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arXiv:1707.05144 · Physical Review A

Many-body strategies for multiqubit gates: Quantum control through Krawtchouk-chain dynamics

Koen Groenland, Kareljan Schoutens

Published Apr 12, 2018• 11 citations
arXivHTMLPDF

Abstract

We propose a strategy for engineering multiqubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number $N$ of qubits, with specific $XX+YY$ couplings between nearest neighbors. For this so-called Krawtchouk chain, a two-body driving term leads to the ${\mathrm{iSWAP}}_{N}$ gate, which we numerically test for $N=4$ and 6.

DOI
10.1103/physreva.97.042321

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We propose a strategy for engineering multiqubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number NNN of qubits, with specific XX+YYXX+YYXX+YY couplings between nearest neighbors. For this so-called Krawtchouk chain, a two-body driving term leads to the iSWAPN{\mathrm{iSWAP}}_{N}iSWAPN​ gate, which we numerically test for N=4N=4N=4 and 6.
Abstract Accurate, nontrivial quantum operations on many qubits are experimentally challenging. As opposed to the standard approach of compiling larger unitaries into sequences of 2-qubit gates, we propose a protocol on Hamiltonian control fields which implements highly selective multi-qubit gates in a strongly-coupled many-body quantum system. We exploit the selectiveness of resonant driving to exchange only 2 out of 2 N eigenstates of some background Hamiltonian, and discuss a basis transformation, the eigengate, that makes this operation relevant to the computational basis. The latter has a second use as a Hahn echo which undoes the dynamical phases due to the background Hamiltonian. We find that the error of such protocols scales favourably with the gate time as t −2 , but the protocol becomes inefficient with a growing number of qubits N . The framework is numerically tested in the context of a spin chain model first described by Polychronakos, for which we show that an earlier solution method naturally gives rise to an eigengate. Our techniques could be of independent interest for the theory of driven many-body systems.
Implementing high-fidelity multiqubit gates is critical for reducing circuit depth in near-term quantum processors and fault-tolerant architectures. However, realizing multiqubit interactions and entanglement remains a critical challenge that limits the implementation of multiqubit gates. Here we propose an all-microwave scheme to realize single-step multiqubit gates incorporating n control and m target qubits, tailored for frequency-tunable superconducting transmon networks. By leveraging cross-resonance (CR) drives, this approach induces effective two-body ZX interactions that are significantly stronger than those achieved in conventional resonant regimes, circumventing the need for tunable couplers. The system's effective Hamiltonian is analytically derived using both quad frame rotation and rigorous block diagonalization. These combined theoretical methods facilitate the identification of optimal parameter regimes that simultaneously enhance desired target couplings and suppress parasitic higher-order terms, such as ZXX interactions. Through numerical simulations and gradient-based pulse-shape optimization, we demonstrate three-qubit gates achieving fidelities exceeding 99.9% within a 60 ns gate duration. Furthermore, we evaluate the fundamental scalability of this framework by extending the optimization to a five-qubit CXXXX architecture, confirming the physical viability of the multi-target driving scheme. Because these multiqubit operations naturally emulate stabilizer measurements, this architecture provides a hardware-efficient strategy for reducing the circuit depth of stabilizer-type operations by replacing sequential two-qubit gate decompositions with single-step multiqubit gates.
The prevalent approach to executing quantum algorithms on quantum computers is to break down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers are still a prominent challenge. Here we propose and investigate multiqubit entangling gates for trapped ions. Our gates couple many qubits at once, allowing us to decrease the total number of gates used while retaining a high gate fidelity. Our method employs all of the normal modes of motion of the ion chain, which allows us to operate outside of the adiabatic regime and at rates comparable to the secular ion-trapping frequency. Furthermore we extend our method for generating Hamiltonians which are suitable for quantum analog simulations, such as a nearest-neighbor spin Hamiltonian or the Su-Schrieffer-Heeger Hamiltonian.
Minimizing gate depth is important for extending the computational power of a noisy quantum processor, and native multiqubit gates could dramatically reduce the gate depth of generic circuits. To that end, although various approaches have been proposed, practical realization may be hindered by stringent control requirements, or by poor compatibility with existing schemes for one- or two-qubit operations. Here researchers employ a scalable architecture comprising two types of qubits to realize switchable coupling. This allows for a simple control strategy to realize native three-qubit gates, which may become a key element in e.g.e.g.e.g. quantum chemistry simulations.
We propose a one-step scheme to implement a multiqubit controlled phase gate with one qubit simultaneously controlling multiple qubits with three-level atoms at distant nodes in coupled cavity arrays. Selective qubit-qubit couplings are achieved by adiabatically eliminating the atomic excited states and photonic states, and the required phase shifts between the control qubit and any target qubit can be realized through suitable choices of the parameters of the external fields. Moreover, the effective model is robust against decoherence because neither the atoms nor the field modes are excited during the gate operation, leading to a useful step toward scalable quantum computing networks.
We present two protocols for realizing deterministic nonlocal multiqubit quantum gates on qubits coupled to a common cavity mode. The protocols rely only on a classical drive of the cavity mode, while no external drive of the qubits is required. Applied to just two qubits, both protocols provide a universal gate set for quantum computing, together with single-qubit gates. In the first protocol, the state of the cavity follows a closed trajectory in phase space and accumulates a geometric phase depending on the state of the qubits. This geometric phase gate can be used together with global single-qubit gates to generate high-fidelity Greenberger--Horne--Zeilinger (GHZ) states. The second protocol uses an adiabatic evolution of the combined qubit-cavity system to accumulate a dynamical phase. Repeated applications of this protocol allow for the realization of a family of phase gates with arbitrary phases, e.g., phase-rotation gates and multi-controlled-Z gates. For both protocols, we provide analytic solutions for the error rates, which scale as $\ensuremath{\sim}N/\sqrt{C}$ in the presence of relevant losses, with CCC the cooperativity and NNN the qubit number. Our protocols are applicable to a variety of systems and can be generalized by replacing the cavity by a different bosonic mode, such as a phononic mode. We provide estimates of gate fidelities and durations for atomic and molecular qubits as well as superconducting fluxonium qubits coupled to optical or microwave cavities, and we outline implications for quantum error correction.