Digital Quantum Research Articles

Performance of Digital SQUID with Sub-Flux Quantum Feedback Resolution Fabricated using 10 kA/cm2 Nb Process

Digital superconducting quantum interference device (SQUID with Single Flux Quantum (SFQ) feedback operates as a Δ-type oversampling A/D converter. Magnetic flux resolution at Nyquist frequency can be improved by taking sub SFQ feedback resolution and large oversampling ratio. Using high critical current density Nb process for fabricating SFQ circuits, we expected more higher operation speed for the digital SQUID and resulting to higher magnetic flux resolutions. We expected a performance of the digital SQUID magnetometer fabricated using 10 kA/cm2 Nb process based on CAD layout, with an up/down counter using T2FF cells and parallel SFQ feedback. For the clock frequency of 13 GHz and the Nyquist frequency of 1.587 MHz, the magnetic field noise was lower than and the slew rate was exceeded 500 mT/s.

Real-time chiral dynamics from a digital quantum simulation

The chiral magnetic effect in a strong magnetic field can be described using the chiral anomaly in the $(1+1)$-dimensional massive Schwinger model with a time-dependent $\theta$-term. We perform a digital quantum simulation of the model at finite $\theta$-angle and vanishing gauge coupling using an IBM-Q digital quantum simulator, and observe the corresponding vector current induced in a system of relativistic fermions by a global {\it chiral quench} -- a sudden change in the chiral chemical potential or $\theta$-angle. At finite fermion mass, there appears an additional contribution to this current that stems from the non-anomalous relaxation of chirality. Our results are relevant for the real-time dynamics of chiral magnetic effect in heavy ion collisions and in chiral materials, as well as for modeling high-energy processes at hadron colliders.

Securing Blockchain Transactions Using Quantum Teleportation and Quantum Digital Signature

Blockchain is the new disruptive technology which is gaining momentum in several domains of real-world applications such as Bitcoin—the most well-known example, and primarily in the financial sector. Distributed ledger system which is the main feature of blockchain technology protected across harmful updates using cryptographic techniques, e.g. hashing and digital signatures, is spread over the network so that no one is the owner of the ledger. This poses a significant challenge in the areas of performance, security, and privacy using this emerging technology. We propose an algorithm to provide a secure mechanism for performing transactions on the Blockchain network by adopting quantum digital signatures (QDS) and quantum teleportation phenomenon of quantum computing. The proposed algorithm uses key pairs to generate private keys and corresponding public keys; the quantum digital signatures are used to sign the message which are then distributed over the blockchain network using the teleportation phenomenon. The security of the keys is dependent on the fundamental principles of quantum mechanics that doesn’t allow forging. The Einstein–Podolsky–Rosen (EPR) pair of particles is used to communicate the quantum information via a quantum channel for teleportation, which is generated by operating Bell measurements with corresponding EPR pairs. The original state of the particle (sender) is destroyed once the information is transported to the other particle (receiver) and the QDS scheme also validates the qubits received. The twofold validation process thereby provides high-level security in the transactions.

Resource-efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians

Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-frac{1}{2} systems. Here, we instead consider encodings of d-level (i.e., qudit) quantum operators into multi-qubit operators, studying resource requirements for approximating operator exponentials by Trotterization. We primarily focus on spin-s and truncated bosonic operators in second quantization, observing desirable properties for approaches based on the Gray code, which to our knowledge has not been used in this context previously. After outlining a methodology for implementing an arbitrary encoding, we investigate the interplay between Hamming distances, sparsity patterns, bosonic truncation, and other properties of local operators. Finally, we obtain resource counts for five common Hamiltonian classes used in physics and chemistry, while modeling the possibility of converting between encodings within a Trotter step. The most efficient encoding choice is heavily dependent on the application and highly sensitive to d, although clear trends are present. These operation count reductions are relevant for running algorithms on near-term quantum hardware because the savings effectively decrease the required circuit depth. Results and procedures outlined in this work may be useful for simulating a broad class of Hamiltonians on qubit-based digital quantum computers.

Hybrid digital-analog simulation of many-body dynamics with superconducting qubits

In recent years, there has been a significant progress in the development of digital quantum processors. The state-of-the-art quantum devices are imperfect, and fully-algorithmic fault-tolerant quantum computing is a matter of future. Until technology develops to the state with practical error correction, computational approaches other than the standard digital one can be used to avoid execution of the most noisy quantum operations. We demonstrate how a hybrid digital-analog approach allows simulating dynamics of a transverse-field Ising model without standard two-qubit gates, which are currently one of the most problematic building blocks of quantum circuits. We use qubit-qubit crosstalks (couplings) of IBM superconducting quantum processors to simulate Trotterized dynamics of spin clusters and then we compare the obtained results with the results of conventional digital computation based on two-qubit gates from the universal set. The comparison shows that digital-analog approach significantly outperforms standard digital approach for this simulation problem, despite of the fact that crosstalks in IBM quantum processors are small. We argue that the efficiency of digital-analog quantum computing can be improved with the help of more specialized processors, so that they can be used to efficiently implement other quantum algorithms. This indicates the prospect of a digital-to-analog strategy for near-term noisy intermediate-scale quantum computers.

Synthetic mean-field interactions in photonic lattices

Photonic lattices are usually considered to be limited by their lack of methods to include interactions. We address this issue by introducing mean-field interactions through optical components which are external to the photonic lattice. The proposed technique to realise mean-field interacting photonic lattices relies on a Suzuki-Trotter decomposition of the unitary evolution for the full Hamiltonian. The technique realises the dynamics in an analogous way to that of a step-wise numerical implementation of quantum dynamics, in the spirit of digital quantum simulation. It is a very versatile technique which allows for the emulation of interactions that do not only depend on inter-particle separations or do not decay with particle separation. We detail the proposed experimental scheme and consider two examples of interacting phenomena, self-trapping and the decay of Bloch oscillations, that are observable with the proposed technique.Graphical abstract

Randomized benchmarking in the analogue setting

Current development in programmable analogue quantum simulators (AQS), whose physical implementation can be realised in the near-term compared to those of large-scale digital quantum computers, highlights the need for robust testing techniques in analogue platforms. Methods to properly certify or benchmark AQS should be efficiently scalable, and also provide a way to deal with errors from state preparation and measurement (SPAM). Up to now, attempts to address this combination of requirements have generally relied on model-specific properties. We put forward a new approach, applying a well-known digital noise characterisation technique called randomized benchmarking (RB) to the analogue setting. RB is a scalable experimental technique that provides a measure of the average error-rate of a gate-set on a quantum hardware, incorporating SPAM errors. We present the original form of digital RB, the necessary alterations to translate it to the analogue setting and introduce the analogue randomized benchmarking protocol (ARB). In ARB we measure the average error-rate per time evolution of a family of Hamiltonians and we illustrate this protocol with two case-studies of analogue models; classically simulating the system by incorporating several physically motivated noise scenarios. We find that for the noise models tested, the data fit with the theoretical predictions and we gain values for the average error rate for differing unitary sets. We compare our protocol with other relevant RB methods, where both advantages (physically motivated unitaries) and disadvantages (difficulty in reversing the time-evolution) are discussed.

Hamiltonian Tomography via Quantum Quench.

We show that it is possible to uniquely reconstruct a generic many-body local Hamiltonian from a single pair of generic initial and final states related by evolving with the Hamiltonian for any time interval. We then propose a practical version of the protocol involving multiple pairs of such initial and final states. Using the eigenstate thermalization hypothesis, we provide bounds on the protocol's performance and stability against errors from measurements and in the ansatz of the Hamiltonian. The protocol is efficient (requiring experimental resources scaling polynomially with system size in general and constant with system size given translation symmetry) and thus enables analog and digital quantum simulators to verify implementation of a putative Hamiltonian.

SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers

An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto qubit degrees of freedom is presented. This new mapping allows for a reduced unphysical Hilbert space. Insensitivity to interactions within this unphysical space is exploited to design more efficient quantum circuits. Local gauge symmetry is used to analytically incorporate the angular momentum alignment, leading to qubit registers encoding the total angular momentum on each link. The results of a multi-plaquette calculation on IBM's quantum hardware are presented.

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp(tH) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. We provide optimized decompositions up to order t6. The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n=2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

Parton physics on a quantum computer

Parton distribution functions and hadronic tensors may be computed on a universal quantum computer without many of the complexities that apply to Euclidean lattice calculations. We detail algorithms for computing parton distribution functions and the hadronic tensor in the Thirring model. Their generalization to QCD is discussed, with the conclusion that the parton distribution function is best obtained by fitting the hadronic tensor, rather than direct calculation. As a side effect of this method, we find that lepton-hadron cross sections may be computed relatively cheaply. Finally, we estimate the computational cost of performing such a calculation on a digital quantum computer, including the cost of state preparation, for physically relevant parameters.

Digital Quantum Simulation of Linear and Nonlinear Optical Elements

We provide a recipe for the digitalization of linear and nonlinear quantum optics in networks of superconducting qubits. By combining digital techniques with boson-qubit mappings, we address relevant problems that are typically considered in analog simulators, such as the dynamical Casimir effect or molecular force fields, including nonlinearities. In this way, the benefits of digitalization are extended in principle to a new realm of physical problems. We present preliminary examples launched in IBM Q 5 Tenerife.

Digital-analog quantum computation

Digital quantum computing paradigm offers highly-desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multi-qubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. We construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and $M$-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise~DAQC) with an always-on multi-qubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.

Synaptic weighting in single flux quantum neuromorphic computing

Josephson junctions act as a natural spiking neuron-like device for neuromorphic computing. By leveraging the advances recently demonstrated in digital single flux quantum (SFQ) circuits and using recently demonstrated magnetic Josephson junction (MJJ) synaptic circuits, there is potential to make rapid progress in SFQ-based neuromorphic computing. Here we demonstrate the basic functionality of a synaptic circuit design that takes advantage of the adjustable critical current demonstrated in MJJs and implement a synaptic weighting element. The devices were fabricated with a restively shunted Nb/AlOx-Al/Nb process that did not include MJJs. Instead, the MJJ functionality was tested by making multiple circuits and varying the critical current, but not the external shunt resistance, of the oxide Josephson junction that represents the MJJ. Experimental measurements and simulations of the fabricated circuits are in good agreement.

Digital-analog quantum algorithm for the quantum Fourier transform

Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.

Prescriptive Modelling System Design for an Armature Multi-coil Rewinding Cobot Machine

Abstract Digital transformation has ushered in the digital economy, powered by digital intelligence and quantum computing. The various winding topologies in rotary machines result from multi-variant design specifications and connection types. Rewinding of rotary machines is a behaviour-based decision-making process conducted within the shop floor, as the procedure is dependent on multi-input multi-output variables. Due to high data variability in service remanufacturing of armature windings in rotary machines, data abstraction for intelligent automation and analytics leads to increased operational productivity and new insights into market dynamics. In this light, the aim of the paper is to illustrate the design of a prescriptive modelling system of a symmetrical multi-coil winding machine for armature winding. The proposed system is a hybrid least squares support vector machine and adaptive neuro-fuzzy inference system for optimizing and maintaining a copper fill factor at 90.7%. A mixed method research was utilized for qualitative and quantitative for the multivariate parameters. The results show that the system through in-slot repetitive orthocyclic winding process, with multi-spindle concentric layering improves the energy efficiency of the induction motors, which in turn lowers winding faults during the remanufacturing process. Streamlining operations through fog computing further enhances system latency and process reliability towards sustainable industrialization.

Monitoring AI progress for corporate governance

Artificial Intelligence technologies are predicted to contribute up to $16 trillion to the global economy by 2030. This rapid increase in AI development will have tremendous significance for all the major players for effective corporate governance and national leadership: boards of directors, owners, regulators, legislators, and the national public interest. While AI is believed to increase both the productivity and competitive advantage, it will lead to rapid transformation in the work force and evolve with a high degree of uncertainty. To facilitate the survival of public and other corporations and entities, all these major players should closely monitor the progress and pay attention to major trends in AI. The main research question of this paper is what are the key threats, challenges, and opportunities of AI. Major threats are the replacement of human activity with AI activity, which may not be able to be controlled by humans. Such control is a major challenge concerning AI as is the control and opportunity of human-AI partnerships. Digital dashboards and quantum computers are also part of all these challenges and opportunities. Accordingly, the paper studies the following AI topics currently being explored in the AI literature: key questions and issues for AI, monitoring trends in AI development, digital board audits for AI action plans, AI robotic process automation, and quantum computers with AI implications, AI progress assessment and conclusions.

Quantum Approximate Optimization With Parallelizable Gates

The quantum approximate optimization algorithm (QAOA) has been introduced as a heuristic digital quantum computing scheme to find approximate solutions of combinatorial optimization problems. We present a scheme to parallelize this approach for arbitrary all-to-all connected problem graphs in a layout of quantum bits (qubits) with nearest-neighbor interactions. The protocol consists of single qubit operations that encode the optimization problem, whereas interactions are problem-independent pairwise CNOT gates among nearest neighbors. This allows for a parallelizable implementation in quantum devices with a planar lattice geometry. The basis of this proposal is a lattice gauge model, which also introduces additional parameters and protocols for QAOA to improve the efficiency.

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

AbstractThe past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present Review aims at giving a comprehensive outlook on the state‐of‐the‐art capabilities offered from these near‐term noisy devices as universal quantum simulators, that is, programmable quantum computers potentially able to calculate the time evolution of many physical models. First, a pedagogic overview on the basic theoretical background pertaining digital quantum simulations is given, with a focus on hardware‐dependent mapping of spin‐type Hamiltonians into the corresponding quantum circuit as a key initial step toward simulating more complex models. Then, the main experimental achievements obtained in the last decade are reviewed, focusing on the digital quantum simulation of such spin models by employing two leading quantum architectures. Their performances are compared, and future challenges are outlined, also in view of prospective hybrid technologies, towards the ultimate goal of reaching the long‐sought quantum advantage for the simulation of complex many‐body models in the physical sciences.

Toward convergence of effective-field-theory simulations on digital quantum computers

We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansaetze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of $E_4=-2.220 \pm 0.179$MeV may be compared with the exact Deuteron ground-state energy $-2.224$MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps for the first time. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.