupled to a Fabry-P\'{e}rot cavity. The backaction we observe exceeds thermal noise by 20 dB and radiation pressure shot noise by 40 dB, despite the thermal motion being 10 times smaller than the cavity linewidth. Our results suggest that mitigating TIN may be critical to reaching the quantum regime from room temperature in a variety of contemporary optomechanical systems.

Abstract: We study the dynamics of the Gaudin magnet ("central-spin model") using machine-learning methods. This model is of practical importance, e.g., for studying non-Markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivity. The Gaudin magnet is also integrable, admitting many conserved quantities: For $N$ spins, the model Hamiltonian can be written as the sum of $N$ independent commuting operators. Despite this high degree of symmetry, a general closed-form analytic solution for the dynamics of this many-body problem remains elusive. Machine-learning methods may be well suited to exploiting the high degree of symmetry in integrable problems, even when an explicit analytic solution is not obvious. Motivated in part by this intuition, we use a neural-network representation (restricted Boltzmann machine) for each variational eigenstate of the model Hamiltonian. We then obtain accurate representations of the ground state and of the low-lying excited states of the Gaudin-magnet Hamiltonian through a variational Monte Carlo calculation. From the low-lying eigenstates, we find the non-perturbative dynamic transverse spin susceptibility, describing the linear response of a central spin to a time-varying transverse magnetic field in the presence of a spin bath. Having an efficient description of this susceptibility opens the door to improved characterization and quantum control procedures for qubits interacting with an environment of quantum two-level systems. These systems include electron-spin and hole-spin qubits interacting with environmental nuclear spins via hyperfine interactions or qubits with charge or flux degrees of freedom interacting with coherent charge or paramagnetic impurities.

Abstract: We assign an arbitrary density matrix to a weighted graph and associate to it a graph zeta function that is both a generalization of the Ihara zeta function and a special case of the edge zeta function. We show that a recently developed bipartite pure state separability algorithm based on the symmetric group is equivalent to the condition that the coefficients in the exponential expansion of this zeta function are unity. Moreover, there is a one-to-one correspondence between the nonzero eigenvalues of a density matrix and the singularities of its zeta function. Several examples are given to illustrate these findings.