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 parametersto 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 and T2 times of the qubits are mitigated by extrapolation to short protocol times.
A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the availablecoherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. Complementing the theoretical work by Barkoutsos et al. [PRA 98, 022322 (2018)], we report on the experimental implementation of a variational algorithm on a superconducting qubit platform to compute the eigenstate energies of molecular hydrogen. We utilize a parametrically driven tunable coupler to realize exchange-type gates that are configurable in amplitude and phase on two fixed-frequency superconducting qubits. With gate fidelities around 95% we are able to compute the eigenstates within an accuracy of 50 mHartree on average, a limit set by the coherence time of the tunable coupler.
We propose a quantum simulator based on driven superconducting qubits where the interactions are generated parametrically by a polychromatic magnetic flux modulation of a tunable buselement. Using a time-dependent Schrieffer-Wolff transformation, we analytically derive a multi-qubit 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 and therefore could be implemented on currently available superconducting circuits. Further applications of this technique may also be found in the simulation of interacting spin systems.
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits.Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed.
With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.
A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two and more quantum bits in arrays of coupled qubits. Gates basedon parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we study theoretically and experimentally 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 multi-qubit setups. Our theoretical results are backed by experimental measurements as well as exact numerical simulations including the effects of higher transmon levels and dissipation.