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arXiv:1301.0459 · Physical Review A

Feedback-controlled adiabatic quantum computation

R. D. Wilson, Alexandre M. Zagoskin, Sergey E. Savel'ev, M. J. Everitt, Franco Nori

Published Nov 5, 2012• 13 citations
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Abstract

We propose a simple feedback-control scheme for adiabatic quantum computation with superconducting flux qubits. The proposed method makes use of existing on-chip hardware to monitor the ground-state curvature, which is then used to control the computation speed to maximize the success probability. We show that this scheme can provide a polynomial speed-up in performance and that it is possible to choose a suitable set of feedback-control parameters for an arbitrary problem Hamiltonian.

DOI
10.1103/physreva.86.052306

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We propose a simple feedback-control scheme for adiabatic quantum computation with superconducting flux qubits. The proposed method makes use of existing on-chip hardware to monitor the ground-state curvature, which is then used to control the computation speed to maximize the success probability. We show that this scheme can provide a polynomial speed-up in performance and that it is possible to choose a suitable set of feedback-control parameters for an arbitrary problem Hamiltonian.
Controllable adiabatic evolution of a multi-qubit system can be used for adiabatic quantum computation (AQC). This evolution ends at a configuration where the Hamiltonian of the system encodes the solution of the problem to be solved. As a first steps towards realization of AQC we have investigated two, three and four flux qubit systems. These systems were characterized by making use of a radio-frequency method. We designed two-qubit systems with coupling energies up to several kelvins. For the three-flux-qubit systems we determined the complete ground-state flux diagram in the three dimensional flux space around the qubits common degeneracy point. We show that the system's Hamiltonian can be completely reconstructed from our measurements. Our concept for the implementation of AQC, by making use of flux qubits, is discussed.
We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results.
Quantum feedback is a technique for measuring a qubit and applying appropriate feedback depending on the measurement results. Here, we propose a new on-chip quantum feedback method where the measurement-result information is not taken from the chip to the outside of a dilution refrigerator. This can be done by using a selective qubit-energy shift induced by measurement apparatus. We demonstrate on-chip quantum feedback and succeed in the rapid initialization of a qubit by flipping the qubit state only when we detect the ground state of the qubit. The feedback loop of our quantum feedback method closed on a chip, and so the operating time needed to control a qubit is of the order of 10 ns. This operating time is shorter than with the convectional off-chip feedback method. Our on-chip quantum feedback technique opens many possibilities such as an application to quantum information processing and providing an understanding of the foundation of thermodynamics for quantum systems.
In circuit quantum electrodynamics the coherence of Cooper pairs in superconductors is employed to create macroscopic electric circuits with quantized energy levels. Such circuits can be coupled with each other and exploited as building blocks of a quantum computer. Accurate and robust control of the quantum state in the circuits is a central condition for the operation of the quantum computer and one of the prerequisites for the implementation of complex algorithms used in quantum information processing, such as quantum error correction. In this thesis adiabatic control in circuit quantum electrodynamics is investigated with the focus on manipulating three-level systems. \n \nIn adiabatic control the eigenstates of the system are slowly modified by changing the external control parameters, which govern the evolution of the system. If the changes in the parameters are slow enough, the state of the system follows the eigenstates in the adiabatic basis, thereby realizing the intended operation. The advantage of adiabatic control is its inherent robustness to small errors or noise in the control parameters; the result of the state manipulation only depends on the asymptotic values of the control parameters, but not on their exact values during the process. \n \nShortcuts to adiabaticity can be used to speed up the otherwise slow adiabatic control by introducing a correction pulse that compensates the diabatic losses during the state manipulation. This allows one to overcome the limitation on the speed of the protocol but simultaneously reduces the method's robustness to the variations in the control parameters. If the level of noise in the control parameters is known, using the shortcut it is possible to find the optimal level of robustness which is required to mitigate the noise. \n \nCircuit quantum electrodynamics offers a perfect experimental platform for investigating quantum control due to the possibility of realizing complicated control schemes using microwave electronics. With commercially available digital-to-analog converters the control signals can be digitally created, which enables accurate and coherent control of the quantum circuit. \n \nIn this thesis both theoretical and experimental results on adiabatic control applied to superconducting transmon circuits are presented. It is shown that stimulated Raman adiabatic passage can be used for population transfer in a three-level transmon, which can be further improved using shortcuts to adiabaticity. Furthermore, a scheme for implementing robust superadiabatic rotation gates in transmon is proposed. Finally, it is demonstrated that superconducting qubit can be used as an ultra-sensitive detector of magnetic flux.
Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While Shor's algorithm demands high-fidelity quantum gates, Hamiltonian optimization schemes, with prime factors encoded as degenerate ground states of a problem Hamiltonian, generally require substantial classical post-processing to determine control parameters. We propose an all-quantum, measurement-based feedback approach that iteratively steers a quantum system toward the target ground state, eliminating the need for classical computation of drive parameters once the problem Hamiltonian is determined and realized. As a proof of principle, we experimentally factor the biprime 551 using a three-qubit NMR quantum register and numerically analyze the robustness of the method against control field-errors. We further demonstrate scalability by numerically implementing the FALQON factorization of larger biprimes, 9,167 and 2,106,287, using 5 and 9 qubits, respectively.
We present a robust pulse optimization method for adiabatic population transfer and adiabatic quantum computation. The approach relies on identifying control pulses that keep the evolving quantum system close to its instantaneous ground state. By combining advanced gradient-free optimization tools with specialized cost functions for adiabatic control, it achieves both efficiency and robustness. To demonstrate its generality, we apply the method to three examples involving both atomic and superconducting qubits. We test different optimization cost functions and discretization bases, showing that the approach outperforms ensemble optimization. Finally, to verify its performance on real quantum hardware, we implement digitized adiabatic qubit control using the optimized pulses on the IBM quantum cloud.