Abstract
In holonomic quantum computation, single-qubit gates are performed using driving protocols that trace out closed loops on the Bloch sphere, making them robust to certain pulse errors. However, dephasing noise that is transverse to the drive, which is significant in many qubit platforms, lies outside the family of correctable errors. Here, we present a general procedure that combines two types of geometry -- holonomy loops on the Bloch sphere and geometric space curves in three dimensions -- to design gates that simultaneously suppress pulse errors and transverse noise errors. We demonstrate this doubly geometric control technique by designing explicit examples of such dynamically corrected holonomic gates.
Highlights
Quantum information processing demands unprecedented precision in the control of qubits
While holonomic gates are resistant to errors along the holonomy loop, they remain susceptible to noise that is transverse to it, a type of noise that is common in many qubit platforms
We present a general technique for constructing nonadiabatic holonomic gates that dynamically correct transverse noise errors
Summary
Quantum information processing demands unprecedented precision in the control of qubits. We present a general technique for constructing nonadiabatic holonomic gates that dynamically correct transverse noise errors This is achieved by bringing together two types of geometry: holonomic trajectories on the Bloch sphere and geometric space curves that quantify the error accrued by transverse noise. We show how to systematically design qubit evolutions that exhibit both closed holonomy loops and closed error curves, achieving the simultaneous cancelation of both control field errors and transverse noise errors that are beyond the reach of purely holonomic methods. We refer to these evolutions as doubly geometric (DoG) gates. Several appendices contain technical details about our general technique and our explicit examples
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