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 available coherence 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.The simulation of the electronic structure of molecular and condensed matter systems is a challenging computational task as the cost of resources increases exponentially with the number of electrons when accurate solutions are required. With the tremendous improvements in our ability to control complex quantum systems this bottleneck may be overcome by the use of quantum computing hardware [1]. In theory, various algorithms for quantum simulation have been designed to that end, including quantum phase estimation [2] or adiabatic algorithms [3]. With these algorithms the challenges for practical applications lie in the efficient mapping of the electronic Hamiltonian onto the quantum computer and in the required number of quantum gates that remains prohibitive on current and near-term quantum hardware [4] without quantum error correction schemes [5]. On the other hand, variational quantum eigensolver (VQE) methods [6, 7] can produce accurate results with a small number of gates [8] using for instance algorithms with low circuit depth [9] and do not require a direct mapping of the electronic Hamiltonian onto the hardware. Moreover, such algorithms are inherently robust against certain errors [8, 10, 11] and are therefore considered as ideal candidates for first practical implementations on non error-corrected, near-term quantum hardware.Recently, the molecular ground state energy of hydrogen and helium have been computed via VQE in proof of concept experiments using NMR quantum simulators [12][13][14], photonic architectures [6] or nitrogenvacancy centers in diamond [15]. Although very accurate energy estimates are obtained, quantum simulation of larger systems remains an intractable problem on these platforms because of the difficulties arising in scaling them up to more than a few qubits. For this reason trapped ions [16][17][18][19] and supe...

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 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 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.Quantum computation is based on accurate and precise control of quantum bits and their interactions to create multi-qubit superpositions and entanglement. With superconducting circuits, single qubit quantum gates can be carried out with fidelities approaching 99.99% [1-4], while errors in two-qubit operations are typically higher with record fidelities around 99% [3,5]. However, the realization of qubit operations with even higher fidelity is required both for reaching the error threshold for quantum computation [6-9] and for carrying out reliable quantum simulations and optimizations in large arrays of coupled qubits [10][11][12][13]. Moreover, the quest for useful quantum computations before full quantum error correction becomes available may be assisted by efficient, short-depth gate sequences based on two-or multi-qubit gates [14,15] with versatile types of interactions. In particular, parametric schemes based on tunable couplers have been proposed and recently realized as a means to achieve fast gates with high fidelities [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].In this context, effective interactions were engineered in Ref.[26] between two transmon qubits mediated by a third, ancilla transmon device (bus), which couples dispersively to both qubits and whose frequency is modulated by an external magnetic flux. Such a flux-modulation scheme provides frequency-selectivity and allows to use fixed-frequency computational qubits, thereby minimizing the sensitvity of the device with respect to magnetic flux noise and disorder effects. For example, modulating at the (fixed) difference frequency of the qubits brings these qubits effectively into resonance in a co-rotating frame such that a single excitation can be swapped efficiently (iSWAP). The effective Hamiltonian in this case is H iSWAP ∝ XX + YY. With this method gate ...

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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 bus element. Using a time-dependent Schrieffer-Wolff transformation, we analytically derive a multi-qubit Hamiltonian which features independently tunable XX and Y Y -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. arXiv:1808.04666v2 [quant-ph]