Explore the vast range of titles available.

Quantum process tomography is a fundamental and critical benchmarking and certification tool that is capable of fully characterizing an unknown quantum process. Standard quantum process tomography suffers from an exponentially scaling number of measurements and complicated data post-processing due to the curse of dimensionality. On the other hand, non-unitary operators are more realistic cases. In this work, we put forward a variational quantum process tomography method based on the supervised quantum machine learning framework. It approximates the unknown non-unitary quantum process utilizing a relatively shallow depth parametric quantum circuit and fewer input states. Numerically, we verified our method by reconstructing the non-unitary quantum mappings up to eight qubits in two cases: the weighted sum of the randomly generated quantum circuits and the imaginary time evolution of the Heisenberg XXZ spin chain Hamiltonian. Results show that those quantum processes could be reconstructed with high fidelities (>99%) and shallow depth parametric quantum circuits (d≤8), while the number of input states required is at least two orders of magnitude less than the demands of the standard quantum process tomography. Our work shows the potential of the variational quantum process tomography method in characterizing non-unitary operators.

Stationary quantum information sources emit sequences of correlated qudits—that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a classical stochastic process. We introduce quantum-information-theoretic properties for separable qudit sequences that serve as bounds on the classical information properties of subsequent measured processes. For sources driven by hidden Markov dynamics, we describe how an observer can temporarily or permanently synchronize to the source’s internal state using specific positive operator-valued measures or adaptive measurement protocols. We introduce a method for approximating an information source with an independent and identically distributed, Markov, or larger memory model through tomographic reconstruction. We identify broad classes of separable processes based on their quantum information properties and the complexity of measurements required to synchronize to and accurately reconstruct them.

We develop an efficient algorithm for determining optimal adaptive quantum estimation protocols with arbitrary quantum control operations between subsequent uses of a probed channel.We introduce a tensor network representation of an estimation strategy, which drastically reduces the time and memory consumption of the algorithm, and allows us to analyze metrological protocols involving up to N  = 50 qubit channel uses, whereas the state-of-the-art approaches are limited to N  < 5. The method is applied to study the performance of the optimal adaptive metrological protocols in presence of various noise types, including correlated noise.

The potential of achieving computational hardware with quantum advantage depends heavily on the quality of quantum gate operations. However, the presence of imperfect two-qubit gates poses a significant challenge and acts as a major obstacle in developing scalable quantum information processors. Google’s Quantum AI and collaborators claimed to have conducted a supremacy regime experiment. In this experiment, a new two-qubit universal gate called the Sycamore gate is constructed and employed to generate random quantum circuits (RQCs), using a programmable quantum processor with 53 qubits. These computations were carried out in a computational state space of size 9 × 10 15 . Nevertheless, even in strictly-controlled laboratory settings, quantum information on quantum processors is susceptible to various disturbances, including undesired interaction with the surroundings and imperfections in the quantum state. To address this issue, we conduct both quantum state tomography (QST) and quantum process tomography (QPT) experiments on Google’s Sycamore gate using different artificial architectural superconducting quantum computer. Furthermore, to demonstrate how errors affect gate fidelity at the level of quantum circuits, we design and conduct full QST experiments for the five-qubit eight-cycle circuit, which was introduced as an example of the programability of Google’s Sycamore quantum processor. These quantum tomography experiments are conducted in three distinct environments: noise-free, noisy simulation, and on IBM Quantum’s genuine quantum computer. Our results offer valuable insights into the performance of IBM Quantum’s hardware and the robustness of Sycamore gates within this experimental setup. These findings contribute to our understanding of quantum hardware performance and provide valuable information for optimizing quantum algorithms for practical applications.

Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors. However, all the previous schemes have to use at least two sequentially implemented gates to realize a general one-qubit gate. Based on two recent reports, we construct two Hamiltonians and experimentally realized nonadiabatic holonomic gates by a single-shot implementation in a two-qubit nuclear magnetic resonance （NMR） system. Two noncommuting one-qubit holonomic gates, rotating along .~ and ~ axes respectively, are implemented by evolving a work qubit and an ancillary qubit nonadiabatically following a quantum circuit designed. Using a sequence compiler developed for NMR quantum information processor, we optimize the whole pulse sequence, minimizing the total error of the implementation. Finally, all the nonadiabatic holonomic gates reach high unattenuated experimental fidelities over 98%.

Hamiltonian exceptional points (HEPs) are spectral degeneracies of non-Hermitian Hamiltonians describing classical and semiclassical open systems with losses and/or gain. However, this definition overlooks the occurrence of quantum jumps in the evolution of open quantum systems. These quantum effects are properly accounted for by considering quantum Liouvillians and their exceptional points (LEPs). Specifically, an LEP corresponds to the coalescence of two or more eigenvalues and the corresponding eigenmatrices of a given Liouvillian at critical values of external parameters (Minganti et al 2019 Phys. Rev. A 100 062131). Here, we explicitly describe how standard quantum process tomography, which reveals the dynamics of a quantum system, can be readily applied to detect and characterize quantum LEPs of quantum non-Hermitian systems. We conducted experiments on an IBM quantum processor to implement a prototype model with one-, two-, and three qubits simulating the decay of a single qubit through competing channels, resulting in LEPs but not HEPs. Subsequently, we performed tomographic reconstruction of the corresponding experimental Liouvillian and its LEPs using both single- and two-qubit operations. This example underscores the efficacy of process tomography in tuning and observing LEPs even in the absence of HEPs.

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time)1/3 and are spatially correlated over a distance ∝(time)2/3 . We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.

Quantum walks are, at present, an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior. For this purpose, we consider an extremely simple model consisting of alternating one-dimensional walks along the two spatial coordinates in bidimensional closed domains (hard wall billiards). The chaotic or regular behavior induced by the boundary shape in the deterministic classical motion translates into chaotic signatures for the quantized problem, resulting in sharp differences in the spectral statistics and morphology of the eigenfunctions of the quantum walker. Indeed, we found, for the Bunimovich stadium—a chaotic billiard—level statistics described by a Brody distribution with parameter δ≃0.1. This indicates a weak level repulsion, and also enhanced eigenfunction localization, with an average participation ratio (PR)≃1150 compared to the rectangular billiard (regular) case, where the average PR≃1500. Furthermore, scarring on unstable periodic orbits is observed. The fact that our simple model exhibits such key signatures of quantum chaos, e.g., non-Poissonian level statistics and scarring, that are sensitive to the underlying classical dynamics in the free particle billiard system is utterly surprising, especially when taking into account that quantum walks are diffusive models, which are not direct quantizations of a Hamiltonian.

Quantum error correction can reduce the effects of noise in quantum systems, e.g. in metrology or most notably in quantum computing. Typically, this requires making measurements that provide information about the errors that have occurred in the system. However, these syndrome measurements themselves introduce noise into the system, for example by using noisy gates. A complete characterization of the measurements is very costly. Here we describe a calibration method to obtain the syndrome statistics taking into account the additional noise sources. All calibration data are extracted from a single experiment in which the syndrome measurement is performed twice in a row. Thus, our method allows an accurate evaluation of syndrome measurements with significantly less effort than existing methods. We give examples of the application of this method to noise estimation and error correction. Finally, we discuss the results of experiments performed on an IBM quantum computer.

Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.