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arXiv:1808.04666 · Physical Review A

Adiabatic quantum simulations with driven superconducting qubits

Marco Roth, Nikolaj Moll, Gian Salis, Marc Ganzhorn, Daniel J. Egger, Stefan Filipp, Sebastian Schmidt

Published Feb 21, 2019• 14 citations
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Abstract

We propose a quantum simulator based on driven superconducting qubits where the interactions are generated parametrically by a bichromatic magnetic flux modulation of a tunable bus element. Using a time-dependent Schrieffer-Wolff transformation, we analytically derive a multiqubit Hamiltonian which features independently tunable $XX$- and $YY$-type interactions as well as local bias fields over a large parameter range. We demonstrate the adiabatic simulation of the ground state of a hydrogen molecule using two superconducting qubits and one tunable bus element. The time required to reach chemical accuracy lies in the few microsecond range. Therefore, the proposed adiabatic protocol could be implemented using currently available superconducting circuits. Further applications of this technique may also be found in the simulation of interacting spin systems.

DOI
10.1103/physreva.99.022323

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We propose a quantum simulator based on driven superconducting qubits where the interactions are generated parametrically by a bichromatic magnetic flux modulation of a tunable bus element. Using a time-dependent Schrieffer-Wolff transformation, we analytically derive a multiqubit Hamiltonian which features independently tunable XXXXXX- and YYYYYY-type interactions as well as local bias fields over a large parameter range. We demonstrate the adiabatic simulation of the ground state of a hydrogen molecule using two superconducting qubits and one tunable bus element. The time required to reach chemical accuracy lies in the few microsecond range. Therefore, the proposed adiabatic protocol could be implemented using currently available superconducting circuits. Further applications of this technique may also be found in the simulation of interacting spin systems.
Nonpairwise multiqubit interactions present a useful resource for quantum information processors. Their implementation would facilitate more efficient quantum simulations of molecules and combinatorial optimization problems, and they could simplify error suppression and error correction schemes. Here, we present a superconducting circuit architecture in which a coupling module mediates two-local and three-local interactions between three flux qubits by design. The system Hamiltonian is estimated via multiqubit pulse sequences that implement Ramsey-type interferometry between all neighboring excitation manifolds in the system. The three-local interaction is coherently tunable over several MHz via the coupler flux biases and can be turned off, which is important for applications in quantum annealing, analog quantum simulation, and gate-model quantum computation.
To do large-scale quantum information processing, it is necessary to control the interactions between individual qubits while retaining quantum coherence. To this end, superconducting circuits allow for a high degree of flexibility. We report on the time-domain tunable coupling of optimally biased superconducting flux qubits. By modulating the nonlinear inductance of an additional coupling element, we parametrically induced a two-qubit transition that was otherwise forbidden. We observed an on/off coupling ratio of 19 and were able to demonstrate a simple quantum protocol.
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A typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of the target Hamiltonian. Such an adiabatic quantum simulation is demonstrated by directly implementing a controllable and smoothly varying Hamiltonian in the rotating frame of two superconducting qubits, including longitudinal and transverse fields and iswap-type two-qubit interactions. The evolution of each eigenstate is tracked using time-resolved state tomography. The energy gaps between instantaneous eigenstates are chosen such that, depending on the energy transition rate, either diabatic or adiabatic passages are observed in the measured energies and correlators. Errors in the obtained energy values induced by finite T1{T}_{1}T1​ and T2{T}_{2}T2​ times of the qubits are mitigated by extrapolation to short protocol times.
A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two or more quantum bits in arrays of coupled qubits. Gates based on parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we theoretically and experimentally study a superconducting qubit setup with two transmon qubits connected via a capacitively coupled tunable bus. We develop a time-dependent Schrieffer-Wolff transformation and derive analytic expressions for exchange-interaction gates swapping excitations between the qubits (iswap) and for two-photon gates creating and annihilating simultaneous two-qubit excitations (bswap). We find that the bswap gate is generally slower than the more commonly used iswap gate, but features favorable scalability properties with less severe frequency-crowding effects, which typically degrade the fidelity in multiqubit setups. Our theoretical results are backed by experimental measurements as well as exact numerical simulations including the effects of higher transmon levels and dissipation.
We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction treated as an oscillator with adjustable frequency. The bus is sequentially coupled to only one qubit at a time. Distant Josephson qubits without any direct interaction can be indirectly coupled with each other by independently interacting with the bus sequentially, via exciting/deexciting vibrational quanta in the bus. This is a superconducting analog of the successful ion trap experiments on quantum computing. Our approach differs from previous schemes that simultaneously coupled two qubits to the bus, as opposed to their sequential coupling considered here. The significant quantum logic gates can be realized by using these tunable and selective couplings. The decoherence properties of the proposed quantum system are analyzed within the Bloch-Redfield formalism. Numerical estimations of certain important experimental parameters are provided.