Digital Quantum Research Articles

Digital lattice gauge theories

We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a $\mathbb{Z}_{3}$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.

Half a state, half an operator: a general formulation of stators

Stators, which may be intuitively defined as ‘half states, half operators’ are mathematical objects which act on two Hilbert spaces and utilize entanglement to create remote operations and exchange information between two physical systems. In particular, they allow to induce effective dynamics on one physical system by acting on the other one, given they have properly been connected with the right stator. In this work, the concept of stators is generalized and formalized in a way that allows the utilization of stators for some physical problems based on symmetry groups, and in particular digital quantum simulation.

Current status and future prospects for solid-state quantum information device development to realize digital universal quantum computing

Current status and future prospects for solid-state quantum information device development to realize digital universal quantum computing

Helmholtz Natural Modes: the universal and discrete spatial fabric of electromagnetic wavefields

The interaction of electromagnetic waves with matter is at the foundation of the way we perceive and explore the world around us. In fact, when a field interacts with an object, signatures on the object’s geometry and physical properties are recorded in the resulting scattered field and are transported away from the object, where they can eventually be detected and processed. An optical field can transport information through its spectral content, its polarization state, and its spatial distribution. Generally speaking, the field’s spatial structure is typically subjected to changes under free-space propagation and any information therein encoded gets reshuffled by the propagation process. We must ascribe to this fundamental reason the fact that spectroscopy was known to the ancient civilizations already, and founded as modern science in the middle of seventeenth century, while to date we do not have an established scientific of field of ‘spatial spectroscopy’ yet. In this work we tackle this issue and we show how any field, whose evolution is dictated by Helmholtz equation, contains a universal and invariant spatial structure. When expressed in the framework of this spatial fabric, the spatial information content carried by any field reveals its invariant nature. This opens the way to novel paradigms in optical digital communications, inverse scattering, materials inspection, nanometrology and quantum optics.

Artificial quantum thermal bath: Engineering temperature for a many-body quantum system

Temperature determines the relative probability of observing a physical system in an energy state when that system is energetically in equilibrium with its environment. In this paper we present a theory for engineering the temperature of a quantum system different from its ambient temperature. We define criteria for an engineered quantum bath that, when coupled to a quantum system with Hamiltonian $H$, drives the system to the equilibrium state $\frac{{e}^{\ensuremath{-}H/T}}{\mathrm{Tr}({e}^{\ensuremath{-}H/T})}$ with a tunable parameter $T$. This is basically an analog counterpart of the digital quantum metropolis algorithm. For a system of superconducting qubits, we propose a circuit-QED approximate realization of such an engineered thermal bath consisting of driven lossy resonators. Our proposal opens the path to simulate thermodynamical properties of many-body quantum systems of size not accessible to classical simulations. Also we discuss how an artificial thermal bath can serve as a temperature knob for a hybrid quantum-thermal annealer.

Supramolecular Complexes for Quantum Simulation

Simulating the evolution of quantum systems on a classical computer is a yellow very challenging task, which could be easily tackled by digital quantum simulators. These are intrinsically quantum devices whose parameters can be controlled in order to mimic the evolution of a broad class of target Hamiltonians. We describe here a quantum simulator implemented on a linear register of molecular Cr7Ni qubits, linked through Co2+ ions which act as switches of the qubit–qubit interaction. This allows us to implement one- and two-qubit gates on the chain with high-fidelity, by means of uniform magnetic pulses. We demonstrate the effectiveness of the scheme by numerical experiments in which we combine several of these elementary gates to implement the simulation of the transverse field Ising model on a set of three qubits. The very good agreement with the expected evolution suggests that the proposed architecture can be scaled to several qubits.

Local spin operators for fermion simulations

Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on spins. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here we re-examine an auxiliary fermion construction which maps fermionic operators to local operators on spins. The local simulation is performed by relaxing the requirement that the number of spins should match the number of fermionic modes. Instead, auxiliary modes are introduced to enable non-consecutive fermionic couplings to be simulated with constant low-rank tensor products on spins. We connect the auxiliary fermion construction to other topological models and give examples of the construction.

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics.

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case.

Digital quantum simulation of many-body non-Markovian dynamics

We present an algorithmic method for the digital quantum simulation of many-body locally indivisible non-Markovian open quantum systems. It consists of two parts: firstly, a Suzuki-Lie-Trotter decomposition of the global system propagator into the product of subsystem propagators, which may not be quantum channels, and secondly, an algorithmic procedure for the implementation of the subsystem propagators through unitary operations and measurements on a dilated space. By providing rigorous error bounds for the relevant Suzuki-Lie-Trotter decomposition, we are able to analyze the efficiency of the method, and connect it with an appropriate measure of the local indivisibility of the system. In light of our analysis, the proposed method is expected to be experimentally achievable for a variety of interesting cases.

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer.

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman's idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments-the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.

Quantum chemistry and charge transport in biomolecules with superconducting circuits.

We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated quantum algorithms to allow the study of environmental effects.

Genetic Algorithms for Digital Quantum Simulations.

We propose genetic algorithms, which are robust optimization techniques inspired by natural selection, to enhance the versatility of digital quantum simulations. In this sense, we show that genetic algorithms can be employed to increase the fidelity and optimize the resource requirements of digital quantum simulation protocols while adapting naturally to the experimental constraints. Furthermore, this method allows us to reduce not only digital errors but also experimental errors in quantum gates. Indeed, by adding ancillary qubits, we design a modular gate made out of imperfect gates, whose fidelity is larger than the fidelity of any of the constituent gates. Finally, we prove that the proposed modular gates are resilient against different gate errors.

Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits

We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms.

FPGA based digital phase-coding quantum key distribution system

Quantum key distribution (QKD) is a technology with the potential capability to achieve information-theoretic security. Phasecoding is an important approach to develop practical QKD systems in fiber channel. In order to improve the phase-coding modulation rate, we proposed a new digital-modulation method in this paper and constructed a compact and robust prototype of QKD system using currently available components in our lab to demonstrate the effectiveness of the method. The system was deployed in laboratory environment over a 50 km fiber and continuously operated during 87 h without manual interaction. The quantum bit error rate (QBER) of the system was stable with an average value of 3.22% and the secure key generation rate is 8.91 kbps. Although the modulation rate of the photon in the demo system was only 200 MHz, which was limited by the Faraday- Michelson interferometer (FMI) structure, the proposed method and the field programmable gate array (FPGA) based electronics scheme have a great potential for high speed QKD systems with Giga-bits/second modulation rate.

Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits.

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model and we numerically simulate the scheme by including the main sources of decoherence.

Analog quantum computing (AQC) and the need for time-symmetric physics

This paper discusses what will be necessary to achieve the full potential capabilities of analog quantum computing (AQC), which is defined here as the enrichment of continuous-variable computing to include stochastic, nonunitary circuit elements such as dissipative spin gates and address the wider range of tasks emerging from new trends in engineering, such as approximation of stochastic maps, ghost imaging and new forms of neural networks and intelligent control. This paper focuses especially on what is needed in terms of new experiments to validate remarkable new results in the modeling of triple entanglement, and in creating a pathway which links fundamental theoretical work with hard core experimental work, on a pathway to AQC similar to the pathway to digital quantum computing already blazed by Zeilinger's group. It discusses the most recent experiments and reviews two families of alternative models based on the traditional eigenvector projection model of polarizers and on a new family of local realistic models based on Markov Random Fields across space---time adhering to the rules of time-symmetric physics. For both families, it reviews lumped parameter versions, continuous time extension and possibilities for extension to continuous space and time.

New technologies and modern planning strategies in CMF trauma cases

As a principle, ideas and visions constantly become real after a period of time. Affected by an incredible fast moving evolution within the digital world quantum jumps can be recorded in all kind of technologies. Internet communication offers a fast immeasurable platform bundling and designing knowledge in a self-learning process moving in an exponential spiral.

Digital quantum simulation of fermionic models with a superconducting circuit.

One of the key applications of quantum information is simulating nature. Fermions are ubiquitous in nature, appearing in condensed matter systems, chemistry and high energy physics. However, universally simulating their interactions is arguably one of the largest challenges, because of the difficulties arising from anticommutativity. Here we use digital methods to construct the required arbitrary interactions, and perform quantum simulation of up to four fermionic modes with a superconducting quantum circuit. We employ in excess of 300 quantum logic gates, and reach fidelities that are consistent with a simple model of uncorrelated errors. The presented approach is in principle scalable to a larger number of modes, and arbitrary spatial dimensions.

Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources which are polynomial in the number of spins and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.

On a propagation-invariant, orthogonal modal expansion on the unit disk: going beyond Nijboer–Zernike theory of aberrations

Nijboer-Zernike's circle polynomials are broadly used for the evaluation of aberrations of optical systems or, more generally, wavefront analysis. This is because they are orthogonal over a unit circle and are directly related to the balanced classical aberrations for imaging systems with circular pupils. However, such expansion and successive extensions of the original theory suffer from a key limitation: it does not preserve its form under propagation. This means that even if a Nijboer-Zernike expansion for a field is known on a given reference plane, as soon as another plane is considered, a new, different set of polynomials for the same field appears. The origin of this problem is to be ascribed to the fact that Nijboer-Zernike polynomials are a useful mathematical tool which, however, are not bound to the physics of the electromagnetic problem they are employed in. In this work, we show that a more appropriate modal expansion does exist that is not only orthogonal on the unit disk but is also invariant on propagation. Besides impacting the field of aberrations analysis and retrieval, the modal expansion introduced here holds an enormous potential for digital classical and quantum optical communications, optical metrology, and adaptive optics too. The practical implementation, physical interpretation, and visualization of this new modal expansion are all very straightforward.