Experimentally efficient methods for estimating the performance of quantum measurements

Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and a well-defined experimental procedure for estimating the distinguishability measure. Here, we propose the average measurement fidelity and error between quantum measurements as distinguishability measures. We present protocols for obtaining bounds on these quantities that are both estimable using experimentally accessible quantities and scalable in the size of the quantum system. We explain why the bounds should be valid in large generality and illustrate the method via numerical examples.

[1]  Daniel Gottesman,et al.  Stabilizer Codes and Quantum Error Correction , 1997, quant-ph/9705052.

[2]  David Poulin,et al.  Practical characterization of quantum devices without tomography. , 2011, Physical review letters.

[3]  D. Gottesman.  Fault-Tolerant Quantum Computation with Higher-Dimensional Systems , 1998, quant-ph/9802007.

[4]  Joseph Emerson,et al.  Scalable protocol for identification of correctable codes , 2007, 0710.1900.

[5]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[6]  E. Knill,et al.  Randomized Benchmarking of Quantum Gates , 2007, 0707.0963.

[7]  T. Monz,et al.  14-Qubit entanglement: creation and coherence. , 2010, Physical review letters.

[8]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[9]  A. G. White,et al.  Ancilla-assisted quantum process tomography. , 2003, Physical review letters.

[10]  R. Feynman.  Simulating physics with computers , 1999 .

[11]  M Steffen,et al.  Efficient measurement of quantum gate error by interleaved randomized benchmarking. , 2012, Physical review letters.

[12]  J. Paz,et al.  Selective and efficient quantum process tomography without ancilla. , 2011, Physical review letters.

[13]  F. Pastawski,et al.  Selective and efficient estimation of parameters for quantum process tomography. , 2008, Physical review letters.

[14]  Isaac L. Chuang,et al.  Prescription for experimental determination of the dynamics of a quantum black box , 1997 .

[15]  Jeroen van de Graaf,et al.  Cryptographic Distinguishability Measures for Quantum-Mechanical States , 1997, IEEE Trans. Inf. Theory.

[16]  N. Langford,et al.  Distance measures to compare real and ideal quantum processes (14 pages) , 2004, quant-ph/0408063.

[17]  Yi-Kai Liu,et al.  Direct fidelity estimation from few Pauli measurements. , 2011, Physical review letters.

[18]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[19]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[20]  Fedor Jelezko,et al.  Processing quantum information in diamond , 2006 .

[21]  Margarita A. Man’ko,et al.  Journal of Optics B: Quantum and Semiclassical Optics , 2003 .

[22]  A. Kitaev.  Fault tolerant quantum computation by anyons , 1997, quant-ph/9707021.

[23]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[24]  E. Knill,et al.  Resilient quantum computation: error models and thresholds , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[26]  Brian J. Smith,et al.  Mapping coherence in measurement via full quantum tomography of a hybrid optical detector , 2012, Nature Photonics.

[27]  V. Paulsen.  Completely Bounded Maps and Operator Algebras: Contents , 2003 .

[28]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[29]  Luigi Frunzio,et al.  Realization of three-qubit quantum error correction with superconducting circuits , 2011, Nature.

[30]  F. Y. Edgeworth,et al.  The theory of statistics , 1996 .

[31]  Joseph Emerson,et al.  Scalable and robust randomized benchmarking of quantum processes. , 2010, Physical review letters.

[32]  Joseph M. Renes,et al.  Symmetric informationally complete quantum measurements , 2003, quant-ph/0310075.

[33]  A. Kitaev.  Quantum computations: algorithms and error correction , 1997 .

[34]  John Calsamiglia,et al.  Distinguishability measures between ensembles of quantum states , 2008, 0812.3832.

[35]  J. Emerson,et al.  Scalable noise estimation with random unitary operators , 2005, quant-ph/0503243.

[36]  Ben Reichardt,et al.  Fault-Tolerant Quantum Computation , 2016, Encyclopedia of Algorithms.

[37]  V. Paulsen.  Completely Bounded Maps and Operator Algebras: Completely Bounded Multilinear Maps and the Haagerup Tensor Norm , 2003 .

[38]  M. Mohseni,et al.  Direct characterization of quantum dynamics. , 2006, Physical review letters.

[39]  S. Lloyd,et al.  Quantum-Enhanced Measurements: Beating the Standard Quantum Limit , 2004, Science.

[40]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[41]  Jens Eisert,et al.  Tomography of quantum detectors , 2009 .

[42]  Salman Beigi,et al.  Simplified instantaneous non-local quantum computation with applications to position-based cryptography , 2011, 1101.1065.

[43]  M. Devoret,et al.  Quantum coherence with a single Cooper pair , 1998 .

[44]  Raymond Laflamme,et al.  Practical experimental certification of computational quantum gates using a twirling procedure. , 2011, Physical review letters.

[45]  Robin Blume-Kohout,et al.  Gate fidelity fluctuations and quantum process invariants , 2009, 0910.1315.

[46]  D. DiVincenzo,et al.  Quantum computation with quantum dots , 1997, cond-mat/9701055.

[47]  Raymond Laflamme,et al.  Symmetrized Characterization of Noisy Quantum Processes , 2007, Science.