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Physical Review A

Interaction- and measurement-free quantum Zeno gates for universal computation with single-atom and single-photon qubits

Y. P. Huang, M. G. Moore

Published Jun 19, 2008• 44 citations
Publisher

Abstract

By extending the concept of interaction-free imaging to the few-atom level, we show that asymptotically on-demand interaction- and measurement-free quantum logic gates can be realized for both single-atom and single-photon qubits. The interaction-free feature suppresses the possibility of qubit decoherence via atomic spontaneous decay, while the elimination of measurements can significantly reduce errors arising from detector inefficiency. We present a general theory of universal quantum Zeno gates, and discuss physical implementations for quantum-information processing with individual atoms and photons. In addition, we propose a loss-tolerant protocol for long-distance quantum communication using quantum Zeno gates incorporated into a Mach-Zehnder interferometer. The efficiency of our Zeno gates is limited primarily by the imprecise control of atom-photon scattering and the finite number of feedback cycles $N$ due to the limited finesse of the optical ring cavity. We find that the success probability scales as $1\ensuremath{-}O(1/N)$, and for realistic parameters could be as high as 98.4%. Successful generation of atom-atom entanglement can be heralded by detection of the ancillary photon, upon which the fidelity scales as $1\ensuremath{-}O(1/{N}^{2})$, with an achievable fidelity of 99.994%, which comes at the cost of reducing the success probability by the detector efficiency.

DOI
10.1103/physreva.77.062332

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By extending the concept of interaction-free imaging to the few-atom level, we show that asymptotically on-demand interaction- and measurement-free quantum logic gates can be realized for both single-atom and single-photon qubits. The interaction-free feature suppresses the possibility of qubit decoherence via atomic spontaneous decay, while the elimination of measurements can significantly reduce errors arising from detector inefficiency. We present a general theory of universal quantum Zeno gates, and discuss physical implementations for quantum-information processing with individual atoms and photons. In addition, we propose a loss-tolerant protocol for long-distance quantum communication using quantum Zeno gates incorporated into a Mach-Zehnder interferometer. The efficiency of our Zeno gates is limited primarily by the imprecise control of atom-photon scattering and the finite number of feedback cycles NNN due to the limited finesse of the optical ring cavity. We find that the success probability scales as 1\ensuremath−O(1/N)1\ensuremath{-}O(1/N)1\ensuremath−O(1/N), and for realistic parameters could be as high as 98.4%. Successful generation of atom-atom entanglement can be heralded by detection of the ancillary photon, upon which the fidelity scales as 1\ensuremath−O(1/N2)1\ensuremath{-}O(1/{N}^{2})1\ensuremath−O(1/N2), with an achievable fidelity of 99.994%, which comes at the cost of reducing the success probability by the detector efficiency.
The problem of on-demand generation of entanglement between single-atom qubits via a common photonic channel is examined within the framework of optical interferometry. As expected, for a Mach-Zehnder interferometer with coherent laser beam as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. We show, however, that with a twin-Fock input, useful entanglement can in principle be created without cavity enhancement. Both approaches require single-photon resolving detectors, and best results would be obtained by combining both cavity feedback and twin-Fock inputs. Such an approach may allow a fidelity of 0.99 using a two-photon input and currently available mirror and detector technology. In addition, we study interferometers based on NOON states, i.e., maximally entangled NNN-particle states, and show that they perform similarly to the twin-Fock states, yet without the need for high-precision photodetectors. The present interferometrical approach can serve as a universal, scalable circuit element for quantum information processing, from which fast quantum gates, deterministic teleportation, entanglement swapping, etc., can be realized with the aid of single-qubit operations.
Scaling quantum computation beyond the capacity of a single quantum processing unit requires quantum interconnects between modular processors. Optical photons are natural carriers for distributing entanglement between these processors. Most loss-resilient protocols use photonic Bell-state measurements based on the linear-optics type-II fusion gate. The resulting entanglement rate scales quadratically with each processor's typically low photon-delivery probability. Here we analyze a memory-assisted quantum interconnect using a near-deterministic, robust photon--atom controlled-ZZZ gate via a single atom trapped in a high-finesse cavity. Detecting and measuring a photon from one processor heralds entanglement between that processor and the atom. This entanglement is preserved while the process repeats with the second processor until the second photon is detected and measured. Reading out the atomic qubit finalizes the entanglement between the processors. As the entanglement is mediated by the atom, the photons from both processors do not need to be indistinguishable, removing a major source of infidelity. Furthermore, by removing the simultaneous photon-arrival requirement, the protocol allows the entanglement rate to scale linearly rather than quadratically with photon-arrival probability over a wide parameter range. We derive entanglement rates under realistic parameters, accounting for decay of the atom's entanglement with the first processor and for decoherence caused by unheralded photon interactions. The nanosecond-scale of the gate and read-out operations leads to orders-of-magnitude entanglement-rate gain over linear optics, removing a key bottleneck in modular quantum computing.
An Elitzur–Vaidman bomb tester demonstrates interaction-free sensing: detecting an object without absorbing a photon. The original protocol, however, has a success probability capped at 25%. We present a scalable quantum circuit that harnesses the quantum Zeno effect to overcome this limit. A single probe qubit undergoes repeated cycles of a small rotation followed by a controlled-NOT (CNOT) with an ancilla qubit representing the obstacle. The circuit requires only two qubits, regardless of the number of cycles N and has depth linear in N, compatible with near-term processors that support mid-circuit measurement and conditional reset. We simulate the circuit under ideal conditions and under a depolarizing noise model with gate errors typical of superconducting qubits (CNOT error 2% and single-qubit gate error rate 0.1%). Under noise, the success probability peaks around N=14 (reaching 72.0%), outperforming the original 25% limit by nearly a factor of three, with a well-defined optimal region. The protocol requires approximately 4.4 times fewer photons than the original Elitzur–Vaidman scheme to achieve 99.9% confidence. Its simple repetitive structure and well-defined optimal regime make it a practical benchmark for quantifying gate errors and decoherence on noisy intermediate-scale quantum hardware for quantum sensing applications.
The use of photons as qubits is a promising implementation for quantum computation. The inability of photons to interact, especially with the environment, makes them an ideal physical candidate. However, this also makes them a difficult system to perform two qubit gates on. Recent breakthroughs in photonic quantum computing have shown methods around the requirement of direct photon-photon interaction. In this thesis we study three recently discovered schemes for optical quantum computation. \n \n We first investigate the so called linear optical quantum computing (LOQC) scheme, exploring a method to improve the original proposal by constructing a photon-number QND detector that succeeds with a high probability. In doing this we present a new type of LOQC teleporter, one that can detect the presence of a single photon in an arbitrary polarisation state when the input state is a sum of vacuum and multi-photon terms. This new type of teleporter is an improvement on the original scheme in that the entangled states required can be made offline with fewer entangling operations. \n \n We next investigate the so called quantum bus (qubus) scheme for photonic quantum computing. We show a scheme to measure the party of n qubit states by using a single qubus mode, controlled rotations and displacements. This allows for the syndrome measurements of any stabilizer quantum error correcting code. We extend these results to a fault tolerant scheme to measure an arbitrary Pauli operator of weight n, incorporating so called single bit teleportations. We investigate the construction of a Toffoli gate by using a single qubus mode, controlled rotations and displacements that works with a success probability of at least 25%. We also investigate the use of single bit teleportations to construct a universal set of gates on coherent state type logic and in the construction of cluster states. \n \nWe finally investigate the optical Zeno gate, a gate that uses the Zeno effect in the form of two photon absorbers to induce a CSIGN. We model realistic two photon absorption and include realistic single photon loss for this gate, examining the use of encoding to overcome the single photon loss, showing that our results are competitive with the leading equivalent LOQC scheme.
Quantum logic gates for photonic qubits can be implemented using the quantum Zeno effect based on strong two-photon absorption. The fidelity of quantum Zeno gates of this kind may be substantially reduced by photon loss. Heralding on those outcomes in which both of the logical qubits emerge from the Zeno gate can increase the fidelity at the expense of a limited success rate (P.M. Leung et al., Phys. Rev. A 74, 062325 (2006)). We analyze the performance of heralded quantum Zeno gates by solving Schrodinger's equation for a system of photons coupled to three-level atoms. This approach identifies several potential error sources that are not described by earlier models that assumed a fixed rate of single-photon loss and two-photon absorption.
High-fidelity and decoherence-insensitive quantum gates are essential for achieving universal quantum computing. In quantum information processing, decoherence arising from excited states significantly contributes to the scheme's infidelity. Therefore, minimizing the average population of the excited state is crucial when designing quantum protocols. A promising approach involves utilizing capture-and-release dynamics to induce a complex phase on the ground state in a two-level system, effectively suppressing the integrated excited-state population. By applying this dynamics protocol to a $\mathrm{\ensuremath{\Lambda}}$ three-level system, we propose a scheme to construct arbitrary decoherence suppressed single-qubit and nontrivial two-qubit gates; meanwhile, by incorporating the Zeno dynamics process in the construction of two-qubit logic gates, the large detuning and excitation of virtual photons render the scheme insensitive to qubit decoherence and cavity dissipation. Applying our scheme to the nitrogen-vacancy (NV) center as an example, we prove our scheme with higher fidelity than conventional nonadiabatic non-Abelian geometric gates while significantly enhancing the robustness against decoherence and frequency shift errors. These studies provide alternative approaches for constructing robust quantum gate operations. We also emphasize that the scheme is feasible for three-level quantum systems, not limited to NV center systems.