The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically extracted from maximum-likelihood estimation. Recently, optimization strategies based on evolutionary and machine-learning techniques have been proposed. Here, we investigate a deep-learning approach that allows for fast and accurate reconstructions of space-dependent SU(2) operators, only processing a minimal set of measurements. We train a convolutional neural network based on a scalable U-Net architecture to process entire experimental images in parallel. Synthetic processes are reconstructed with average fidelity above 90%. The performance of our routine is experimentally validated on complex polarization transformations. Our approach further expands the toolbox of data-driven approaches to Quantum Process Tomography and shows promise in the real-time characterization of complex optical gates.
Characterizing the noise in the set of gate operations that form the building blocks of a quantum computational device is a necessity for assessing the quality of the device. Here, we introduce randomized linear gate set tomography, an easy-to-implement gate set tomography procedure that combines the idea of state-preparation-and-measurement-error-free characterization of standard gate set tomography with no-design randomized tomographic circuits and computational ease brought about by an appropriate linear approximation. We demonstrate the performance of our scheme through simulated examples …
We propose an efficient protocol to fully reconstruct a set of high-fidelity quantum gates. Usually, the efficiency of reconstructing high-fidelity quantum gates is limited by the sampling noise. Our protocol is based on a perturbative approach and has two stages. In the first stage, the initial part of noisy quantum gates is reconstructed by measuring traces of maps, and the trace can be measured by amplifying the noise in a way similar to randomised benchmarking and quantum spectral tomography. In the second stage, by amplifying the non-unital part using the unital part, we can efficiently r…
We introduce spectral quantum tomography, a simple method to extract the eigenvalues of a noisy few-qubit gate, represented by a trace-preserving superoperator, in a SPAM-resistant fashion, using low resources in terms of gate sequence length. The eigenvalues provide detailed gate information, supplementary to known gate-quality measures such as the gate fidelity, and can be used as a gate diagnostic tool. We apply our method to one- and two-qubit gates on two different superconducting systems available in the cloud, namely the QuTech Quantum Infinity and the IBM Quantum Experience. We discuss…
Flexible characterization techniques that identify and quantify experimental imperfections under realistic assumptions are crucial for the development of quantum computers. Gate set tomography is a characterization approach that simultaneously and self-consistently extracts a tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data. Obtaining such a detailed picture of the experimental implementation is associated with high requirements on the number of sequences and their design, making gate set tomog…
Quantum tomography is an important tool for the characterisation of quantum operations. In this paper, we present a framework of quantum tomography in fermionic systems. Compared with qubit systems, fermions obey the superselection rule, which sets constraints on states, processes and measurements in a fermionic system. As a result, we can only partly reconstruct an operation that acts on a subset of fermion modes, and the full reconstruction always requires at least one ancillary fermion mode in addition to the subset. We also report a protocol for the full reconstruction based on gates in Ma…
Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail. The most important feature of GST, compared to older state and process tomography protocols, is that it is calibration-free. GST does not rely on pre-calibrated state preparations and measurements. Instead, it characterizes all the operations in a ga…
Benchmarking and characterising quantum states and logic gates is essential in the development of devices for quantum computing. We introduce a Bayesian approach to self-consistent process tomography, called fast Bayesian tomography (FBT), and experimentally demonstrate its performance in characterising a two-qubit gate set on a silicon-based spin qubit device. FBT is built on an adaptive self-consistent linearisation that is robust to model approximation errors. Our method offers several advantages over other self-consistent tomographic methods. Most notably, FBT can leverage prior informatio…
Crosstalk is a leading source of failure in multiqubit quantum information processors. It can arise from a wide range of disparate physical phenomena, and can introduce subtle correlations in the errors experienced by a device. Several hardware characterization protocols are able to detect the presence of crosstalk, but few provide sufficient information to distinguish various crosstalk errors from one another. In this article we describe how gate set tomography, a protocol for detailed characterization of quantum operations, can be used to identify and characterize crosstalk errors in quantum…
Encoding quantum information in the photon temporal mode (TM) offers a robust platform for high-dimensional quantum protocols. The main practical challenge, however, is to design a device that operates on single photons in specific TMs and all coherent superpositions. The quantum pulse gate (QPG) is a mode-selective sum-frequency generation designed for this task. Here, we perform a full modal characterisation of a QPG using weak coherent states in well-defined TMs. We reconstruct a full set of measurement operators, which show an average fidelity of 0.85 to a theoretically ideal device when o…
In the current work we address the problem of quantum process tomography (QPT) in the case of imperfect preparation and measurement of the states which are used for QPT. The fuzzy measurements approach which helps us to efficiently take these imperfections into account is considered. However, to implement such a procedure one should have a detailed information about the errors. An approach for obtaining the partial information about them is proposed. It is based on the tomography of the ideal identity gate. This gate could be implemented by performing the measurement right after the initial st…
Time-bin qubits, where information is encoded in a single photon at different times, have been widely used in optical fiber and waveguide based quantum communications. With the recent developments in distributed quantum computation, it is logical to ask whether time-bin encoded qubits may be useful in that context. We have recently realized a time-bin qubit controlled-phase (C-Phase) gate using a 2 X 2 optical switch based on a lithium niobate waveguide, with which we demonstrated the generation of an entangled state. However, the experiment was performed with only a pair of input states, and …
The experimental implementation of selective quantum process tomography (SQPT) involves computing individual elements of the process matrix with the help of a special set of states called quantum 2-design states. However, the number of experimental settings required to prepare input states from quantum 2-design states to selectively and precisely compute a desired element of the process matrix is still high, and hence constructing the corresponding unitary operations in the lab is a daunting task. In order to reduce the experimental complexity, we mathematically reformulated the standard SQPT …
Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and measurement errors complicates the practical use of this procedure. In this work, we investigate the possibility of estimating these errors from experiment. These estimates are subsequently used to build a robust quantum tomography model. The model allows one to accurately reconstruct unitary errors of single-qubit gates. We show that, having such imperfect single-qu…
In circuit-based quantum computing, the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs of qubits. In certain physical architectures, however, some qubits may be 'hidden' and lacking direct addressability through dedicated control and readout lines, for instance because of limited on-chip routing capabilities, or because the number of control lines becomes a limiting factor for many-qubit systems. In this case, no single-qubit operations can be applied to the hidden qubits and their state cannot be measu…
Measurements that occur within the internal layers of a quantum circuit -- mid-circuit measurements -- are an important quantum computing primitive, most notably for quantum error correction. Mid-circuit measurements have both classical and quantum outputs, so they can be subject to error modes that do not exist for measurements that terminate quantum circuits. Here we show how to characterize mid-circuit measurements, modelled by quantum instruments, using a technique that we call quantum instrument linear gate set tomography (QILGST). We then apply this technique to characterize a dispersive…
The efficiency of Quantum Characterisation, Verification, and Validation (QCVV) protocols highly hinges on the agreement between the assumed noise model and the underlying error mechanisms. As a matter of fact, errors in Quantum Processing Units (QPUs) incorporate various aspects of context-dependability which are overlooked by the majority of the commonly used QCVV protocols. As QCVV protocols are indispensable when it comes to characterizing and evaluating quantum operations, there is a serious need for a detailed characterization taking into account such aspects. In this work, we address th…
We present a framework for quantum process tomography of two-ion interactions that leverages modulations of the trapping potential and composite pulses from a global laser beam to achieve individual-ion addressing. Tomographic analysis of identity and delay processes reveals dominant error contributions from laser decoherence and slow qubit frequency drift during the tomography experiment. We use this framework on two co-trapped $^{40}$Ca$^+$ ions to analyze both an optimized and an overpowered Mølmer-Sørensen gate and to compare the results of this analysis to a less informative Bell-state to…
Quantum process tomography has become increasingly critical as the need grows for robust verification and validation of candidate quantum processors. Here, we present an approach for efficient quantum process tomography that uses a physically motivated ansatz for an unknown quantum process. Our ansatz bootstraps to an effective description for an unknown process on a multi-qubit processor from pairwise two-qubit tomographic data. Further, our approach can inherit insensitivity to system preparation and measurement error from the two-qubit tomography scheme. We benchmark our approach using nume…
We have implemented a Walsh-Hadamard gate, which performs a quantum Fourier transform, in a superconducting qutrit. The qutrit is encoded in the lowest three energy levels of a capacitively shunted flux device, operated at the optimal flux-symmetry point. We use an efficient decomposition of the Walsh-Hadamard gate into two unitaries, generated by off-diagonal and diagonal Hamiltonians respectively. The gate implementation utilizes simultaneous driving of all three transitions between the three pairs of energy levels of the qutrit, one of which is implemented with a two-photon process. The gat…
