There is a tremendous interest in fabricating superconducting flux circuits that are nonstoquastic -- i.e., have positive off-diagonal matrix elements -- in their qubit representation, as these circuits are thought to be unsimulable by classical approaches due to the presence of a sign problem and thus could play a key role in the demonstration of speedups in quantum annealing protocols. We show, however, that the elimination of the sign problem in these systems is possible by the direct simulation of the flux circuits. Our approach not only obviates the reduction of flux circuits to their qubit representation but also produces results that are more in the spirit of the experimental setup. We discuss the implications of our work, arguing that our findings cast doubt on the conception that superconducting flux circuits represent the correct avenue for universal adiabatic quantum computers.
We analyze whether circuit-QED Hamiltonians are stoquastic focusing on systems of coupled flux qubits: we show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. Despite this, we corroborate the recent finding [arXiv:1903.06139] that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits. We find that if the capacitive coupling is sufficiently small, this non-stoquasticity of the effective qubit Hamiltonian can be avoided if we perform a canonical transformation prior to projectin…
We present a classical Monte Carlo (MC) scheme which efficiently estimates an imaginary-time, decaying signal for stoquastic (i.e. sign-problem-free) local Hamiltonians. The decay rates in this signal correspond to Hamiltonian eigenvalues (with associated eigenstates present in an input state) and can be classically extracted using a classical signal processing method like ESPRIT. We compare the efficiency of this MC scheme to its quantum counterpart in which one extracts eigenvalues of a general local Hamiltonian from a real-time, oscillatory signal obtained through quantum phase estimation c…
We have analyzed and proposed coupling mechanisms between Three Josephson Junction Flux Qubits (3JJQ). For this, we have developed a numerical method to extract the effective Hamiltonian of a system of coupled qubits via the Schrieffer-Wolff transformation (SWT). We then give a comprehensive introduction to the 3JJQ, and study it analytically by approximating its potential with a Harmonic well. With a clear understanding of the 3JJQs, we use the SWT to gain intuition about their effective dipolar interaction with the electromagnetic field, and use that intuition to propose and study analytical…
An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits, the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method. This method does not require any ad hoc assumpt…
For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paper we derive the general interaction mediated by such a circuit under the Born-Oppenheimer Approximation. This interaction naturally decomposes into a classical part, with origin in the classical circuit equations, and a quantum part, associated with the coupler's zero-point energy. Our result is non-perturbative in the qubit-coupler coupling strengths and in the coupler nonlinearity. This can lead to significant …
Coherent pulse control for quantum memory is viable in the optical domain but nascent in microwave quantum circuits. We show how to realize coherent storage and on-demand pulse retrieval entirely within a superconducting circuit by exploiting and extending existing electromagnetically induced transparency technology in superconducting quantum circuits. Our scheme employs a linear array of superconducting artificial atoms coupled to a microwave transmission line.
We present a framework for modeling superconducting circuits that integrates classical microwave analysis with circuit quantization. Our framework enables the calculation of the lossy eigenmodes of superconducting circuits, and we demonstrate the method by analyzing several circuits relevant to multiplexed, Purcell filtered transmon readout architectures. We show that the transmon relaxation times obtained by our method agree with the established approximation $T_1 \approx C/\text{Re}[Y(iω_q)]$ away from environmental resonances and do not vanish on resonance. We also show that the hybridizati…
We develop a theory for the quantum circuit consisting of a superconducting loop interrupted by four Josephson junctions and pierced by a magnetic flux (either static or time-dependent). In addition to the similarity with the typical three-junction flux qubit in the double-well regime, we demonstrate the difference of the four-junction circuit from its three-junction analogue, including its advantages over the latter. Moreover, the four-junction circuit in the single-well regime is also investigated. Our theory provides a tool to explore the physical properties of this four-junction supercondu…
We introduce CircuitQ, an open-source toolbox for the analysis of superconducting circuits implemented in Python. It features the automated construction of a symbolic Hamiltonian of the input circuit and a dynamic numerical representation of the Hamiltonian with a variable basis choice. Additional features include the estimation of the T1 lifetimes of the circuit states under various noise mechanisms. We review previously established circuit quantization methods and formulate them in a way that facilitates the software implementation. The toolbox is then showcased by applying it to practically…
Superconducting circuits and trapped ions are promising architectures for quantum information processing. However, the natural frequencies for controlling these systems -- radio frequency ion control and microwave domain superconducting qubit control -- make direct Hamiltonian interactions between them weak. In this paper we describe a technique for coupling a trapped ion's motion to the fundamental mode of a superconducting circuit, by applying to the circuit a carefully modulated external magnetic flux. In conjunction with a non-linear element (Josephson junction), this gives the circuit an …
Superconducting circuits have emerged as a promising platform to build quantum processors. The challenge of designing a circuit is to compromise between realizing a set of performance metrics and reducing circuit complexity and noise sensitivity. At the same time, one needs to explore a large design space, and computational approaches often yield long simulation times. Here we automate the circuit design task using SCILLA, a software for automated discovery of superconducting circuits. SCILLA performs a parallelized, closed-loop optimization to design circuit diagrams that match pre-defined pr…
Superconducting quantum circuits, such as the superconducting phase qubit, have multiple quantum states that can interfere with ideal qubit operation. The use of multiple frequency control pulses, resonant with the energy differences of the multi-state system, is theoretically explored. An analytical method to design such control pulses is developed, using a generalization of the Floquet method to multiple frequency controls. This method is applicable to optimizing the control of both superconducting qubits and qudits, and is found to be in excellent agreement with time-dependent numerical sim…
We introduce an efficient tensor network toolbox to compute the low-energy excitations of large-scale superconducting quantum circuits up to a desired accuracy. We benchmark this algorithm on the fluxonium qubit, a superconducting quantum circuit based on a Josephson junction array with over a hundred junctions. As an example of the possibilities offered by this numerical tool, we compute the pure-dephasing coherence time of the fluxonium qubit due to charge noise and coherent quantum phase slips, taking into account the array degrees of freedom corresponding to a Hilbert space as large as$~15…
We investigate theoretically the ground-state property of a two-dimensional array of superconducting circuits including the on-site superconducting qubits (SQs) with weak anharmonicity. In particular, we analyse the influence of this anharmonicity on the Mott insulator to superfluid quantum phase transition. The complete ground-state phase diagrams are presented under the mean field approximation. Interestingly, the anharmonicity of SQs affects the Mott lobes enormously, and the single excitation Mott lobe disappears when the anharmonicity become zero. Our results can be used to guide the impl…
We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
We report the observation of Electromagnetically Induced Transparency (EIT) of a mechanical field, where a superconducting artificial atom is coupled to a 1D-transmission line for surface acoustic waves. An electromagnetic microwave drive is used as the control field, rendering the superconducting transmon qubit transparent to the acoustic probe beam. The strong frequency dependence of the acoustic coupling enables EIT in a ladder configuration due to the suppressed relaxation of the upper level. Our results show that superconducting circuits can be engineered to interact with acoustic fields …
Artificial atoms realized by superconducting circuits offer unique opportunities to store and process quantum information with high fidelity. Among them, implementations of circuits that harness intrinsic noise protection have been rapidly developed in recent years. These noise-protected devices constitute a new class of qubits in which the computational states are largely decoupled from local noise channels. The main challenges in engineering such systems are simultaneously guarding against both bit- and phase-flip errors, and also ensuring high-fidelity qubit control. Although partial noise …
Superconducting, flux-based qubits are promising candidates for the construction of a large scale quantum computer. We present an explicit quantum mechanical calculation of the coherent behavior of a flux based quantum bit in a noisy experimental environment such as an integrated circuit containing bias and control electronics. We show that non-thermal noise sources, such as bias current fluctuations and magnetic coupling to nearby active control circuits, will cause decoherence of a flux-based qubit on a timescale comparable to recent experimental coherence time measurements.
The development of new superconducting circuits and the improvement of existing ones rely on the accurate modeling of spectral properties which are key to achieving the needed advances in qubit performance. Systematic circuit analysis at the lumped-element level, starting from a circuit network and culminating in a Hamiltonian appropriately describing the quantum properties of the circuit, is a well-established procedure, yet cumbersome to carry out manually for larger circuits. We present work utilizing symbolic computer algebra and numerical diagonalization routines versatile enough to tackl…
We present a method to identify the coupled, normal modes of a superconducting transmission-line with an embedded lumped element circuit. We evaluate the effective transmission-line non-linearities in the case of Kerr-like Josephson interactions in the circuit and in the case where the embedded circuit constitutes a qubit degree of freedom, which is Rabi coupled to the field in the transmission-line. Our theory quantitatively accounts for the very high and positive Kerr non-linearities observed in a recent experiment [M. Rehák et.al., Appl. Phys. Lett. 104, 162604], and we can evaluate the acc…
We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum bus or direct capacitive couplings. We apply our method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest and next-nearest neighbours. Furthermore, we propose an optimal architecture for this model and discuss the benchmarking of the simulations in realistic circuit quantum electrodynamics setups.
In view of the fundamental importance and many promising potential applications, non-Abelian statistics of topologically protected states have attracted much attention recently. However, due to the operational difficulties in solid-state materials, experimental realization of non-Abelian statistics is lacking. The superconducting quantum circuit system is scalable and controllable, and thus is a promising platform for quantum simulation. Here we propose a scheme to demonstrate non-Abelian statistics of topologically protected zero-energy edge modes on a chain of superconducting circuits. Speci…
A model of repeated quantum measurements of magnetic flux in superconducting circuits manifesting tunneling is discussed. The perturbation due to the previous measurements of magnetic flux is always present unless quantum nondemolition measurements are performed. By replacing the classical notion of noninvasivity with this condition, temporal Bell-like inequalities allows one to test the observability at the macroscopic level of the conflict between realism and quantum theory.
Parasitic crosstalk in superconducting quantum devices is a leading limitation for quantum gates. We demonstrate the suppression of static ZZ crosstalk in a two-qubit, two-coupler superconducting circuit, where the frequency of a tunable coupler can be adjusted such that the ZZ interaction from each coupler destructively interfere. We verify the crosstalk elimination with simultaneous randomized benchmarking, and use a parametrically activated iSWAP interaction to achieve a Bell state preparation fidelity of 98.5% and a $\sqrt{\textrm{iSWAP}}$ gate fidelity of 94.8% obtained via quantum proces…
We propose a superconducting circuit that shows a super-radiant phase transition (SRPT) in the thermal equilibrium. The existence of the SRPT is confirmed analytically in the limit of an infinite number of artificial atoms. We also perform numerical diagonalization of the Hamiltonian with a finite number of atoms and observe an asymptotic behavior approaching the infinite limit as the number of atoms increases. The SRPT can also be interpreted intuitively in a classical analysis.
Superconducting quantum circuits is one of the leading candidates for a universal quantum computer. Designing novel qubit and multiqubit superconducting circuits requires the ability to simulate and analyze the properties of a general circuit. In particular, going outside the transmon approach, we cannot make assumptions on anharmonicity, thus precluding blackbox quantization approaches and necessitating the formal circuit quantization approach. We consider and solve two issues involved in simulating general superconducting circuits. One of the issues is the handling of free modes in the circu…
A scheme for coupling superconducting charge qubits via a one-dimensional superconducting transmission line resonator is proposed. The qubits are working at their optimal points, where they are immune to the charge noise and possess long decoherence time. Analysis on the dynamical time evolution of the interaction is presented, which is shown to be insensitive to the initial state of the resonator field. This scheme enables fast gate operation and is readily scalable to multiqubit scenario.
We propose the implementation of a digital quantum simulation of spin chains coupled to bosonic field modes in superconducting circuits. Gates with high fidelities allows one to simulate a variety of Ising magnetic pairing interactions with transverse field, Tavis-Cummings interaction between spins and a bosonic mode, and a spin model with three-body terms. We analyze the feasibility of the implementation in realistic circuit quantum electrodynamics setups, where the interactions are either realized via capacitive couplings or mediated by microwave resonators.
We show how a quantum walk can be implemented for the first time in a quantum quincunx created via superconducting circuit quantum electrodynamics (QED), and how interpolation from quantum to random walk is implemented by controllable decoherence using a two resonator system. Direct control over the coin qubit is difficult to achieve in either cavity or circuit QED, but we show that a Hadamard coin flip can be effected via direct driving of the cavity, with the result that the walker jumps between circles in phase space but still exhibits quantum walk behavior over 15 steps.
We propose a quantum analog of the internal combustion engine used in most cars. Specifically, we study how to implement the Otto-type quantum heat engine (QHE) with the assistance of a Maxwell's demon. Three steps are required: thermalization, quantum measurement, and quantum feedback controlled by the Maxwell demon. We derive the positive-work condition of this composite QHE. Our QHE can be constructed using superconducting quantum circuits. We explicitly demonstrate the essential role of the demon in this macroscopic QHE.
Liquid metal printing for superconducting circuits
Institute of Nanotechnology, Karlsruhe Institute of Technology（纳米技术研究所，卡尔斯鲁厄理工学院）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（量子材料与技术研究所，卡尔斯鲁厄理工学院）；Karlsruhe Nano Micro Facility (KNMFi), Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄纳米微设施（KNMFi），卡尔斯鲁厄理工学院（KIT））；Physikalisches Institut, Karlsruhe Institute of Technology (KIT)（物理研究所，卡尔斯鲁厄理工学院（KIT））
We discuss the known construction of two interacting superconducting circuits, based on Josephson junctions, that can be precisely engineered and easily controlled. In particular, we use the parametric excitation of two circuits, realized by an instant change of the qubit coupling, to study entropic and information properties of the density matrix of the composite system. The density matrix is obtained from the initial thermal state and is then analyzed in the approximation of small perturbation parameter and sufficiently low temperature. We also check the subadditivity condition for this syst…
We describe the implementation of weak quantum measurements in superconducting qubits, focusing specifically on transmon type devices in the circuit quantum electrodynamics architecture. To access this regime, the readout cavity is probed with on average a single microwave photon. Such low-level signals are detected using near quantum-noise-limited superconducting parametric amplifiers. Weak measurements yield partial information about the quantum state, and correspondingly do not completely project the qubit into an eigenstate. As such, we use the measurement record to either sequentially rec…
The growing field of quantum computing is based on the concept of a q-bit which is a delicate superposition of 0 and 1, requiring cryogenic temperatures for its physical realization along with challenging coherent coupling techniques for entangling them. By contrast, a probabilistic bit or a p-bit is a robust classical entity that fluctuates between 0 and 1, and can be implemented at room temperature using present-day technology. Here, we show that a probabilistic coprocessor built out of room temperature p-bits can be used to accelerate simulations of a special class of quantum many-body syst…
High quality factor coplanar resonators are critical elements in superconducting quantum circuits. We describe the design, fabrication and measurement of stepped impedance resonators (SIRs), which are more compact in size than commonly used uniform impedance resonators (UIRs). With properly chosen impedance ratio, SIRs can be 27% shorter than UIRs. As a result, the area occupied by SIRs can be reduced. Two kinds of designs containing both SIRs and UIRs are fabricated and measured. The power dependence of the extracted internal quality factors (Qi) for all the resonators showed that SIRs and UI…
We theoretically investigate the dynamical Casimir effect in electrical circuits based on superconducting microfabricated waveguides with tunable boundary conditions. We propose to implement a rapid modulation of the boundary conditions by tuning the applied magnetic flux through superconducting quantum interference devices (SQUIDs) that are embedded in the waveguide circuits. We consider two circuits: (i) An open waveguide circuit that corresponds to a single mirror in free space, and (ii) a resonator coupled to a microfabricated waveguide, which corresponds to a single-sided cavity in free s…
During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of Quantum Supremacy with fifty qubits is anticipated in just a few years. Quantum Supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software de…
The gedanken experiment of Maxwell's demon has led to the studies concerning the foundations of thermodynamics and statistical mechanics. The demon measures fluctuations of a system's observable and converts the information gain into work via feedback control. Recent developments have elucidated the relationship between the acquired information and the entropy production and generalized the second law of thermodynamics and the fluctuation theorems. Here we extend the scope to a system subject to quantum fluctuations by exploiting techniques in superconducting circuit quantum electrodynamics. W…
We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon-electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn-Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular e…
A qudit ($d$-level quantum systems) has a large Hilbert space and thus can be used to achieve many quantum information and communication tasks. Here, we propose a method to transfer arbitrary $d$-dimensional quantum states (known or unknown) between two superconducting qudits coupled to a single cavity. The state transfer can be performed fast because of employing resonant interactions only. In addition, quantum states can be deterministically transferred without measurement. Numerical simulations show that high-fidelity transfer of quantum states between two superconducting transmon qudits ($…
Studying out-of-equilibrium physics in quantum systems under quantum quench is of vast experimental and theoretical interests. Using periodic quantum quenches, we present an experimentally accessible scheme to simulate the quantum Zeno and anti-Zeno effects in an open quantum system of a single superconducting qubit interacting with an array of transmission line resonators. The scheme is based on the following two observations: Firstly, compared with conventional systems, the short-time non-exponential decay in our superconducting circuit system is readily observed; and secondly, a quench-off …
This paper provides an overview of the first experimental realizations of quantum-mechanical Maxwell's demons based on superconducting circuits. The principal results of these experiments are recalled and put into context. We highlight the versatility offered by superconducting circuits for studying quantum thermodynamics.
