Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies

López, Cecilia C.; Bendersky, Ariel; Paz, Juan Pablo; Cory, David G.

doi:10.1103/physreva.81.062113

Cited by 18 publications

(23 citation statements)

References 34 publications

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“…4. The probabilities p A can also be directly measured experimentally without complete process tomography: They are the diagonal elements of the χ matrix in the Pauli basis [16][17][18][19].…”

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confidence: 99%

“…consisting of the 4 n distinct tensor products of Pauli matrices I, X, Y , and Z. Twirling (1) over the Pauli basis (3) results in a new mapΛ that is diagonal in the Pauli basis [15][16][17][18][19]…”

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confidence: 99%

“…The process Λ does not need to be trace preserving. Twirling [15][16][17][18][19] a process Λ refers to the pre-multiplication of the input state by an operation A, running the original process Λ, and then post-multiplying by A −1 ; this procedure is then averaged over a set of K operations A = {A k } K k=1 . Denoting the twirled process byΛ, we havẽ…”

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Efficient error models for fault-tolerant architectures and the Pauli twirling approximation

Geller

Zhou

2013

Phys. Rev. A

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The design and optimization of realistic architectures for fault-tolerant quantum computation requires error models that are both reliable and amenable to large-scale classical simulation. Perhaps the simplest and most practical general-purpose method for constructing such an error model is to twirl a given completely positive channel over the Pauli basis, a procedure we refer to as the Pauli twirling approximation (PTA). In this work we test the accuracy of the PTA for a small stabilizer measurement circuit relevant to fault-tolerant quantum computation, in the presence of both intrinsic gate errors and decoherence, and find excellent agreement over a wide range of physical error rates. The combined simplicity and accuracy of the PTA, along with its direct connection to the χ matrix of process tomography, suggests that it be used as a standard reference point for more refined error model constructions. I. PAULI TWIRLING APPROXIMATIONThe principal obstacle to large-scale quantum computation is the introduction errors caused by decoherence, noise, leakage to non-computational states, incorrect implementation of quantum gates, qubit loss, and inaccurate state initialization and measurement. The standard approach for mitigating these errros is to use a faulttolerant error-correction protocol, which enables arbitrarily large computations as long as the strength of the errors are below a threshold value [1-5] and are not overly correlated in space or time [6][7][8][9][10]. The fault-tolerant error threshold is a measure of the robustness of a quantum computing platform and an estimate of its value is one of the most important tasks for practical quantum computer design.A straightforward approach for calculating logical error rates and associated error thresholds would be to do a full Hilbert space simulation of quantum codes of increasing size, in the presence of decoherence and other errors, but this approach quickly becomes intractable. This difficulty can be circumvented by using special error models that are efficient to simulate classically. The existence of a broad class of these efficient error models, which includes the Pauli and Clifford channels, is provided by the Gottesman-Knill theorem: This theorem states that any quantum circuit consisting only of Clifford-group unitaries and measurement in the Pauli basis can be simulated classically in polynomial time [11,12]. The circuits used to implement stabilizer-based error detection and correction-in the absence of any errors-are important examples. However, after including decoherence and intrinsic gate errors, which are required to assess fault-tolerance and calculate error thresholds, the simulations are no longer efficient. By intrinsic we mean an error, such as a unitary qubit rotation by the wrong angle, which does not result from noise or decoherence. The resulting inefficiency of classical simulation is the main motivation for the widely used stochastic approach of modeling nonideal stabilizer circuits by a sequence of one-and two-qubit operations, ea...

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Efficient error models for fault-tolerant architectures and the Pauli twirling approximation

Geller

Zhou

2013

Phys. Rev. A

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“…Despite the difficulty to fully and universally characterize a quantum process, two other methods, i.e., the partial (selective) characterization of quantum dynamics [7][8][9][10] and the simplified QPT by incorporating prior knowledge, 11,12 have recently been proposed to reduce the required resources. The former makes efficient estimation for the selected elements of the matrix χ , and the latter dramatically reduces the resources based on the prior knowledge of the process.…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of simplified quantum process tomography

Zheng

et al. 2013

The Journal of Chemical Physics

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The essential tool to characterize dynamics of an open quantum system is quantum process tomography (QPT). Although standard QPT methods are hard to be scalable, simplified QPT approach is available if we have the prior knowledge that the system Hamiltonian commutes with the system-environment interaction Hamiltonian. Using a nuclear magnetic resonance (NMR) quantum simulator, we experimentally simulate dephasing channels to demonstrate the simplified QPT as well as the standard QPT method as a comparison. The experimental results agree well with our predictions which confirm the validity and better efficiency of the simplified QPT.

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“…However, there are some quantum algorithms that allow to efficiently extract important information about a given quantum process [10][11][12][13][14][15][16]. These algorithms do not require performing QST on the final states but measuring quantities such as survival probabilities (or transition probabilities).…”

Section: Introductionmentioning

confidence: 99%

Selective and efficient quantum state tomography and its application to quantum process tomography

Bendersky

Paz

2013

Phys. Rev. A

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We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is written can be efficiently prepared in a controlled manner. Furthermore, we show how this algorithm is well suited for quantum process tomography, enabling to perform selective and efficient quantum process tomography.

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Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies

Cited by 18 publications

References 34 publications

Efficient error models for fault-tolerant architectures and the Pauli twirling approximation

Efficient error models for fault-tolerant architectures and the Pauli twirling approximation

Experimental demonstration of simplified quantum process tomography

Selective and efficient quantum state tomography and its application to quantum process tomography

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