Learning and forecasting open quantum dynamics with correlated noise

Alternatively to the full reconstruction of an unknown quantum process, the so-called selective and efficient quantum process tomography (SEQPT) allows estimating, individually and up to the required accuracy, a given element of the matrix that describes such an operation with a polynomial amount of resources. The implementation of this protocol has been carried out with success to characterize the evolution of a quantum system that is well described by a trace-preserving quantum map. Here, we deal with a more general type of quantum process that does not preserve the trace of the input quantum state, which naturally arises in the presence of imperfect devices and system-environment interactions, in the context of quantum information science or quantum dynamics control. In that case, we show with the aid of a priori information on the losses structure of the quantum channel that the SEQPT reconstruction can be adapted to reconstruct the non-trace-preserving map. We explicitly describe how to implement the reconstruction in an arbitrary Hilbert space of finite dimension $d$. The method is experimentally verified on a superconducting quantum processor provided by IBM Quantum services, by estimating several non-trace-preserving quantum processes in dimensions up to $d=6$. Our results show that it is possible to efficiently reconstruct non-trace-preserving processes, with high precision, and with significantly higher fidelity than when the process is assumed to be trace preserving.

Quantum computing has gained considerable attention, especially after the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era. Quantum processors and cloud services have been made worldwide increasingly available. Unfortunately, jobs on existing quantum processors are often executed in series, and the workload could be heavy to the processor. Typically, one has to wait for hours or even longer to obtain the result of a single quantum job on public quantum cloud due to long queue time. In fact, as the scale grows, the qubit utilization rate of the serial execution mode will further diminish, causing the waste of quantum resources. In this paper, to our best knowledge for the first time, the Quantum Job Scheduling Problem (QJSP) is formulated and introduced, and we accordingly aim to improve the utility efficiency of quantum resources. Specifically, a noise-aware quantum job scheduler (NAQJS) concerning the circuit width, number of measurement shots, and submission time of quantum jobs is proposed to reduce the execution latency. We conduct extensive experiments on a simulated Qiskit noise model, as well as on the Xiaohong (from QuantumCTek) superconducting quantum processor. Numerical results show the effectiveness in both the QPU time and turnaround time.

How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information science. While existing studies have been mostly focusing on the approximation of two observables with a single measurement, in practice multiple observables are often encountered, for which the errors of the approximations are little understood. Here we provide a framework to study the implementation of an arbitrary finite number of observables with a single measurement. Our methodology yields novel analytical bounds on the errors of these implementations, significantly advancing our understanding of this fundamental problem. Additionally, we introduce a more stringent bound utilizing semi-definite programming that, in the context of two observables, generates an analytical bound tighter than previously known bounds. The derived bounds have direct applications in assessing the trade-off between the precision of estimating multiple parameters in quantum metrology, an area with crucial theoretical and practical implications. To validate the validity of our findings, we conducted experimental verification using a superconducting quantum processor. This experimental validation not only confirms the theoretical results but also effectively bridges the gap between the derived bounds and empirical data obtained from real-world experiments. Our work paves the way for optimizing various tasks in quantum information science that involve multiple noncommutative observables.

Besides noticeable challenges in implementing low-error single- and two-qubit quantum gates in superconducting quantum processors, the readout technique and analysis are a key factor in determining the efficiency and performance of quantum processors. Being able to efficiently implement quantum algorithms involving entangling gates and asses their output is mandatory for quantum utility. In a transmon-based 5-qubit superconducting quantum processor, we compared the performance of quantum circuits involving an increasing level of complexity, from single-qubit circuits to maximally entangled Bell circuits. This comparison highlighted the importance of the readout analysis and helped us optimize the protocol for more advanced quantum algorithms. Here, we report the results obtained from the analysis of the outputs of quantum circuits using two readout paradigms, referred to as “multiplied readout probabilities” and “conditional readout probabilities.” The first method is suitable for single-qubit circuits, while the second is essential for accurately interpreting the outputs of circuits involving two-qubit gates.

Most near-term quantum information processing devices will not be capable of implementing quantum error correction and the associated logical quantum gate set. Instead, quantum circuits will be implemented directly using the physical native gate set of the device. These native gates often have a parameterization (e.g., rotation angles) which provide the ability to perform a continuous range of operations. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we demonstrate a procedure for sample-efficient verification of continuously-parameterized quantum gates for small quantum processors of up to approximately 10 qubits. This procedure involves generating random sequences of randomly-parameterized layers of gates chosen from the native gate set of the device, and then stochastically compiling an approximate inverse to this sequence such that executing the full sequence on the device should leave the system near its initial state. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking. This provides an experimentally-relevant advantage in sample efficiency when estimating the fidelity loss to some desired precision. We describe the experimental realization of this technique using continuously-parameterized quantum gate sets on a trapped-ion quantum processor from Sandia QSCOUT and a superconducting quantum processor from IBM Q, and we demonstrate the sample efficiency advantage of this technique both numerically and experimentally.

The Google Quantum AI team's long-term goal is to realize a large-scale fault-tolerant quantum computer. Of the technologies available to implement the quantum processor at the core of such a system, solid-state superconducting circuits based on Josephson junctions (JJs) are among the strongest contenders. Recent demonstrations with this technology include computation beyond the capabilities of today's most powerful supercomputers [1] and execution of quantum error correction (QEC) codes that can detect and correct either bit or phase flip errors [2]. These exciting results were enabled by low-error-rate quantum processors with tens of qubits and the supporting infrastructure to run these devices. However, today's quantum computers still have orders of magnitude fewer qubits than is required for a useful fault-tolerant quantum computer; for this, an estimated million or more qubits will be needed and scaling-up today's technology to this extent is non-trivial. Here, we review the Google Quantum AI team's recent progress and future plans. Specifically, we describe our post-classical Sycamore quantum computer and discuss the Google Quantum AI roadmap to fault-tolerant quantum computing.

Security of modern classical data encryption often relies on computationally hard problems, which can be trivialized with the advent of quantum computers. A potential remedy for this is quantum communication which takes advantage of the laws of quantum physics to provide secure exchange of information. Here, quantum key distribution (QKD) represents a powerful tool, allowing for unconditionally secure quantum communication between remote parties. At the same time, microwave quantum communication is set to play an important role in future quantum networks because of its natural frequency compatibility with superconducting quantum processors and modern near-distance communication standards. To this end, we present an experimental realization of a continuous-variable QKD protocol based on propagating displaced squeezed microwave states. We use superconducting parametric devices for generation and single-shot quadrature detection of these states. We demonstrate unconditional security in our experimental microwave QKD setting. The security performance is shown to be improved by adding finite trusted noise on the preparation side. Our results indicate feasibility of secure microwave quantum communication with the currently available technology in both open-air (up to ~ 80 m) and cryogenic (over 1000 m) conditions.

Quantum computation, a paradigm of computing that is completely different from classical methods, benefits from theoretically proved speed-ups for certain problems and can be used to study the properties of quantum systems1. Yet, because of the inherently fragile nature of the physical computing elements (qubits), achieving quantum advantages over classical computation requires extremely low error rates for qubit operations, as well as substantialphysical qubits, to realize fault tolerance via quantum error correction2,3. However, recent theoretical work4,5 has shown that the accuracy of computation (based on expectation values of quantum observables) can be enhanced through an extrapolation of results from a collection of experiments of varying noise. Here we demonstrate this errormitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors in canonical single- and two-qubit experiments and then extend its application to the variational optimization6-8 of Hamiltonians for quantum chemistry and magnetism9. We effectively demonstrate that the suppression of incoherent errors helps to achieve an otherwise inaccessible level of accuracy in the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will enable substantial improvements in the capabilities of near-term quantum computing hardware.

Quantum information can not be perfectly cloned, but approximate copies of quantum information can be generated. Quantum telecloning combines approximate quantum cloning, more typically referred as quantum cloning, and quantum teleportation. Quantum telecloning allows approximate copies of quantum information to be constructed by separate parties, using the classical results of a Bell measurement made on a prepared quantum telecloning state. Quantum telecloning can be implemented as a circuit on quantum computers using a classical co-processor to compute classical feed forward instructions using if statements based on the results of a mid-circuit Bell measurement in real time. We present universal, symmetric, optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1 \rightarrow M$</tex-math></inline-formula> telecloning circuits, and experimentally demonstrate these quantum telecloning circuits for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M=2$</tex-math></inline-formula> up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M=10$</tex-math></inline-formula> , natively executed with real time classical control systems on IBM Quantum superconducting processors, known as dynamic circuits. We perform the cloning procedure on many different message states across the Bloch sphere, on 7 IBM Quantum processors, optionally using the error suppression technique X-X sequence digital dynamical decoupling. Two circuit optimizations are utilized, one which removes ancilla qubits for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M=2, 3$</tex-math></inline-formula> , and one which reduces the total number of gates in the circuit but still uses ancilla qubits. Parallel single qubit tomography with MLE density matrix reconstruction is used in order to compute the mixed state density matrices of the clone qubits, and clone quality is measured using quantum fidelity. These results present one of the largest and most comprehensive NISQ computer experimental analyses on (single qubit) quantum telecloning to date. The clone fidelity sharply decreases to 0.5 for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M &gt; 5$</tex-math></inline-formula> , but for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M=2$</tex-math></inline-formula> we are able to achieve a mean clone fidelity of up to 0.79 using dynamical decoupling.

Quantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the pursuit of chemical accuracy requiring the inclusion of electronic correlation effects. In this work we implement the quantum computed moments (QCM) approach for hydrogen chain molecular systems up to H_6. On a superconducting quantum processor, Hamiltonian moments, langle H^prangle are computed with respect to the Hartree–Fock state, which are then employed in Lanczos expansion theory to determine an estimate for the ground-state energy which incorporates electronic correlations and manifestly improves on the direct energy measurement. Post-processing purification of the raw QCM data takes the estimate below the Hartree–Fock energy to within 99.9% of the exact electronic ground-state energy for the largest system studied, H_6. Calculated dissociation curves indicate precision at about 10mH for this system and as low as 0.1mH for molecular hydrogen, H_2, over a range of bond lengths. In the context of stringent precision requirements for chemical problems, these results provide strong evidence for the error suppression capability of the QCM method, particularly when coupled with post-processing error mitigation. While calculations based on the Hartree–Fock state are tractable to classical computation, these results represent a first step towards implementing the QCM method in a quantum chemical trial circuit. Greater emphasis on more efficient representations of the Hamiltonian and classical preprocessing steps may enable the solution of larger systems on near-term quantum processors.

Many of the biggest challenges in expanding the nation’s access to clean and low-cost energy resources are fundamentally chemistry or materials challenges. An important case is the development of new catalysts for the up-conversion of cheap and readily available materials such as methane or water into materials suitable for use as a fuel such as methanol or oxygen. To understand and exploit such processes, computer simulations of chemical reactions provide a natural complement to experimental studies. Unfortunately, most catalytic reactions involve so-called “strongly correlated” molecules which are notoriously difficult to study with simulation algorithms that can be executed on existing (classical) computers. The recent growth in quantum information science offers an alternative potential route for simulating these difficult systems. As a result, an increasing number of computational chemists are becoming interested in quantum computing. At the same time, quantum information scientists have identified chemistry simulation as a possible first demonstration of a quantum computer providing an improvement over a classical computer. The objective of this project is to accurately simulate strongly correlated molecules on a quantum processor. To meet the high challenges of this objective, new hybrid quantum/classical algorithms will be co-designed with advanced quantum gate developments and computed on customized quantum hardware. Some of the developed techniques will be transferable to study other molecular systems, while the project as a whole will help define better strategies for advancing the quantum simulation of matter more generally.

The spectral form factor (SFF) captures universal spectral fluctuations as signatures of quantum chaos, and has been instrumental in advancing multiple frontiers of physics including the studies of black holes and quantum many-body systems. The measurement of the SFF in many-body systems is however challenging due to the difficulty in resolving level spacings that become exponentially small with increasing system size. Here, we utilize the random measurement toolbox to perform a direct experimental measurement of the SFF, and hence probe the presence or absence of chaos in quantum many-body systems on superconducting quantum processors. For a Floquet chaotic system, we observe signatures of both short- and long-range spectral correlations in the SFF given by the ramp-plateau behavior. Furthermore, for a Hamiltonian system we utilize the SFF to distinguish a quantum many-body chaotic phase and the prethermal many-body localization. We observe the dip-ramp-plateau behavior of random matrix theory in the chaotic phase and contrast the scaling of the plateau time in system size between the many-body chaotic and localized phases. Finally, we probe the eigenstate statistics by measuring a generalization of the SFF, known as the partial SFF, and observe distinct behaviors in the purity of the reduced density matrices in these two phases. This work unveils a new experimental way of extracting the universal signatures of many-body quantum chaos in quantum devices by probing short- and long-range correlations in the energy spectrum and eigenstates.

Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of high-dimensional quantum technology, a significant effort is underway to progressively enhance the entanglement dimension between two particles. An alternative effective strategy involves not only increasing the dimensionality but also expanding the number of particles that are entangled. We present an experimental study demonstrating multi-partite quantum non-locality beyond qubit constraints, thus moving into the realm of strongly entangled high-dimensional multi-particle quantum systems. In the experiment, quantum states were encoded in the path degree of freedom (DoF) and controlled via polarization, enabling efficient operations in a two-dimensional plane to prepare three- and four-particle Greenberger-Horne-Zeilinger (GHZ) states in three-level systems. Our experimental results reveal ways in which high-dimensional systems can surpass qubits in terms of violating local-hidden-variable theories. Our realization of multiple complex and high-quality entanglement technologies is an important primary step for more complex quantum computing and communication protocols.

Recent advancements of quantum technologies have triggered tremendous interest in exploring practical quantum advantage. The simulation of fluid dynamics, a highly challenging problem in classical physics but vital for practical applications, emerges as a potential direction. Here, we report an experiment on the digital simulation of unsteady flows with a superconducting quantum processor. The quantum algorithm is based on the Hamiltonian simulation using the hydrodynamic formulation of the Schrödinger equation. With the median fidelities of 99.97% and 99.67% for parallel single- and two-qubit gates respectively, we simulate the dynamics of a two-dimensional (2D) compressible diverging flow and a 2D decaying vortex with ten qubits. Note that the former case is an inviscid potential flow, and the latter one is an artificial vortical flow with an external body force. The experimental results well capture the temporal evolution of averaged density and momentum profiles, and qualitatively reproduce spatial flow fields with moderate noises. This work demonstrates the potential of quantum computing in simulating more complex flows, such as turbulence, for practical applications.

The observation of genuine quantum effects in systems governed by non-Hermitian Hamiltonians has been an outstanding challenge in the field. Here we simulate the evolution under such Hamiltonians in the quantum regime on a superconducting quantum processor by using a dilation procedure involving an ancillary qubit. We observe the parity–time ({mathcal{PT}})-symmetry breaking phase transition at the exceptional points, obtain the critical exponent, and show that this transition is associated with a loss of state distinguishability. In a two-qubit setting, we show that the entanglement can be modified by local operations.