The real-time flux dynamics of up to three superconducting quantum interference devices (SQUIDs) are studied by numerically solving the time-dependent Schr\"odinger equation. The numerical results are used to scrutinize the mapping of the flux degrees of freedom onto two-level systems (the qubits) as well as the performance of the intermediate SQUID as a tunable coupling element. It is shown that the qubit representation yields a good description of the flux dynamics during quantum annealing and the presence of the tunable coupling element does not have negative effects on the overall performance. Additionally, data obtained from a simulation of the dynamics of two-level systems during quantum annealing are compared to experimental data produced by the D-Wave 2000Q quantum annealer. The effects of finite temperature are incorporated in the simulation by coupling the qubit system to a bath of two-level systems. It is shown that an environment modeled as noninteracting two-level systems coupled to the qubits can produce data which matches the experimental data much better than the simulation data of the qubits without coupling to an environment and better than data obtained from a simulation of an environment modeled as interacting two-level systems coupling to the qubits.
The real-time flux dynamics of up to three superconducting quantum interference devices (SQUIDs) are studied by numerically solving the time-dependent Schr"odinger equation. The numerical results are used to scrutinize the mapping of the flux degrees of freedom onto two-level systems (the qubits) as well as the performance of the intermediate SQUID as a tunable coupling element. It is shown that the qubit representation yields a good description of the flux dynamics during quantum annealing and the presence of the tunable coupling element does not have negative effects on the overall performance. Additionally, data obtained from a simulation of the dynamics of two-level systems during quantum annealing are compared to experimental data produced by the D-Wave 2000Q quantum annealer. The effects of finite temperature are incorporated in the simulation by coupling the qubit system to a bath of two-level systems. It is shown that an environment modeled as noninteracting two-level systems coupled to the qubits can produce data which matches the experimental data much better than the simulation data of the qubits without coupling to an environment and better than data obtained from a simulation of an environment modeled as interacting two-level systems coupling to the qubits.
In this thesis, we study the operation of existing quantum annealers by simulating the real-time dynamics of two coupled flux qubits based on SQUIDs (superconducting quantum interference devices) during quantum annealing processes. We investigate two aspects. First, we study the influence of the higher energy levels which are neglected when deriving the qubit Hamiltonian from the superconducting circuit model including the tunable coupler. Second, we investigate the influence of an environment on the qubit system during quantum annealing. For the latter, we examine two different models for the environment, a generic spin bath and non-interacting two-level systems. For simulating the dynamics, we use the Suzuki-Trotter product-formula algorithm to solve the time-dependent Schrödinger equation numerically. We find that the higher energy levels as well as the presence of the tunable coupler have little influence on the performance of the quantum annealing process for most of the investigated problem instances, suggesting that the two-level approximation works very well. However, we find that for a particular class of instances, the results of the SQUID model and the qubit model show certain deviations. Additionally, we perform experiments on the D-Wave 2000Q quantum annealer. Our study of the two models for the environment suggests that the model of non-interacting two-level systems is better suited to describe the data obtained from the real device than the generic spin bath model.
The field of quantum information has been a fast growing field of research in the last few decades. The reason for this development is the potentially immense power of quantum computers, capable of solving hard problems in a fraction of the time it would take a classical computer. Quantum annealers are a type of quantum computer that seek to solve computational problems by finding the ground state of a quantum system. This type of quantum computer has been implemented on a large scale using superconducting flux quantum bits, but the computational power is limited. One potential improvement to help in this context is the implementation of multi-body interactions between quantum bits. Many-body interactions would be useful in allowing quantum annealers to solve more complex problems that are relevant in various areas of quantum information and science and implementing quantum error correction. \n \nWe present a superconducting device that implements a strong and tunable in sign and magnitude three-body interaction between superconducting flux quantum bits. The circuit design proposed has vanishing two-body interactions and robustness against noise and parameter variations. This circuit behaves as an ideal computational basis ZZZ coupler in a simulated three-qubit quantum annealing experiment. These properties are confirmed by calculations based on the Born-Oppenheimer approximation, a two-level spin model for the coupling circuit, and full numerical diagonalization. \n \nThe proposed circuit is based on already available technology and therefore could be readily implemented in the next generation of quantum annealing hardware. This work will be relevant for advanced quantum annealing protocols and future developments of high-order many-body interactions in quantum computers and simulators.
We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamics of two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a superconducting quantum interference device. Those two elements allow to engineer qubits Hamiltonians with XX, YY, and ZZ interactions, including ultrastrongly coupled ones. We present an exhaustive numerical study for two three-Josephson junctions flux qubit that can be directly used in experimental work. The method developed here, namely, the numerical tool to extract qubit effective Hamiltonians at strong coupling, can be applied to replicate our analysis for general systems of many qubits and any type of coupling.
Quantum annealing can potentially be used to find better solutions to hard optimization problems faster than purely classical hardware. To take full advantage of quantum effects such as tunneling, a physical annealer should be comprised of qubits with a sufficient degree of quantum coherence. In addition, to encode useful problems, an annealer should provide a dense physical connectivity graph between qubits. Towards these goals, we develop superconducting ``fluxmon'' flux qubits suitable for high-connectivity quantum annealing without the use of performance-degrading lossy dielectrics. We carry out in-depth studies of noise and dissipation, and of qubit-qubit coupling in the strongly nonlinear regime. We perform the first frequency-resolved measurements extracting both the quantum and classical parts of the 1/f flux noise intrinsic to superconducting devices, and observe the classical-to-quantum crossover of the noise. We also identify atomic hydrogen as a magnetic dissipation source. We then implement tunable inter-qubit coupling compatible with high connectivity, and provide direct spectroscopic measurements of ultra-strong coupling between qubits. Finally, we use our system to explore quantum annealing faster than the system thermalization time, a previously unaccessed regime.
Abstract : Quantum annealing is a general strategy for solving difficult optimization problems with the aid of quantum adiabatic evolution [1, 2]. Both analytical and numerical evidence suggests that under idealized, closed system conditions, quantum annealing can outperform classical thermalization-based algorithms such as simulated annealing [3, 4]. Do engineered quantum annealing devices effectively perform classical thermalization when coupled to a decohering thermal environment? To address this we establish, using superconducting flux qubits with programmable spin-spin couplings, an experimental signature which is consistent with quantum annealing, and at the same time inconsistent with classical thermalization, in spite of a decoherence timescale which is orders of magnitude shorter than the adiabatic evolution time. This suggests that programmable quantum devices, scalable with current superconducting technology, implement quantum annealing with a surprising robustness against noise and imperfections.
This chapter focuses on the application of Nb Josephson junctions (JJs) in quantum annealing (QA). It begins with a brief introduction to diffident strategies for implementing quantum computation (QC) with an emphasis on quantum annealing. The chapter presents the basic physics of the simplest superconducting flux qubit: radio frequency superconducting quantum interference devices (RF-SQUID). It gives a brief description on the design and realization of couplers, and control and measurement circuitry using Nb Josephson junctions. The chapter describes a scalable architecture upon which quantum annealing processors consisting up to 1024 superconducting flux qubits made of more than 104 Nb Josephson junctions. It discusses evidence on whether D-Wave 2X, which is the latest quantum annealing processor available, works as expected. The chapter also focuses on the physics and application of RF-SQUID flux qubits because the fundamental building blocks of the most advanced quantum annealers demonstrated so far are variations of superconducting flux qubits with one Josephson junction, a.k.a. the RF-SQUID.