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arXiv:1701.04062 · Physical Review A

Experimental replication of single-qubit quantum phase gates

Michal Mičuda, Robert Stárek, Ivo Straka, Martina Miková, Michal Sedlák, Miroslav Ježek, Jaromı́r Fiurášek

Published May 16, 2016• 3 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate the underlying physical mechanism of the recently proposed protocol for superreplication of quantum phase gates [W. D\"ur, P. Sekatski, and M. Skotiniotis, Phys. Rev. Lett. 114, 120503 (2015)], which allows producing up to ${N}^{2}$ high-fidelity replicas from $N$ input copies in the limit of large $N$. Our implementation of $1\ensuremath{\rightarrow}2$ replication of the single-qubit phase gates is based on linear optics and qubits encoded into states of single photons. We employ the quantum Toffoli gate to imprint information about the structure of an input two-qubit state onto an auxiliary qubit, apply the replicated operation to the auxiliary qubit, and then disentangle the auxiliary qubit from the other qubits by a suitable quantum measurement. We characterize the replication protocol by full quantum process tomography and observe good agreement of the experimental results with theory.

DOI
10.1103/physreva.93.052318

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We experimentally demonstrate the underlying physical mechanism of the recently proposed protocol for superreplication of quantum phase gates [W. D"ur, P. Sekatski, and M. Skotiniotis, Phys. Rev. Lett. 114, 120503 (2015)], which allows producing up to N2{N}^{2}N2 high-fidelity replicas from NNN input copies in the limit of large NNN. Our implementation of 1\ensuremath→21\ensuremath{\rightarrow}21\ensuremath→2 replication of the single-qubit phase gates is based on linear optics and qubits encoded into states of single photons. We employ the quantum Toffoli gate to imprint information about the structure of an input two-qubit state onto an auxiliary qubit, apply the replicated operation to the auxiliary qubit, and then disentangle the auxiliary qubit from the other qubits by a suitable quantum measurement. We characterize the replication protocol by full quantum process tomography and observe good agreement of the experimental results with theory.
Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O(M/N 2), where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i) an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii) a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N 2, and iii) a protocol that generates O(N 2) nearly perfect copies of a generic pure state U |0〉 while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M 2/N 2.
We design linear-optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto the state of a single photon in two modes (e.g., spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In particular, we propose an interferometric implementation of the Toffoli gate in the coincidence basis, which does not require any ancilla photons and is experimentally feasible with current technology.
We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear optical implementation is based on the encoding of qubits into polarization states of single photons, two-photon interference on a polarizing beam splitter, and measurement on the output program qubit. We fully characterize the programmable gate by quantum process tomography. The achieved average quantum process fidelity exceeding 97% illustrates very good performance of the gate for all values of the encoded phase shift. We also show that by using a different set of program states the device can operate as a programmable partial polarization filter.
Hyper-encoding enables storing several qubits in a single photon using its different degrees of freedom like polarization and spatial ones. This approach enables feasible implementation of multi-qubit operations. One of the basic manipulations of two or more qubits is to swap their quantum state. Here we report on feasible and stable experimental implementation of a deterministic single photon two-qubit SWAP gate that interchanges path and polarization qubits. We discuss the principle of its operation and give detailed information about experimental demonstration employing two Mach-Zehnder interferometers with one common arm. The gate characterization is done by full quantum process tomography using photons produced by heralded single-photon source. The achieved quantum process fidelity reached more than 0.94 with an effective phase uncertainty of the whole setup, evaluated by means of Allan deviation, below 2.5 deg for 2.5 h without any active stabilization. Our design provides a contribution to the hyper-encoded linear quantum optics toolbox.
We report on a detailed characterization of a three-qubit linear optical quantum Toffoli gate. Our experiment utilizes correlated photon pairs generated in the process of spontaneous parametric down-conversion. Two qubits are encoded into polarization and spatial degrees of freedom of a signal photon, and the third qubit is represented by polarization of an idler photon. The linear optical Toffoli gate is implemented by interference of photons on a partially polarizing beam splitter inserted inside a Mach Zehnder interferometer formed by two calcite beam displacers. We have measured 4032 different two-photon coincidences, which allows us to estimate the fidelity of the gate to be 90%. Although these data are not tomographically complete, we show that they are sufficient for a reliable reconstruction of the quantum process matrix of the gate via the recently proposed maximum likelihood--maximum entropy estimation procedure. To probe the entangling capability of the gate, we have investigated generation of three-qubit GHZ states from fully and partially separable input states and we have performed a full tomography of the output states. We compare the reconstructed states with theoretical predictions obtained with the use of the estimated quantum process matrix and obtain a very good agreement.
Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can be replicated deterministically at nearly quadratic rates, with an error vanishing on most inputs except for an exponentially small fraction. The result is not in contradiction with the no-cloning theorem, since the impossibility of deterministically transforming pure states into unitary gates prevents the application of the gate replication protocol to states. In addition to gate replication, we show that N parallel uses of a completely unknown unitary gate can be compressed into a single gate acting on O(log_{2}N) qubits, leading to an exponential reduction of the amount of quantum communication needed to implement the gate remotely.