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arXiv:0909.2843 · Physical Review Letters

Cluster-State Quantum Computing Enhanced by High-Fidelity Generalized Measurements

Devon N. Biggerstaff, Rainer Kaltenbaek, Deny R. Hamel, Gregor Weihs, Terry Rudolph, Kevin J. Resch

Published Dec 11, 2009• 36 citations
arXivHTMLPDF

Abstract

We introduce and implement a technique to extend the quantum computational power of cluster states by replacing some projective measurements with generalized quantum measurements (POVMs). As an experimental demonstration we fully realize an arbitrary three-qubit cluster computation by implementing a tunable linear-optical POVM, as well as fast active feedforward, on a two-qubit photonic cluster state. Over 206 different computations, the average output fidelity is 0.9832+/-0.0002; furthermore the error contribution from our POVM device and feedforward is only of O(10(-3)), less than some recent thresholds for fault-tolerant cluster computing.

DOI
10.1103/physrevlett.103.240504

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We introduce and implement a technique to extend the quantum computational power of cluster states by replacing some projective measurements with generalized quantum measurements (POVMs). As an experimental demonstration we fully realize an arbitrary three-qubit cluster computation by implementing a tunable linear-optical POVM, as well as fast active feedforward, on a two-qubit photonic cluster state. Over 206 different computations, the average output fidelity is 0.9832+/-0.0002; furthermore the error contribution from our POVM device and feedforward is only of O(10(-3)), less than some recent thresholds for fault-tolerant cluster computing.
This thesis describes a linear-optical device for performing generalized quantum measurements \non quantum bits (qubits) encoded in photon polarization, the implementation \nof said device, and its use in two diff erent but related experiments. The device works by \ncoupling the polarization degree of freedom of a single photon to a `mode' or `path' degree \nof freedom, and performing a projective measurement in this enlarged state space in order \nto implement a tunable four-outcome positive operator-valued measure (POVM) on the \ninitial quantum bit. In both experiments, this POVM is performed on one photon from a \ntwo-photon entangled state created through spontaneous parametric down-conversion. \nIn the fi rst experiment, this entangled state is viewed as a two-qubit photonic cluster \nstate, and the POVM as a means of increasing the computational power of a given resource \nstate in the cluster-state model of quantum computing. This model traditionally \nachieves deterministic outputs to quantum computations via successive projective measurements, \nalong with classical feedforward to choose measurement bases, on qubits in a highly entangled \nresource called a cluster state; we show that `virtual qubits' can be appended to a \ngiven cluster by replacing some projective measurements with POVMs. Our experimental \ndemonstration fully realizes an arbitrary three-qubit cluster computation by implementing \nthe POVM, as well as fast active feed-forward, on our two-qubit photonic cluster state. \nOver 206 diff erent computations, the average output delity is 0.9832 +/- 0.0002; furthermore \nthe error contribution from our POVM device and feedforward is only of order 10^-3, less \nthan some recent thresholds for fault-tolerant cluster computing. \nIn the second experiment, the POVM device is used to implement a deterministic \nprotocol for remote state preparation (RSP) of arbitrary photon polarization qubits. RSP \nis the act of preparing a quantum state at a remote location without actually transmitting \nthe state itself. We are able to remotely prepare 178 diff erent pure and mixed qubit \nstates with an average delity of 0.995. Furthermore, we study the the fidelity achievable \nby RSP protocols permitting only classical communication, without shared entanglement, \nand compare the resulting benchmarks for average fidelity against our experimental results. \nOur experimentally-achieved average fi delities surpass the classical thresholds whenever \nclassical communication alone does not trivially allow for perfect RSP.
We propose a measurement-based model for fault-tolerant quantum computation that can be realized with one-dimensional cluster states and fusion measurements only; basic resources that are readily available with scalable photonic hardware. Our simulations demonstrate high thresholds compared with other measurement-based models realized with basic entangled resources and 2-qubit fusion measurements. Its high tolerance to noise indicates that our practical construction offers a promising route to scalable quantum computing with quantum emitters and linear-optical elements.
Cluster states are the essential resource used in the implementation of fusion-based quantum computation (FBQC). We introduce a method to generate high-fidelity optical cluster states by utilizing the concept of unitary averaging. This error-averaging technique is entirely passive and can be readily incorporated into the proposed PsiQuantum FBQC architecture. Using postselection and the redundant encoding of fusion gates, we observe an enhancement in the average fidelity of the output cluster state. As a generalization, we also show an improvement in the linear optical Bell-state measurement (BSM) success probability when the BSM is imperfect.
We explore basic necessary protocols to achieve fault tolerance for quantum computation in the cluster state and circuit models. For the cluster state model we simulate the implementation of an arbitrary rotation via only measurement on a decohered cluster state. Fidelity is used to quantify the accuracy of the initial cluster state and a gate fidelity for the arbitrary rotation is determined. In the circuit model we compare the accuracy of two methods that can be used to construct a logical zero state appropriate for the [7, 1, 3] Steane quantum error correction code in a non-equiprobable Pauli operator error environment: a fault tolerant method done by applying error correction on seven qubits all in the state zero, and a non-fault tolerant method done by implementing the encoding gate sequence. We find that the latter construction method, in spite of its lack of "fault tolerance," outputs a seven qubit state with a higher fidelity than the first (fault tolerant) method. However, the fidelity of the single qubit of stored information exhibits almost equivalent values between the two construction methods.
The Measurement Based Quantum Computation (MBQC) model achieves universal quantum computation by employing projective single qubit measurements with classical feedforward on a highly entangled multipartite cluster state. Rapid advances in improving scalability of quantum computing systems have enabled the generation of large cluster states for implementing MBQC on various platforms. This review focuses on three such efforts, each utilizing a different quantum computing technology viz., superconducting qubits, trapped ion qubits and squeezed photon states. MBQC is being increasingly employed on optical platforms which can generate large entangled resource states but lack the ability to perform deterministic entangling gates.
Integrated photonics provides a versatile platform for encoding and processing quantum information.However, the encoded quantum states are sensitive to noise, which limits their capability to perform complicated quantum computations.Here, we use a five-qubit linear cluster state on a silicon photonic chip to implement a quantum error-correction code and demonstrate its capability of identifying and correcting a single-qubit error.The encoded quantum information is reconstructed from a single-qubit error and an average state fidelity of 0.863 ± 0.032 is achieved for different input states.We further extend the scheme to demonstrate a fault-tolerant measurement-based quantum computation (MBQC) on stabilizer formalism that allows us to redo the qubit operation against the failure of the teleportation process.Our work provides a proof-of-concept working prototype of error correction and MBQC in an integrated photonic chip.