Single-Loop Realization of Arbitrary Nonadiabatic Holonomic Single-Qubit Quantum Gates in a Superconducting Circuit

Abstract

Geometric phases are noise resilient, and thus provide a robust way towards high-fidelity quantum manipulation. Here we experimentally demonstrate arbitrary nonadiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmarking and the ones on the cavity show an averaged fidelity of 0.978 based on a full quantum process tomography. In principle, a nontrivial two-qubit holonomic gate between the qubit and the cavity can also be realized based on our presented experimental scheme. Our experiment thus paves the way towards practical nonadiabatic holonomic quantum manipulation with both qubits and cavities in a superconducting circuit.

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

“…In contrast to the earlier adiabatic-process-based geometric quantum computation [35][36][37][38], nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) based on Abelian [39][40][41][42][43][44][45][46] and non-Abelian geometirc phases [47][48][49][50][51][52][53][54][55][56] in two-and threelevel system, respectively, can intrinsically protect against environment-induced decoherence, since the the construction times of geometric quantum gates is reduced. The nonadiabatic geometric gates of NGQC and NHQC have been experimentally demonstrated in many systems including superconducting qubit [57][58][59][60][61], NMR [62][63][64][65], NV center in diamond [66][67][68][69]. However, there are many theoretical proposals to apply geometric quantum computation [70][71][72][73] and NGQC [42,[74][75][76][77] in Rydberg atom platform.…”

Universal speeded-up adiabatic geometric quantum computation in three-level systems via counterdiabatic driving

“…With the results of the inverse calculations in Eq. (15) with Ω ′ eff (t) replacing Ω eff (t), it is indeterminate to conversely satisfy Ω ′ eff (t) = Ω p (t)Ω * s (t)/2∆ that is definitely necessary because the effective two-level Hamiltonian must be from the Hamiltonian of the threelevel system. In this proposal, therefore, we would not choose easily this way to speed up the adiabatic U 0−1 .…”

Transferring entangled states of photonic cat-state qubits in circuit QED

“…Based on circuit QED, many proposals have been presented for implementing quantum state transfer between SC qubits [1,[13][14][15], quantum logic gates of SC qubits [16][17][18][19][20][21], and entanglement in SC qubits [22][23][24][25][26][27][28]. By using SC qubits, the experimental demonstrations of single-qubit gates [29,30], two-qubit gates [31,32], three-qubit gates [33,34], 10-qubit entanglement [35], 12-qubit entanglement [36], 18-qubit entanglement [37], and 20-qubit Schrödinger cat states [37] have been reported. Moreover, quantum teleportation between two distant SC qubits [38], quantum state transfer in a SC qubit chain [39], entanglement swapping in superconducting circuit [40], and quantum walks in a 12-qubit superconducting processor [41] have been realized in experiments.…”