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arXiv:1911.04806 · Physical Review Applied

Rescaling Interactions for Quantum Control

Gaurav Bhole, Takahiro Tsunoda, Peter Leek, Jonathan A. Jones

Published Mar 2, 2020• 7 citations
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Abstract

A powerful control method in experimental quantum computing is the use of spin echoes, employed to select a desired term in the system's internal Hamiltonian, while refocusing others. Here, we address a more general problem, describing a method to not only turn on and off particular interactions but also to rescale their strengths so that we can generate any desired effective internal Hamiltonian. We propose an algorithm based on linear programming for achieving time-optimal rescaling solutions in fully coupled systems of tens of qubits, which can be modified to obtain near-time-optimal solutions for rescaling systems with hundreds of qubits.

DOI
10.1103/physrevapplied.13.034002

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A powerful control method in experimental quantum computing is the use of spin echoes, employed to select a desired term in the system's internal Hamiltonian, while refocusing others. Here, we address a more general problem, describing a method to not only turn on and off particular interactions but also to rescale their strengths so that we can generate any desired effective internal Hamiltonian. We propose an algorithm based on linear programming for achieving time-optimal rescaling solutions in fully coupled systems of tens of qubits, which can be modified to obtain near-time-optimal solutions for rescaling systems with hundreds of qubits.
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We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local not gates. This methodology is well known in nuclear magnetic resonance implementations, but previous approaches do not scale efficiently for the general fully connected Hamiltonian, where the complexity of finding time-optimal solutions makes them only practical up to a few tens of qubits. Given the rapid growth in the number of qubits in cutting-edge quantum processors, it is of interest to investigate the applicability of this control scheme to much larger-scale systems with realistic restrictions on connectivity. Here we present an efficient scheme to find near time-optimal solutions that can be applied to engineered qubit arrays with local connectivity for any number of qubits, indicating the potential for practical quantum computing in such systems.
The development of quantum control methods is an essential task for emerging quantum technologies. In general, the process of optimizing quantum controls scales very unfavorably in system size due to the exponential growth of the Hilbert space dimension. Here, I present a scalable subsystem-based method for quantum optimal control on a large quantum system. The basic idea is to cast the original problem as a robust control problem on subsystems with requirement of robustness in respect of inter-subsystem couplings, thus enabling a drastic reduction of problem size. The method is in particular suitable for target quantum operations that are local, e.g., elementary quantum gates. As an illustrative example, I employ it to tackle the demanding task of pulse searching on a 12-spin coupled system, achieving substantial reduction of memory and time costs. This work has significant implications for coherent quantum engineering on near-term intermediate-scale quantum devices.
Superconducting circuits form one of the most promising hardware platforms for building a quantum computer. As the quantum computing system gets more complex as we increase the size, employing simple circuit designs and control strategies can make the task of building a large scale quantum computer easier. This thesis describes a novel control strategy that utilises spin-echo techniques and native interaction in superconducting circuits, which reduces the cost of calibrating pulsed two-qubit gates. Spin-echo pulses are used to rescale the always-on Hamiltonian, and the timings of spin-echo pulses encode the effective coupling strengths. In collaboration with the NMR group in Oxford, two methods for scaling this technique to large numbers of qubits were explored. In the first approach, pulse sequences for an all-to-all coupled system are obtained numerically using linear programming, and it finds the time-optimal solution for up to twenty qubits and the near time-optimal solution for up to hundreds of qubits. Another approach based on graph colouring finds the near time-optimal pulse sequence analytically, allowing pulse sequences for any number of qubits. An idea based on the Hamiltonian rescaling technique was applied to implementing the variational quantum eigensolver algorithm and error mitigation on two superconducting qubits. In contrast to previous studies, the residual dispersive coupling between qubits was used for computation instead of regarding it as a source of error. Lastly, the detailed dynamics of the residual dispersive coupling in superconducting circuits were investigated to predict the practicality of spin-echo-based quantum computing on superconducting circuits. The Hamiltonian rescaling protocol assumes the always-on coupling to be diagonal, such as Ising Hamiltonian, but deviation from the pure Ising interaction was observed in the strongly coupled superconducting qubits. The origin of the deviation was identified analytically, and the circuit design criteria to suppress the deviation are presented.
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A fundamental problem in experiments with open quantum systems is to ensure steady-state convergence within a given operational time window. Here, we devise a general state preparation recipe to control relaxation timescales and achieve steady-state convergence within experimental run times. We do so by constructing a unitary operation that cancels multiple relaxation modes. We provide an example in a few-body interacting system (long-range qubit chain), taking into account limitations of experimentally accessible unitary operations in quantum simulators.