Experimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubit

Abstract

While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (∼10) operations. This occurs inspite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. We have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.

Fast magnetic field manipulations and nonadiabatic geometric phases of nitrogen-vacancy center spin in diamond

“…It is believed that the study of geometric phases is an attempt to understand quantum mechanics better. Geometric phase is an observable quantity in the experiment with a solid-state spin qubit via spin echo interferometry [41][42][43]. It has been proposed to measure Berry phase in mechanically rotating diamond crystal [44].…”

Interplay between geometric and dynamic phases in a single-spin system

“…Here reversing the cyclic variation of the Hamiltonian, in the form of the rotation direction of the microwave field inverts the sign of the geometric phase but leaves unchanged the dynamic phase. A spin-echo pulse sequence [44] can then be employed to measure only the geometric phase [6,14,21,39]. In the trajectories considered here, reverse evolution on the cone circuit can be achieved only by a second pulse with inverted detuning, which from Eqs.…”

“…The advent of solid-state, single-quantum spin systems has triggered renewed interest in geometric phase, with notable measurements using superconducting qubits [6,7] and spin qubits in diamond [8,9]. Nitrogen-vacancy (NV) centers in diamond [10][11][12] offer a particularly attractive system to study and utilize geometric phases, featuring a ground-state spin triplet with millisecond coherence times [13] at room temperature, quantum states amenable to microwave geometric gates [14], optical fields [15,16], and even physical rotation [17,18].…”

Observation of a Quantum Phase from Classical Rotation of a Single Spin

“…al. used optical transitions to drive the NV spin along closed paths on the Bloch sphere [14], while other work used an additional off-resonant microwave driving field varied along a circuit in the rotating frame [15,16], similar to the first observations of Berry's phase in solidstate qubits [17] and NMR systems [18]. Recent experimental work has simulated rotation with phase-shifted microwave pulses, emulating rotation of the microwave field [19].…”