ON-LINE QLunch: Morten Kjaergaard

Speaker: Morten Kjaergaard from NBI

Title: Programming quantum computers with quantum instructions

Abstract: A quantum algorithm consists of a sequence of operations and measurements applied to a quantum processor. To date, the instructions defining this sequence have been provided by a classical computer and passed via control hardware to the quantum system. I will discuss our recent results showing the first experimental use of quantum instructions: a fixed sequence of classically-defined gates performs an operation that uniquely depends only on the setting of an auxiliary quantum instruction state [1] (the Density Matrix Exponentiation algorithm [2]). The ability to directly use quantum instructions, without tomographically reconstructing and recompiling the quantum input into an equivalent set of classical instructions opens the door to exponential speedups in many algorithms, including principal component analysis of large quantum states [2], quantum semi-definite programming [3], and efficient measurement of entanglement spectra [4]. The algorithm is executed on two superconducting transmon qubits, with a 99.7% fidelity controlled-phase gate (measured with randomized benchmarking), and we demonstrate circuits to depth 70 with algorithm fidelities close to 90%. To achieve this performance we developed several novel strategies for tuning up quantum gates specifically in the context of structured quantum algorithms. Finally, to demonstrate the algorithm we developed a stochastic quantum operation which approximately resets a known quantum state without using classical feedback, with applications to open-loop error mitigation in logical states [5].

[1] M. Kjaergaard, M. Schwartz et al, arXiv:2001.08838 (2020)
[2] S. Lloyd et al, Nat. Phys, 10 (2014)
[3] F. Brandao et al arXiv:1710.02581 (2017)
[4] H. Pichler et al, PRX, 6, (2016)
[5] A. Greene, M. Kjaergaard et al, in preparation (2020)

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