Session D35: Focus Session: Superconducting Qubits: Simulation & Annealing

Catch and Release of Microwave Photons

Quantum information is often encoded in photons, which can both propagate freely along transmission lines and be stored in cavity resonators. To store photons efficiently, the resonator should have negligible coupling with the outside world. On the other hand, the resonator should be strongly coupled to a transmission line through which photons can be transmitted and received. These contrary requirements can be resolved with adjustable coupling. We experimentally demonstrate a superconducting resonator with variable coupling to a measurement transmission line. The resonator coupling can be adjusted through zero to a photon emission rate 300 times the intrinsic resonator decay rate. We demonstrate the catch and shaped release of microwave photons as well as the control of nonclassical Fock states. We achieve a high-fidelity catch efficiency (99.4{\%}) for a ``time-reversed'' shaped photon. These results will enable high fidelity quantum state transfer between distant cavities.   

Imaging the mode structure of a kagome lattice of superconducting resonators with a scanning defect

It has been theoretically shown that a lattice of coupled electromagnetic cavities each strongly coupled to a two-level system exhibit quantum phase transitions of polaritons. Such a system consists of a lattice of coupled sites each described by the Jaynes-Cummings Hamiltonian. The circuit quantum electrodynamics architecture is a natural choice for such experiments because of the ease of fabrication, and the easily obtainable strong coupling limit. In these systems an important first step is to build and understand a large photonic lattice of microwave resonators without qubits. Here we present measurements of the mode structure of microwave photons in an array of 49 niobium CPW resonators that are capacitively coupled to form a kagome lattice. Our method for extracting the mode structure is a piece of sapphire mounted to a three-axis positioning stage that we bring into contact with each resonator. This scanning defect locally perturbs each lattice site and the shifted transmission spectrum can then be used as a metric to extract the internal mode structure. When compared to calculations from a tight binding Hamiltonian, measured modes show good agreement. These results demonstrate our ability to fabricate and understand large lattices of microwave resonators.   

Circuit-QED-based superconducting quantum simulator for the Holstein-polaron model

We propose an analog quantum simulator for the Holstein molecular-crystal model based on a superconducting circuit-QED system in the dispersive regime. The many-body Hamiltonian of this model includes both bosonic and fermionic degrees of freedom. By varying the driving field on the superconducting resonators, one can readily access both the adiabatic and anti-adiabatic regimes of this model, and reach the strong e-ph coupling limit required for small-polaron formation. We show that small-polaron state of arbitrary quasimomentum can be generated by applying a microwave pulse to the resonators. We also show that significant squeezing in the resonator modes can be achieved in the polaron-crossover regime through a measurement-based scheme.   

Dynamics of macroscopic quantum self-bound states in arrays of transmon qubits

We consider the many-body physics of an array of transmon qubits in a cavity. Due to the negative anharmonicity and the exchange coupling between the qubits, such a system realizes a Bose-Hubbard model with attractive interactions and thus the $N$-excitation manifold is expected to have self-bound states. We study the existence of such macroscopic states in the one-dimensional case with open boundary conditions as a function of the parameters of the model, comparing the classical and the quantum predictions. We then analyze the dynamics of the self-bound states in the experimentally relevant scenario of an open dissipative system, where the qubits have a finite energy relaxation time $T_1$. We numerically simulate the dynamics with a quantum trajectory approach supported by a Lanczos diagonalization procedure.   

Detecting elementary excitations of a quantum simulator with superconducting resonator

Analog quantum simulators can emulate various many-body systems and can be used to study novel quantum correlations in such systems. One essential question in quantum simulation is how to detect the properties of the simulated many-body system, such as ground state property and spectrum of elementary excitations. Here we present a circuit QED approach for detecting the excitation spectrum of a quantum simulator by measuring the correlation spectrum of a superconducting resonator. For illustration, we apply this approach to a simulator for the transverse field Ising model coupling to a coplanar waveguide resonator. The simulator can be implemented with an array of superconducting flux qubits. We show that the resonance peaks in the correlation spectrum reveal exactly the frequencies of the excitations.   

Simulating quantum field theories with superconducting circuits

In this contribution, we present the quantum simulation of fermionic field modes interacting via a continuum of bosonic modes with superconducting circuits. Unlike many quantum technologies, superconducting circuits offer naturally the continuum of bosonic modes by means of one-dimensional transmission lines. In particular, we consider a simplified version of 1+1 quantum electrodynamics (QED), which may describe Yukawa interactions, and the coupling of fermions to the Higgs field. Our proof-of-principle proposal is designed within the state-of-the-art circuit QED technology, where fermionic fields are encoded in superconducting flux qubits, in a scalable approach that may lead to a full-fledged quantum simulation of quantum field theories.   

Digital Quantum Simulation of Heisenberg Spin-Spin Interactions with Superconducting Qubits

A major application of a scalable quantum computer is the simulation of intricate quantum systems, including spin models, which cannot be carried out efficiently on classical computers for more than a few tens of qubits. The Heisenberg model describes a spin system that cannot be obtained directly from available interactions in circuit QED. Nevertheless, it can be achieved by a stroboscopic decomposition in terms of elementary gates in a digital quantum simulation approach. In our experiments, we digitally simulate a system of two spin-1/2 particles interacting via an isotropic Heisenberg XYZ interaction in the circuit QED architecture. The XYZ interaction is decomposed into a set of discrete two-qubit gates based on the exchange interaction mediated by the dispersive coupling of both qubits to a common cavity mode. The state evolution during the simulation is analyzed tomographically after each step for varying interaction strengths. This technique can be extended to general spin models, such that our experiments represent a first step towards the digital quantum simulation of larger spin systems with controllable lattice topology.   

Transmon-based simulator of nonlocal electron-phonon coupling: a platform for observing sharp small-polaron transitions

We propose an analog simulator for a one-dimensional model with momentum-dependent (nonlocal) electron-phonon couplings of Su-Schrieffer-Heeger and ``breathing-mode'' types. The superconducting circuit behind this simulator entails an array of transmon qubits and microwave resonators. Using a microwave-driving based protocol, small-polaron Bloch states with arbitrary quasimomentum can be prepared in this system within times several orders of magnitude shorter than the qubit decoherence time. We show that -- by varying the circuit parameters -- one can readily reach the critical coupling strength for observing the sharp transition from a nondegenerate single-particle ground state at zero quasimomentum ($K_{\textrm{gs}}=0$) to a twofold degenerate small-polaron ground state corresponding to equal and opposite (nonzero) quasimomenta $K_{\textrm{gs}}$ and $-K_{\textrm{gs}}$. Through exact diagonalization of our effective model, we show how this nonanalyticity is reflected in the relevant single-particle properties (ground-state energy, quasiparticle residue, average number of phonons). Our work paves the way for understanding the physical implications of strongly momentum-dependent electron-phonon interactions.   

Simulating systems of itinerant spin-carrying particles using arrays of superconducting qubits and resonators

We propose potential setups for the quantum simulation of itinerant spin-carrying particles in a superconducting qubit-resonator array. These proposals include the use of multiple polariton branches, multiple resonator modes and multiple qubits coupled to each resonator. We argue that a combination of using multiple qubits and multiple resonator modes is a promising route in this context, allowing the simulation of external magnetic fields and various forms of spin-dependent inter-site hopping, including spin-orbit coupling. This proposal could be implemented in state-ofthe-art superconducting circuits in the near future.   

Quantum Simulation with Arrays of Transmon Qubits

We present progress toward quantum simulation of one-dimensional spin chains using planar transmon qubits in a circuit QED architecture. In particular, we discuss the Ising model as realized by an array of capacitively-coupled transmon qubits with the terminal qubit dispersively coupled to a microwave resonator. We engineer an approximation to the Ising Hamiltonian with the ground and excited states playing the role of spin-up and spin-down atoms. We present preliminary spectroscopic data and coherent manipulations in chains of varying length.   

Novel Architecture for High Speed and High Fidelity Readout of a Quantum Annealing Processor

Hysteretic dc SQUIDs provide an easy method to read the state of hundreds of qubits\footnote{Supercond. Sci. Technol. \textbf{23}, 105014 (2010)}. However, this approach becomes impractical for circuits with an even larger number of qubits due to heating when dc SQUIDs switch, the relatively slow retrapping dynamics of high quality devices, and suboptimal scaling of the number of control lines with increasing numbers of qubits. The D-Wave Two processor uses an architecture that addresses all three of these issues. This new architecture makes use of Quantum Flux Parametron based shift registers that transfer the classical information produced as the output of the quantum annealing algorithm to a small number of fast non-dissipative and high fidelity microwave readout devices. We will provide an introduction to our implementation, and present data pertaining to readout performance from a 512-qubit quantum annealing processor.   

Programmable flux DACs in a Quantum Annealing Processor

Programming the D-Wave Two processor to solve a given problem involves adjustment of thousands of independent flux biases. This is accomplished with an array of 4480 on-chip digital-to-analog converters (DACs), addressed using 56 external lines. Each DAC comprises a superconducting loop and control circuitry that allows injection of a deterministic number of flux quanta, up to a maximum value determined by the device parameters and the addressing scheme. In-depth characterization is performed to determine DAC transfer-functions and the addressing levels needed for fast and reliable programming. In contrast with traditional single-flux-quanta (SFQ) circuitry, zero static power during programming is dissipated on-chip, allowing efficient operation at mK temperatures.