Control Of Quantum Systems Research Articles

Distributed Quantum Computing and Network Control for Accelerated VQE

Interconnecting small quantum computers will be essential in the future for creating large scale, robust quantum computers. Methods for distributing monolithic quantum algorithms efficiently are thus needed. In this work we consider an approach for distributing the accelerated variational quantum eigensolver (AVQE) algorithm over arbitrary sized - in terms of number of qubits - distributed quantum computers. We consider approaches for distributing qubit assignments of the Ansatz states required to estimate the expectation value of Hamiltonian operators in quantum chemistry in a parallelized computation and provide a systematic approach to generate distributed quantum circuits for distributed quantum computing. Moreover, we propose an architecture for a distributed quantum control system in the settings of centralized and decentralized network control.

Digital quantum simulation of Floquet topological phases with a solid-state quantum simulator

Harnessing the dynamics of complex quantum systems is an area of much interest and a quantum simulator has emerged as a promising platform to probe exotic topological phases. Since the flexibility offered by various controllable quantum systems has helped gain insight into the quantum simulation of such complicated problems, an analog quantum simulator has recently shown its feasibility to tackle the problems of exploring topological phases. However, digital quantum simulation and the detection of topological phases still remain elusive. Here, we develop and experimentally realize the digital quantum simulation of topological phases with a solid-state quantum simulator at room temperature. Distinct from previous works dealing with static topological phases, the topological phases emulated here are Floquet topological phases. Furthermore, we also illustrate the procedure of digitally simulating a quantum quench and observing the nonequilibrium dynamics of Floquet topological phases. Using a quantum quench, the 0- and π -energy topological invariants are unambiguously detected through measuring time-averaged spin polarizations. We believe our experiment opens up a new avenue to digitally simulate and detect Floquet topological phases with fast-developed programmable quantum simulators.

Sufficient conditions and constraints for reversing general quantum errors

Reversing the effects of a quantum evolution, for example as is done in error correction, is an important task for controlling quantum systems in order to produce reliable quantum devices. When the evolution is governed by a completely positive map, there exist reversibility conditions, known as the quantum error correcting code conditions, which are necessary and sufficient conditions for the reversibility of a quantum operation on a subspace, the code space. However, if we suppose that the evolution is not described by a completely positive map, necessary and sufficient conditions are not known. Here we consider evolutions that do not necessarily correspond to a completely positive map. We prove that the completely positive map error correcting code conditions can lead to a code space that is not in the domain of the map, meaning that the output of the map is not positive. A corollary to our theorem provides a class of relevant examples. Finally, we provide a set of sufficient conditions that will enable the use of quantum error correcting code conditions while ensuring positivity.

Geometrizing Quantum Dynamics of a Bose-Einstein Condensate

We show that quantum dynamics of Bose-Einstein condensates in the weakly interacting regime can be geometrized by a Poincaré disk. Each point on such a disk represents a thermofield double state, the overlap between which equals the metric of this hyperbolic space. This approach leads to a unique geometric interpretation of stable and unstable modes as closed and open trajectories on the Poincaré disk, respectively. The resonant modes that follow geodesics naturally equate fundamental quantities including the time, the length, and the temperature. Our work suggests a new geometric framework to coherently control quantum systems and reverse their dynamics using SU(1,1) echoes. In the presence of perturbations breaking the SU(1,1) symmetry, SU(1,1) echoes deliver a new means to measure these perturbations such as the interactions between excited particles.

Drawing together control landscape and tomography principles

The ability to control quantum systems using shaped fields as well as to infer the states of such controlled systems from measurement data are key tasks in the design and operation of quantum devices. Here we associate the success of performing both tasks to the structure of the underlying control landscape. We relate the ability to control and reconstruct the full state of the system to the absence of singular controls, and show that for sufficiently long evolution times singular controls rarely occur. Based on these findings, we describe a learning algorithm for finding optimal controls that makes use of measurement data obtained from partially accessing the system. Open challenges stemming from the concentration of measure phenomenon in high dimensional systems are discussed.

Solid-State Qubits: 3D Integration and Packaging

Quantum processing has the potential to transform the computing landscape by enabling efficient solutions to problems that are intractable using classical processors. The field was sparked by a suggestion from physicist Richard Feynman in 1981 that a controllable quantum system can be used to simulate other quantum systems, such as the energy band structure of complex materials or the chemical reaction rates of intricate molecules. In the 1990s, interest in quantum computing grew rapidly with the introduction of the first quantum "killer app"-the potential of a large-scale quantum processor to break certain types of public encryption schemes [1]. Recently, there has been growing consensus that myriad other fields besides data security could be impacted by the development of a quantum processor, including machine learning [2], many optimization problems [3], and Feynman's original idea of the simulation of materials properties [4]. In recent years, the field has progressed rapidly, but many technical challenges must be overcome before a large-scale quantum processor can be built. This article focuses on the development of packaging for solid-state qubits and the use of 3D integration to address this challenge.

Enabling Pulse-Level Programming, Compilation, and Execution in XACC

Noisy gate-model quantum processing units (QPUs) are currently available from vendors over the cloud, and digital quantum programming approaches exist to run low-depth circuits on physical hardware. These digital representations are ultimately lowered to pulse-level instructions by vendor quantum control systems to affect unitary evolution representative of the submitted digital circuit. Vendors are beginning to open this pulse-level control system to the public via specified interfaces. Robust programming methodologies, software frameworks, and backend simulation technologies for this analog model of quantum computation will prove critical to advancing pulse-level control research and development. Prototypical use cases for this include error mitigation, optimal pulse control, and physics-inspired pulse construction. Here we present an extension to the XACC quantum-classical software framework that enables pulse-level programming for superconducting, gate-model quantum computers, and a novel, general, and extensible pulse-level simulation backend for XACC that scales on classical compute clusters via MPI. Our work enables custom backend Hamiltonian definitions and gate-level compilation to available pulses with a focus on performance and scalability. We end with a demonstration of this capability, and show how to use XACC for pertinent pulse-level programming tasks.

Lyapunov-based unified control method for closed quantum systems

A Lyapunov-based unified control method for closed quantum systems is proposed in this paper for the state transfers from an arbitrary initial state to a desired target state. Especially, the proposed control method can be used in the cases that the free Hamiltonian of the system is not strongly regular, and (or) the control Hamiltonian is not fully connected. Three types of control laws are proposed simultaneously based on the implicit Lyapunov control theory, in which two implicit functions and one Lyapunov function with virtual mechanical quantity are well-designed. The largest invariant set of the quantum control system is investigated, and the convergence of the control system designed is proved. A numerical simulation is implemented in detail to instruct the design procedure and demonstrate the effectiveness of the control method proposed.

Quantum Computing for Microwave Engineers [From the Guest Editor's Desk

The articles in this special section focus on quantum computing. After decades of research and development, quantum computing has recently grown into one of the hottest and most promising of all emerging fields. While large-scale quantum computing was just a pipe dream even a decade ago, today there is an intense race around the globe to build a practical quantum computer. So, as a microwave engineer, why should you be interested in quantum computing? It turns out that there is actually a significant amount of microwave engineering involved in the implementation of many controllable quantum systems.

Thermodynamics of a quantum annealer

The D-wave processor is a partially controllable open quantum system that exchanges energy with its surrounding environment (in the form of heat) and with the external time dependent control fields (in the form of work). Despite being rarely thought as such, it is a thermodynamic machine. Here we investigate the properties of the D-Wave quantum annealers from a thermodynamical perspective. We performed a number of reverse-annealing experiments on the D-Wave 2000Q via the open access cloud server Leap, with the aim of understanding what type of thermal operation the machine performs, and quantifying the degree of dissipation that accompanies it, as well as the amount of heat and work that it exchanges. The latter is a challenging task in view of the fact that one can experimentally access only the overall energy change occurring in the processor, (which is the sum of heat and work it receives). However, recent results of non-equilibrium thermodynamics (namely, the fluctuation theorem and the thermodynamic uncertainty relations), allow to calculate lower bounds on the average entropy production (which quantifies the degree of dissipation) as well as the average heat and work exchanges. The analysis of the collected experimental data shows that (1) in a reverse annealing process the D-Wave processor works as a thermal accelerator and (2) its evolution involves an increasing amount of dissipation with increasing transverse field.

Nagaoka ferromagnetism observed in a quantum dot plaquette.

Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers1. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been debated for decades2,3. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots4 to demonstrate Nagaoka ferromagnetism5. This form of itinerant magnetism has been rigorously studied theoretically6-9 but has remained unattainable in experiments. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find that the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and we can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any experimental system. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.

Enhancing quantum transport efficiency by tuning non-Markovian dephasing

We consider the problem of energy transport in a chain of coupled dissipative quantum systems in the presence of non-Markovian dephasing. We use a model of non-Markovianity which is experimentally realizable in the context of controlled quantum systems. We show that non-Markovian dephasing can significantly enhance quantum transport, and we characterize this phenomenon in terms of internal coupling strengths of the chain for some chain lengths. Finally, we show that the phenomenon of dephasing-assisted quantum transport is also enhanced in the non-Markovian scenario when compared to the Markovian case. Our work brings together engineered environments, which are a reality in quantum technologies, and energy transport, which is typically discussed in terms of complex molecular systems. We then expect that it may motivate experimental work and further theoretical investigations on resources which can enhance transport efficiency in a controllable way. This can help in the design of quantum devices with lower dissipation rates, an important concern in any practical application.

On Some New Possibilities for Controlling Quantum Systems Using Unipolar Extremely Short Pulses

Based on an approximate solution of the Schrodinger equation, the effect that a pair of extremely short small-amplitude subcycle pulses has on a quantum system is studied. It is shown that, if the pulses are shorter than the inverse frequencies of atomic transitions, the probability of transitions between levels is determined by the electric area of the pulses and the time delay between them. As a consequence, a unipolar pulse can more efficiently affect the system than a bipolar one, while a sequence of pulses realizes a selective action on quantum objects, despite a nonresonant character of the interaction.

Unitary dilations of discrete-time quantum-dynamical semigroups

We show that the discrete-time evolution of an open quantum system generated by a single quantum channel T can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e., we construct a unitary dilation of the discrete-time quantum-dynamical semigroup (Tn)n∈N0. In the case of a cyclic channel T, the auxiliary space may be chosen (partially) finite-dimensional. We further investigate discrete-time quantum control systems generated by finitely many commuting quantum channels and prove a similar unitary dilation result as in the case of a single channel.

Design and Characterization of a 28-nm Bulk-CMOS Cryogenic Quantum Controller Dissipating Less Than 2 mW at 3 K

Implementation of an error-corrected quantum computer is believed to require a quantum processor with a million or more physical qubits, and, in order to run such a processor, a quantum control system of similar scale will be required. Such a controller will need to be integrated within the cryogenic system and in close proximity with the quantum processor in order to make such a system practical. Here, we present a prototype cryogenic CMOS quantum controller designed in a 28-nm bulk CMOS process and optimized to implement a 16-word (4-bit) XY gate instruction set for controlling transmon qubits. After introducing the transmon qubit, including a discussion of how it is controlled, design considerations are discussed, with an emphasis on error rates and scalability. The circuit design is then discussed. Cryogenic performance of the underlying technology is presented, and the results of several quantum control experiments carried out using the integrated controller are described. This article ends with a comparison to the state of the art and a discussion of further research to be carried out. It has been shown that the quantum control IC achieves promising performance while dissipating less than 2 mW of total ac and dc power and requiring a digital data stream of less than 500 Mb/s.

Controlling a quantum system via its boundary conditions

We numerically study a particle in a box with moving walls. In the case where the walls are oscillating sinusoidally with a small amplitude, we show that states up to the fourth state can be populated with more than 80 percent population, while higher lying states can also be selectively excited. This work introduces a way of controlling quantum systems which does not rely on (dipole) selection rules.Graphical abstract

Simulation of Quantum Universe

Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and isotropic field in the Friedmann-Robertson-Walker universe can be simulated by a charge in an electrically modulated ion trap. The quantum states of these time-dependent oscillators are constructed by quantum invariants. Further, we propose simulation of quantum Friedmann-Robertson-Walker universe with a minimal massive scalar field by a charged scalar field in a homogeneous, time-dependent, magnetic field in quantum electrodynamics and investigate the Cauchy problem of how the wave functions evolve.

Reachability in Infinite-Dimensional Unital Open Quantum Systems with Switchable GKS–Lindblad Generators

In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite-dimensional open quantum dynamical systems following a unital Kossakowski–Lindblad master equation extended by controls. More precisely, their time evolution shall be governed by an inevitable potentially unbounded Hamiltonian drift term H0, finitely many bounded control Hamiltonians Hj allowing for (at least) piecewise constant control amplitudes [Formula: see text] plus a bang-bang (i.e., on-off) switchable noise term ГV in Kossakowski–Lindblad form. Generalizing standard majorization results from finite to infinite dimensions, we show that such bilinear quantum control systems allow to approximately reach any target state majorized by the initial one as up to now it only has been known in finite dimensional analogues. The proof of the result is currently limited to the bounded control Hamiltonians Hj and for noise terms ГV with compact normal V.

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model

Scrambling is the process by which information stored in local degrees of freedom spreads over the many-body degrees of freedom of a quantum system, becoming inaccessible to local probes and apparently lost. Scrambling and entanglement can reconcile seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes. Here, we demonstrate that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect). We compute FOTOCs for the paradigmatic Dicke model, and show they can measure subsystem Rényi entropies and inform about quantum thermalization. Moreover, we illustrate why FOTOCs give access to a simple relation between quantum and classical Lyapunov exponents in a chaotic system without finite-size effects. Our results open a path to experimental use FOTOCs to explore scrambling, bounds on quantum information processing and investigation of black hole analogs in controllable quantum systems.

Multipartite-entanglement tomography of a quantum simulator

Multipartite-entanglement tomography, namely the quantum Fisher information (QFI) calculated with respect to different collective operators, allows to fully characterize the phase diagram of the quantum Ising chain in a transverse field with variable-range interaction. In particular, it recognizes the phase stemming from long-range (LR) antiferromagnetic interaction, a capability also shared by the spin squeezing. Furthermore, the QFI locates the quantum critical points, both with vanishing and nonvanishing mass gap. In this case, we also relate the finite-size power-law exponent of the QFI to the critical exponents of the model, finding a signal for the breakdown of conformal invariance in the deep LR regime. Finally, the effect of a finite temperature on the multipartite entanglement, and ultimately on the phase stability, is considered. In light of the current realizations of the model with trapped ions and of the potential measurability of the QFI, our approach yields a promising strategy to probe LR physics in controllable quantum systems.