Parametrically Activated Entangling Gates Using Transmon Qubits

Abstract

We describe and implement a family of entangling gates activated by radio-frequency flux modulation applied to a tunable transmon that is statically coupled to a neighboring transmon. The effect of this modulation is the resonant exchange of photons directly between levels of the two-transmon system, obviating the need for mediating qubits or resonator modes and allowing for the full utilization of all qubits in a scalable architecture. The resonance condition is selective in both the frequency and amplitude of modulation and thus alleviates frequency crowding. We demonstrate the use of three such resonances to produce entangling gates that enable universal quantum computation: one iSWAP gate and two distinct controlled Z gates. We report interleaved randomized benchmarking results indicating gate error rates of 6% for the iSWAP (duration 135ns) and 9% for the controlled Z gates (durations 175 ns and 270 ns), limited largely by qubit coherence.A central challenge in building a scalable quantum computer with superconducting qubits is the execution of high-fidelity, two-qubit gates within an architecture containing many resonant elements. As more elements are added, or as the multiplicity of couplings between elements is increased, the frequency space of the design becomes crowded and device performance suffers. In architectures composed of transmon qubits [1], there are two main approaches to implementing two-qubit gates. The first utilizes fixed-frequency qubits with static couplings where the two-qubit operations are activated by applying transverse microwave drives [2][3][4][5][6][7][8]. While fixedfrequency qubits generally have long coherence times, this architecture requires satisfying stringent constraints on qubit frequencies and anharmonicities [5,6,8] which requires some tunability to scale to many qubits [9]. The second approach relies on frequency-tunable transmons, and two-qubit gates are activated by tuning qubits into and out of resonance with a particular transition [10][11][12][13][14][15][16]. However, tunability comes at the cost of additional decoherence channels, thus significantly limiting coherence times [17]. In this approach the delivery of shaped unbalanced control signals poses a challenge [15]. Such gates are furthermore sensitive to frequency crowdingavoiding unwanted crossings with neighboring qubit energy levels during gate operations limits the flexibility and connectivity of the architecture.An alternative to these approaches is to modulate a circuit's couplings or energy levels at a frequency corresponding to the detuning between particular energy levels of interest [18][19][20][21][22][23][24][25][26]. This enables an entangling gate between a qubit and a single resonator [21,22], a qubit and many resonator modes [26], two transmon qubits coupled by a tunable mediating qubit [16,25], or two tunable transmons coupled to a mediating resonator [23,24].Building on these earlier results, we implement two entangling gates, iSWAP and controlled Z (CZ), between a flux-tunable transmon an...

A quantum engineer's guide to superconducting qubits

“…The two-qubit gates available in the transmonlike superconducting qubit architecture can roughly be split into two broad families as outlined previously: one group requiring local magnetic fields to tune the transition frequency of qubits and one group consisting of all-microwave control. There exist several hybrid schemes that combine various aspects of these two categories and, in particular, the notions of tunable coupling and parametric driving are proving to be important ingredients in modern superconducting qubit processors 63,67,89,103,106,[207][208][209][210][211][212][213] . In this section, however, we start by introducing the iSWAP gate, and then review the CPHASE (controlled-phase) in Section IV F and the CR (cross-resonance) in Section IV G. We briefly review a few other two-qubit gates and discuss their merits in Sections IV G 4 and IV H.…”

“…A hybrid approach, in which a combination of tunable and fixed-frequency qubits is used, was recently demonstrated for both iSWAP and CPHASE gates 67,105,211 . This scheme has no added tunable qubits (or resonators) acting as the coupling element, but rather, relies solely on an always-on capacitive coupling between the qubits, and the effective coupling is roughly half that of the always-on coupling.…”

Scalable nonadiabatic holonomic quantum computation on a superconducting qubit lattice

“…We first review the used ac magnetic flux induced parametric tunable coupling, which can be implemented between a qubit and a quantum bus [48][49][50], or two qubits [51][52][53][54]. As shown in Fig.…”

Two-Qubit Circuit Depth and the Monodromy Polytope

“…We use these results to explore the space of possible choices for the native gate set, with an emphasis on those appearing via Rigetti's choice of interaction Hamiltonian [10] (cf. also [42]): the gates CZ, iSWAP, CPHASE, and XY, where by XY we intend the unitary family…”