Practical Characterization of Quantum Devices without Tomography

Abstract

Quantum tomography is the main method used to assess the quality of quantum information processing devices. However, the amount of resources needed for quantum tomography is exponential in the device size. Part of the problem is that tomography generates much more information than is usually sought. Taking a more targeted approach, we develop schemes that enable (i) estimating the fidelity of an experiment to a theoretical ideal description, (ii) learning which description within a reduced subset best matches the experimental data. Both these approaches yield a significant reduction in resources compared to tomography. In particular, we demonstrate that fidelity can be estimated from a number of simple experiments that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.

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“…In order to solve this self-certification problem, we would therefore like a procedure which makes a small number of measurements, can easily be implemented experimentally, and certifies that the state produced is approximately equal to |φ . This question has been considered by da Silva et al [155], and independently Flammia and Liu [69], who show that certain states |φ can be certified using significantly fewer copies of |φ than would be required for full tomography, and indeed that any state |φ can be certified using quadratically fewer copies (O(2 n ) rather than O(2 2n )). The measurements used are also simple: Pauli measurements.…”

Characterizing quantum gates via randomized benchmarking

“…One can estimate p directly using any of standard process tomography [15], ancilla-assisted/entanglement-assisted process tomography [48] or Monte-Carlo methods [23,24]. The tomography based schemes suffer from the unrealistic assumptions of negligible state-preparation and measurement errors, and clean ancillary states/operations.…”

“…A complete characterization of the noise is useful because it allows for the determination of good error-correction schemes, and thus the possibility of reliable transmission of quantum information. Since complete process tomography is infeasible for large systems, there is growing interest in scalable methods for partially characterizing the noise affecting a quantum system [17][18][19][20][21][22][23][24].…”

Process estimation in the presence of time-invariant memory effects

“…It is known to be a complex task, however, under certain assumptions it can be efficiently applied also to large systems [6][7][8][9][10][11] and even the accuracy can be assessed [12][13][14][15]. QPT deals with a scenario when an experimenter is given an unknown input-output black box E. In each run of the experiment he prepares some test state ̺ and performs a measurement M , thus, he choses the setting x = (̺, M ), and, records the outcome E k , where E k ∈ M .…”