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Numerical Gate Synthesis for Quantum Heuristics on Bosonic Quantum Processors

A. Barış Özgüler

Published Dec 13, 2021• 1 citation
OpenAlex

Abstract

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Peterson and Garcia, 2021), we showcase universal control of single-qudit operations up to 8 states, and two-qutrit operations, mapped respectively on a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement quantum approximate optimization (QAOA) qudits algorithms. The results show that high fidelity (> 0.99) is achievable with sufficient computational effort on HPC for most cases under study, and extension to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in cQED systems.

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Numerical gate synthesis for quantum heuristics on bosonic quantum processors

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There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity ( > 0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.

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There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Peterson and Garcia, 2021), we showcase universal control of single-qudit operations up to 8 states, and two-qutrit operations, mapped respectively on a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement quantum approximate optimization (QAOA) qudits algorithms. The results show that high fidelity (> 0.99) is achievable with sufficient computational effort on HPC for most cases under study, and extension to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in cQED systems.
There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity ( > 0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.
Qudit gates for high-dimensional quantum computing can be synthesized with high precision using numerical quantum optimal control techniques. Large circuits are broken down into modules and the tailored pulses for each module can be used as primitives for a qudit compiler. Application of the pulses of each module in the presence of extra modes may decrease their effectiveness due to crosstalk. In this paper, we address this problem by simulating qudit dynamics for circuit quantum electrodynamics systems. As a test case, we take pulses for single-qudit swap gates optimized in isolation and then apply them in the presence of spectator modes each of which are in Fock states. We provide an experimentally relevant scaling formula that can be used as a bound on the fidelity decay. Our results show that frequency shift from spectator mode populations has to be $\ensuremath{\lesssim}0.1%$ of the qudit's nonlinearity in order for high-fidelity single-qudit gates to be useful in the presence of occupied spectator modes.
Advanced simulations and calculations on quantum computers require high-fidelity implementations of quantum operations. The universal gateset approach builds complex unitaries from a small set of primitive gates, often resulting in a long gate sequence, which is typically a leading factor in the total accumulated error. Compiling a complex unitary for processors with higher-dimensional logical elements, such as qutrits, exacerbates the accumulated error per unitary, since an even longer gate sequence is required. Optimal control methods promise time- and resource-efficient compact gate sequences and, therefore, higher fidelity. These methods generate pulses that can directly implement any complex unitary on a quantum device. In this work, we demonstrate that any arbitrary qubit and qutrit gate can be realized with high fidelity, which can significantly reduce the length of a gate sequence. We generate and test pulses for a large set of randomly selected arbitrary unitaries on several quantum processing units (QPUs): the Lawrence Livermore National Laboratory Quantum Device and Integration Testbed's (QuDIT's) standard QPU and three of Rigetti's QPUs: Ankaa-2, Ankaa-9Q-1, and Aspen-M-3. On the QuDIT platform's standard QPU, the average fidelity of random qutrit gates is $97.9\ifmmode\pm\else\textpm\fi{}0.5\mathrm{%}$ measured with conventional QPT and $98.8\ifmmode\pm\else\textpm\fi{}0.6\mathrm{%}$ from QPT with gate folding. Rigetti's Ankaa-2 achieves random qubit gates with an average fidelity of $98.4\ifmmode\pm\else\textpm\fi{}0.5\mathrm{%}$ (conventional QPT) and $99.7\ifmmode\pm\else\textpm\fi{}0.1\mathrm{%}$ (QPT with gate folding). On Ankaa-9Q-1 and Aspen-M-3, the average fidelities with conventional qubit QPT measurements were higher than 99% (see Appendix). We show that optimal control gates are robust to drift for at least 3 h and that the same calibration parameters can be used for all implemented gates. Our work promises that the calibration overheads for optimal control gates can be made small enough to enable efficient quantum circuits based on this technique.
Gate-based quantum computers typically encode and process information in two-dimensional units called qubits.Using d-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction.In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels.We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond 99% in the d = 4 case of ququarts with realistic experimental parameters.Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives.As proof-of-concept applications, we numerically demonstrate the synthesis of SU(16) gates for noisy quantum hardware and an embedded error-correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise.We conclude that universal qudit control-a valuable extension to the operational toolbox of superconducting quantum information processing-is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.
High-coherence superconducting cavities offer a hardware-efficient platform for quantum information processing. To achieve universal operations of these bosonic modes, the requisite nonlinearity is realized by coupling them to a transmon ancilla. However, this configuration is susceptible to crosstalk errors in the dispersive regime, where the ancilla frequency is Stark shifted by the state of each coupled bosonic mode. This leads to a frequency mismatch of the ancilla drive, lowering the gate fidelities. To mitigate such coherent errors, we employ quantum optimal control to engineer ancilla pulses that are robust to the frequency shifts. These optimized pulses are subsequently integrated into a recently developed echoed conditional displacement protocol for executing single- and two-mode operations. Through numerical simulations, we examine two representative scenarios: the preparation of single-mode Fock states in the presence of spectator modes and the generation of two-mode entangled Bell-cat states. Our approach markedly suppresses crosstalk errors, outperforming conventional ancilla control methods by orders of magnitude. These results provide guidance for experimentally achieving high-fidelity multimode operations and pave the way for developing high-performance bosonic quantum information processors.
Qudits, generalizations of qubits to multilevel quantum systems, offer enhanced computational efficiency by encoding more information per lattice cell, avoiding costly swap operations and providing even exponential speedup in some cases. Utilizing the d -level manifold, however, requires high-speed gate operations because of the stronger decoherence at higher levels. While analytical control methods have proven effective for qubits in achieving fast gates with minimal control errors, their extension to qudits is nontrivial due to the increased complexity of the energy-level structure arising from additional ancillary states. In this work, we present a universal pulse construction for generating rapid, high-fidelity unitary rotations between adjacent qudit levels, thereby providing a prescription for any gate in SU ( d ) . Control errors in these operations are effectively analyzed within a four-level subspace, including two leakage levels with approximately opposite detuning. By identifying the optimal degrees of freedom, we derive concise analytical pulse schemes that suppress multiple control errors and outperform existing methods. Remarkably, our approach achieves consistent coherent error scaling across all levels, approaching the quantum speed limit independently of parameter variations between levels. Numerical validation on transmon circuits demonstrates significant improvements in gate fidelity for various qudit sizes aiming for 10 − 4 error. This method provides a scalable solution for improving qudit control and can be broadly applied to other quantum systems with ladder structures or operations involving multiple ancillary levels.