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arXiv:1805.06877

Quantum Zeno effect: A possible resolution to the leakage problem in superconducting quantum computing architectures

Andrei Galiautdinov

Published May 17, 2018• 3 citations
arXivHTMLPDF

Abstract

We propose to use the continuous version of the quantum Zeno effect to eliminate leakage to higher energy states in superconducting quantum computing architectures based on Josephson phase and flux qubits. We are particularly interested in the application of this approach to the single-step Greenberger-Horne-Zeilinger (GHZ) state protocol described in [A. Galiautdinov and J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)]. While being conceptually appealing, the protocol was found to be plagued with a number of spectral crowding and leakage problems. Here we argue that by coupling the qubits to a measuring device which continuously monitors leakage to higher energy states (say, to a very lossy resonator of frequency omega = E3(qubit)-E1(qubit), with 1 labeling the ground state of the qubit), we could potentially restrict the multi-qubit system's evolution to its computational subspace, thus circumventing the above mentioned problems.

DOI
10.48550/arxiv.1805.06877

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We propose to use the continuous version of the quantum Zeno effect to eliminate leakage to higher energy states in superconducting quantum computing architectures based on Josephson phase and flux qubits. We are particularly interested in the application of this approach to the single-step Greenberger-Horne-Zeilinger (GHZ) state protocol described in [A. Galiautdinov and J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)]. While being conceptually appealing, the protocol was found to be plagued with a number of spectral crowding and leakage problems. Here we argue that by coupling the qubits to a measuring device which continuously monitors leakage to higher energy states (say, to a very lossy resonator of frequency omega = E3(qubit)-E1(qubit), with 1 labeling the ground state of the qubit), we could potentially restrict the multi-qubit system's evolution to its computational subspace, thus circumventing the above mentioned problems.
Real-time monitoring of a quantum state provides powerful tools for studying the backaction of quantum measurement and performing quantum feedback. Historically, this monitoring capability has been the exclusive province of atomic and optical physics. This thesis describes the implementation of the first such high-fidelity readout scheme in a solid state circuit, a superconducting quantum bit (qubit) coupled to a microwave cavity in the circuit quantum electrodynamics (circuit QED) architecture. The qubit-state-dependent resonance frequency of the cavity is probed with a microwave drive tone, and the resulting signal amplified using a fast, ultralow-noise superconducting parametric amplifier. This arrangement enables the observation of quantum jumps between the qubit states in real time. The ability to monitor the qubit continuously with high fidelity and resolve quantum jumps can be used to investigate the backaction of the measurement process on the qubit. This thesis examines the quantum Zeno effect--where strong measurement inhibits the evolution of a quantum system-- as well as the transition to non-ideal measurement with increasing measurement strength in the circuit QED architecture, a phenomenon shown to be due to the upconversion of low-frequency dephasing noise. These data allow probes of ``universal'' flux noise in previously inaccessible frequency ranges. The work presented here opens the door for quantum feedback and error correction in solid-state quantum systems using continuous weak measurement.
We study the dynamics of the Josephson flux qubit, which consists on a SQUID loop with three Josephson junctions operated at or near a magnetic flux of half quantum. We perform simulations of the time dependent Schrödinger equation when the system is started in the ground state. The leakage from the two lowest energy levels of the qubit computational subspace to higher energy levels is calculated, when pulses in the magnetic field are applied. We obtain, as expected, that constant field pulses have a higher leakage than rf field pulses at the resonant Rabi frequency. In the case of the constant field pulse we study the average leakage as a function of the pulse intensity, f p . For low f p we obtain that the leakage is quadratic in f p and we compare with a perturbative calculation.
When a quantum state is subjected to frequent measurements, the time evolution of the quantum state is frozen. This is called the quantum Zeno effect. Here, we observe such an effect by performing frequent discrete measurements in a macroscopic quantum system, a superconducting quantum bit. The quantum Zeno effect induced by discrete measurements is similar to the original idea of the quantum Zeno effect. By using a Josephson bifurcation amplifier pulse readout, we have experimentally suppressed the time evolution of Rabi oscillation using projective measurements, and also observed the enhancement of the quantum state holding time by shortening the measurement period time. This is a crucial step to realize quantum information processing using the quantum Zeno effect.
We examine the appearance of Zeno and anti-Zeno effects (Misra and Sudarshan 1977 J. Math. Phys. 18 756; Kofman and Kurizki 2000 Nature 405 546; Kofman and Kurizki 1996 Phys. Rev. A 54 3750; Facchi et al 2001 Phys. Rev. Lett. 86 2699) in the entanglement dynamics of two qubits off-resonantly coupled to the same lossy cavity when the unitary evolution of the system is interrupted by repeated projective measurements. We describe in detail these quantum effects by comparing the measurement-induced coarse-grained dynamics to the entanglement evolution in the absence of measurements in several scenarios (Francica et al 2009 Phys. Rev. A 79 032310). In particular, we examine the strong and weak coupling regimes, the role of the relative coupling strengths between the two qubits and the reservoir and the effect of the detuning from the main cavity frequency. We show that the anti-Zeno effect can occur in the entanglement dynamics when the qubit frequencies are detuned from the main reservoir frequency. Furthermore, we find that Zeno and anti-Zeno effects can even appear sequentially many times as a function of the interval between the measurements. Finally, we show that, in the off-resonant regime, we can preserve the entanglement using the quantum Zeno effect more efficiently than in the resonant limit (Maniscalco et al 2008 Phys. Rev. Lett. 100 090503), even if, in this case, no sub-radiant state exists.
Adiabatic quantum computing has demonstrated how the quantum Zeno effect can be used to construct quantum optimizers. However, much less work has been done to understand how more general Zeno effects could be used in a similar setting. We use a construction based on three-state systems rather than directly in qubits, so that a qubit can remain after projecting out one of the states. We find that our model of computing is able to recover the dynamics of a transverse field Ising model. Several generalizations are possible, but our methods allow for constraints to be implemented nonperturbatively and do not need tunable couplers, unlike simple transverse field implementations. We further discuss how to implement the protocol physically using methods building on stimulated Raman adiabatic passage (STIRAP) protocols for state transfer. We find a substantial challenge that settings defined exclusively by measurement or dissipative Zeno effects do not allow for frustration, and in these settings pathological spectral features arise leading to unfavorable runtime scaling. We discuss methods to overcome this challenge, for example including gain as well as loss as is often done in an optical setting.