Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1306.1141 · Physical Review Letters

Efficient Experimental Estimation of Fidelity of Linear Optical Quantum Toffoli Gate

Michal Mičuda, Michal Sedlák, Ivo Straka, Martina Miková, Miloslav Dušek, Miroslav Ježek, Jaromı́r Fiurášek

Published Oct 17, 2013• 64 citations
arXivHTMLPDF

Abstract

We propose an efficiently measurable lower bound on quantum process fidelity of N-qubit controlled-Z gates. This bound is determined by average output state fidelities for N partially conjugate product bases. A distinct advantage of our approach is that only fidelities with product states need to be measured while keeping the total number of measurements much smaller than what is necessary for full quantum process tomography. As an application, we use this method to experimentally estimate quantum process fidelity F of a three-qubit linear optical quantum Toffoli gate and we find that F≥0.83. We also demonstrate the entangling capability of the gate by preparing Greenberger-Horne-Zeilinger-type three-qubit entangled states from input product states.

DOI
10.1103/physrevlett.111.160407

Related papers

Tomographic characterization of a linear optical quantum Toffoli gate

Michal Mičuda, Martina Miková, Ivo Straka +4 more

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.

Physical Review A•Sep 8, 2015•18 citations

Process-fidelity estimation of a linear optical quantum-controlled- Z gate: A comparative study

Michal Mičuda, Michal Sedlák, Ivo Straka +4 more

We present a systematic comparison of different methods of fidelity estimation of a linear optical quantum-controlled-$Z$ gate implemented by two-photon interference on a partially polarizing beam splitter. We utilize a linear fidelity estimator based on the Monte Carlo sampling technique as well as a nonlinear estimator based on maximum likelihood reconstruction of a full quantum-process matrix. In addition, we evaluate the lower bound on quantum-gate fidelity determined by average quantum-state fidelities for two mutually unbiased bases. In order to probe various regimes of operation of the gate we introduce a tunable time delay between the two photons. This allows us to move from high-fidelity operation to a regime where the photons become distinguishable and the success probability of the scheme significantly depends on the input state. We discuss in detail possible systematic effects that could influence the gate-fidelity estimation.

arXiv:1403.4863•Physical Review A•Apr 7, 2014•9 citations

Quantum Process Tomography of a Controlled-NOT Gate

Jeremy L. O’Brien, Geoff J. Pryde, Alexei Gilchrist +4 more

We demonstrate complete characterization of a two-qubit entangling process--a linear optics controlled-NOT gate operating with coincident detection--by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively.

arXiv:quant-ph/0402166•Physical Review Letters•Aug 20, 2004•499 citations

Quantum process fidelity bounds from sets of input states

Karl Mayer, Emanuel H. Knill

We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove convexity of the minimum process fidelity as a function of the errors on the output states. We characterize the conditions required to uniquely determine a process in the case of no errors and derive a lower bound on its fidelity in the limit of small errors for any set of input states satisfying these conditions. We then consider sets of input states whose one-dimensional projectors form a symmetric positive operator-valued measure (POVM). We prove that for such sets the minimum fidelity is bounded by a linear function of the average output state error. A symmetric POVM with minimal number of elements contains $d+1$ states, where $d$ is the Hilbert space dimension. Our bounds applied to such states provide an efficient method for estimating the process fidelity without the use of full process tomography.

arXiv:1805.04491•Physical Review A•Nov 21, 2018•16 citations

Estimating Fidelity Lower Bounds of Quantum Subroutines

Karl Mayer, Charlie Baldwin

We define scalable benchmarks for two important quantum subroutines, namely the quantum Fourier transform (QFT) and the multi-controlled-Z gate. Our benchmarks are based on applying the subroutines to a set of states that are sufficient for lower-bounding the process fidelity from the set of measured output state fidelities. By randomly sampling from the set of input states, the lower boundonthe process fidelity can be estimated. We implement the QFT and multi-controlled-Z circuits with up to 20 and 12 qubits, respectively, on the Quantinuum H1-1 quantum computer. Our circuits make use of parameterized-angle entangling gates, which for these circuits reduces the number of two-qubit gates significantly.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•0 citations

Bounds on quantum process fidelity from minimum required number of quantum state fidelity measurements

Jaromı́r Fiurášek, Michal Sedlák

To certify that an experimentally implemented quantum transformation is a certain unitary operation $U$ on a $d$-dimensional Hilbert space, it suffices to determine fidelities of output states for $d+1$ suitably chosen pure input states [Reich et al., Phys. Rev. A 88, 042309 (2013)]. The set of these $d+1$ probe states can consist of $d$ orthogonal states that form a basis and one additional state which is a balanced superposition of all $d$ basis states. Here we provide an analytical lower bound on quantum process fidelity for two-qubit quantum gates which results from the knowledge of average state fidelity for the basis states and the fidelity of the superposition state. We compare this bound with the Hofmann bound that is based on knowledge of average state fidelities for two mutually unbiased bases. We also discuss the possible extension of our findings to $N$-qubit operations.

arXiv:1401.5964•Physical Review A•Jan 22, 2014•7 citations
We propose an efficiently measurable lower bound on quantum process fidelity of N-qubit controlled-Z gates. This bound is determined by average output state fidelities for N partially conjugate product bases. A distinct advantage of our approach is that only fidelities with product states need to be measured while keeping the total number of measurements much smaller than what is necessary for full quantum process tomography. As an application, we use this method to experimentally estimate quantum process fidelity F of a three-qubit linear optical quantum Toffoli gate and we find that F≥0.83. We also demonstrate the entangling capability of the gate by preparing Greenberger-Horne-Zeilinger-type three-qubit entangled states from input product states.
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.
We present a systematic comparison of different methods of fidelity estimation of a linear optical quantum-controlled-ZZZ gate implemented by two-photon interference on a partially polarizing beam splitter. We utilize a linear fidelity estimator based on the Monte Carlo sampling technique as well as a nonlinear estimator based on maximum likelihood reconstruction of a full quantum-process matrix. In addition, we evaluate the lower bound on quantum-gate fidelity determined by average quantum-state fidelities for two mutually unbiased bases. In order to probe various regimes of operation of the gate we introduce a tunable time delay between the two photons. This allows us to move from high-fidelity operation to a regime where the photons become distinguishable and the success probability of the scheme significantly depends on the input state. We discuss in detail possible systematic effects that could influence the gate-fidelity estimation.
We demonstrate complete characterization of a two-qubit entangling process--a linear optics controlled-NOT gate operating with coincident detection--by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively.
We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove convexity of the minimum process fidelity as a function of the errors on the output states. We characterize the conditions required to uniquely determine a process in the case of no errors and derive a lower bound on its fidelity in the limit of small errors for any set of input states satisfying these conditions. We then consider sets of input states whose one-dimensional projectors form a symmetric positive operator-valued measure (POVM). We prove that for such sets the minimum fidelity is bounded by a linear function of the average output state error. A symmetric POVM with minimal number of elements contains d+1d+1d+1 states, where ddd is the Hilbert space dimension. Our bounds applied to such states provide an efficient method for estimating the process fidelity without the use of full process tomography.
We define scalable benchmarks for two important quantum subroutines, namely the quantum Fourier transform (QFT) and the multi-controlled-Z gate. Our benchmarks are based on applying the subroutines to a set of states that are sufficient for lower-bounding the process fidelity from the set of measured output state fidelities. By randomly sampling from the set of input states, the lower boundonthe process fidelity can be estimated. We implement the QFT and multi-controlled-Z circuits with up to 20 and 12 qubits, respectively, on the Quantinuum H1-1 quantum computer. Our circuits make use of parameterized-angle entangling gates, which for these circuits reduces the number of two-qubit gates significantly.
To certify that an experimentally implemented quantum transformation is a certain unitary operation UUU on a ddd-dimensional Hilbert space, it suffices to determine fidelities of output states for d+1d+1d+1 suitably chosen pure input states [Reich et al., Phys. Rev. A 88, 042309 (2013)]. The set of these d+1d+1d+1 probe states can consist of ddd orthogonal states that form a basis and one additional state which is a balanced superposition of all ddd basis states. Here we provide an analytical lower bound on quantum process fidelity for two-qubit quantum gates which results from the knowledge of average state fidelity for the basis states and the fidelity of the superposition state. We compare this bound with the Hofmann bound that is based on knowledge of average state fidelities for two mutually unbiased bases. We also discuss the possible extension of our findings to NNN-qubit operations.