High-speed linear optics quantum computing using active feed-forward

Prevedel, Robert; Walther, Philip; Tiefenbacher, F.; Böhi, Pascal; Kaltenbaek, Rainer; Jennewein, Thomas; Zeilinger, Anton

doi:10.1038/nature05346

Cited by 355 publications

(310 citation statements)

References 29 publications

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“…In our experimental implementation we use the iterative approach with post-selection in place of measurement and feed-forward; measurement and feed-forward operations have been achieved in the context of cluster state quantum computing with photons 23 . The quantum order finding circuit of Fig.…”

Section: Figmentioning

confidence: 99%

Experimental realization of Shor's quantum factoring algorithm using qubit recycling

et al. 2012

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Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms 1-3 . Shor's quantum algorithm 4 for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer 5 . However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations 6-9 . Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol [10][11][12] . Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N = 21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.Shor's factoring algorithm consists of a quantum order finding algorithm, preceded and succeeded by various classical routines. While the classical tasks are known to be efficient on a classical computer, order finding is understood to be intractable classically. However, it is known that this part of the algorithm can be performed efficiently on a quantum computer. To determine the prime factors of an odd integer N , one chooses a coprime of N , x. The order r relates x to N according to x r mod N = 1, and can be used to obtain the factors, given by the greatest common divisor gcd(x r 2 ± 1, N ). The quantum order finding circuit involves two registers: a work register and a control register. In the standard protocol, the work register performs modular arithmetic with m = log 2 N qubits, enough to encode the number N , and the n qubit control register provides the algorithmic output, with n bits of precision.Measuring the control register in the computational basis will yield a result of k2 n /r where k is an integer between 0 and r − 1, with the value of k occurring probabilistically. Dividing the result by 2 n gives the first n bits of k/r and r may be found with classical processing, using the continued fraction algorithm. For large n, and a perfectly functioning circuit, the output probability distribution of the control register is a series of well defined peaks at values of k2 n /r (Fig. 1b). (See Appendix for details.)Here we implement an iterative version of the order finding algorithm 10,11 , in which the control register contains only a single qubit which is recycled n times, using a sequence of measurement and feed-forward operations, with each step providing an additional bit of precision (Fig. 1a). Reducing the number of qubits in quantum simulations and quantum chemistry has been achieved with recursive phase estimation 13-16 , while ground state projections have been demonstrated by exploiting similar techniques in NMR 17 .The iterative version of...

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Section: Figmentioning

confidence: 99%

Experimental realization of Shor's quantum factoring algorithm using qubit recycling

et al. 2012

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“…2c. The auxiliary qubit is randomly prepared by the client in one of the four rotated BB84 states, P y Z d þ i j , using waveplates and Pockels' cells as fast optical switches [24][25][26] (see Methods), and then sent to the server. The Pockels' cells are switched at 1 MHz-two orders of magnitude faster than the single-photon detection rate from spontaneous parametric downconversion.…”

Section: Article Nature Communications | Doi: 101038/ncomms4074mentioning

confidence: 99%

Quantum computing on encrypted data

et al. 2014

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The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.

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“…Optical quantum computation (QC) has been suggested [6,7] using cluster states [8][9][10][11][12][13][14]. Oneway optical QC using a four-photon cluster state has been demonstrated experimentally [4,5,15]. In spite of this progress, scalable optical one-way QC still remains elusive because of the difficulty in generating cluster states with a large number of qubits.…”

Section: Introductionmentioning

confidence: 99%

“…), combined with single-photon sources and detectors can be used for efficient quantum information processing [1]. Experimental progress in optical systems has demonstrated control of photonic qubits, quantum gates, and small quantum algorithms (e.g., [2][3][4][5]). Optical quantum computation (QC) has been suggested [6,7] using cluster states [8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Robust and scalable optical one-way quantum computation

2010

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We propose an efficient approach for deterministically generating scalable cluster states with photons. This approach involves unitary transformations performed on atoms coupled to optical cavities. Its operation cost scales linearly with the number of qubits in the cluster state, and photon qubits are encoded such that single-qubit operations can be easily implemented by using linear optics. Robust optical one-way quantum computation can be performed since cluster states can be stored in atoms and then transferred to photons that can be easily operated and measured. Therefore, this proposal could help in performing robust large-scale optical one-way quantum computation.

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High-speed linear optics quantum computing using active feed-forward

Cited by 355 publications

References 29 publications

Experimental realization of Shor's quantum factoring algorithm using qubit recycling

Experimental realization of Shor's quantum factoring algorithm using qubit recycling

Quantum computing on encrypted data

Robust and scalable optical one-way quantum computation

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