We present a benchmarking protocol for universal quantum computers, achieved through the simulation of random dynamical quantum maps. This protocol provides a holistic assessment of system-wide error rates, encapsulating both gate inaccuracies and the errors associated with mid-circuit qubit measurements and resets. By employing random quantum circuits and segmenting mid-circuit qubit measurement and reset in a repeated fashion, we steer the system of qubits to an ensemble of steady-states. These steady-states are described by random Wishart matrices, and align with the steady-state characteristics previously identified in random Lindbladian dynamics, including the universality property. The protocol assesses the resulting ensemble probability distribution measured in the computational basis, effectively avoiding a tomographic reconstruction. Our various numerical simulations demonstrate the relationship between the final distribution and different error sources. Additionally, we implement the protocol on state-of-the-art transmon qubits provided by IBM Quantum, drawing comparisons between empirical results, theoretical expectations, and simulations derived from a fitted noise model of the device.
We present a benchmarking protocol for universal quantum computers, achieved through the simulation of random dynamical quantum maps. This protocol provides a holistic assessment of system-wide error rates, encapsulating both gate inaccuracies and the errors associated with mid-circuit qubit measurements and resets. By employing random quantum circuits and segmenting mid-circuit qubit measurement and reset in a repeated fashion, we steer the system of qubits to an ensemble of steady-states. These steady-states are described by random Wishart matrices, and align with the steady-state characteristics previously identified in random Lindbladian dynamics, including the universality property. The protocol assesses the resulting ensemble probability distribution measured in the computational basis, effectively avoiding a tomographic reconstruction. Our various numerical simulations demonstrate the relationship between the final distribution and different error sources. Additionally, we implement the protocol on state-of-the-art transmon qubits provided by IBM Quantum, drawing comparisons between empirical results, theoretical expectations, and simulations derived from a fitted noise model of the device.
High-fidelity mid-circuit measurements, which read out the state of specific qubits in a multiqubit processor without destroying them or disrupting their neighbors, are a critical component for useful quantum computing. They enable fault-tolerant quantum error correction, dynamic circuits, and other paths to solving classically intractable problems. But there are few methods to assess their performance comprehensively. In this work, we address this gap by introducing the first randomized benchmarking protocol that measures the rate at which mid-circuit measurements induce errors in many-qubit circuits. Using this protocol, we detect and eliminate previously undetected measurement-induced crosstalk in a 20-qubit trapped-ion quantum computer. Then, we use the same protocol to measure the rate of measurement-induced crosstalk error on a 27-qubit IBM Q processor, and quantify how much of that error is eliminated by dynamical decoupling. Characterisation of quantum operations is fundamental in quantum technologies - quantum computing in particular - but there’s currently no reliably efficient method to assess mid-circuit measurements, which are a key component for subfields like quantum error correction. Here, the authors fill this gap, integrating MCMs into the framework of randomized benchmarking.
Abstract Mid-circuit measurements are a key component in many quantum information computing protocols, including quantum error correction, fault-tolerant logical operations, and measurement based quantum computing. As such, techniques to quickly and efficiently characterize or benchmark their performance are of great interest. Beyond the measured qubit, it is also relevant to determine what, if any, impact mid-circuit measurement has on adjacent, unmeasured, spectator qubits. Here, we present a mid-circuit measurement benchmarking suite developed from the ubiquitous paradigm of randomized benchmarking. We show how our benchmarking suite can be used to both detect as well as quantify errors on both measured and spectator qubits, including measurement-induced errors on spectator qubits and entangling errors between measured and spectator qubits. We demonstrate the scalability of our suite by simultaneously characterizing mid-circuit measurement on multiple qubits from an IBM Quantum Falcon device, and support our experimental results with numerical simulations. Further, using a mid-circuit measurement tomography protocol we establish the nature of the errors identified by our benchmarking suite.
Randomized benchmarking (RB) protocols are the most widely used methods for assessing the performance of quantum gates.However, the existing RB methods either do not scale to many qubits or cannot benchmark a universal gate set.Here, we introduce and demonstrate a technique for scalable RB of many universal and continuously parametrized gate sets, using a class of circuits called randomized mirror circuits.Our technique can be applied to a gate set containing an entangling Clifford gate and the set of arbitrary single-qubit gates, as well as gate sets containing controlled rotations about the Pauli axes.We use our technique to benchmark universal gate sets on four qubits of the Advanced Quantum Testbed, including a gate set containing a controlled-S gate and its inverse, and we investigate how the observed error rate is impacted by the inclusion of non-Clifford gates.Finally, we demonstrate that our technique scales to many qubits with experiments on a 27-qubit IBM Q processor.We use our technique to quantify the impact of crosstalk on this 27-qubit device, and we find that it contributes approximately 2=3 of the total error per gate in random many-qubit circuit layers.
Randomised benchmarking is a widely used experimental technique to characterise the average error of quantum operations. Benchmarking procedures that scale to enable the characterisation of n-qubit circuits rely on efficient procedures for manipulating those circuits and, as such, have been limited to subgroups of the Clifford group. However, universal quantum computers require additional, non-Clifford gates to approximate arbitrary unitary transformations. We define a scalable randomised benchmarking procedure over n-qubit unitary matrices that correspond to protected non-Clifford gates for a class of stabiliser codes. We present efficient methods for representing and composing group elements, sampling them uniformly and synthesising corresponding poly(n)-sized circuits. The procedure provides experimental access to two independent parameters that together characterise the average gate fidelity of a group element. A scalable procedure to determine the error of quantum operations has been developed by researchers in the United States. Andrew Cross and colleagues at the IBM T.J. Watson Research Center have expanded previously used protocols to a broader range of quantum circuits, thereby enabling error benchmarking for all common logical operations used in leading quantum computing protocols. The standard technique for error characterization in these devices is randomized benchmarking, which provides benefits such as insensitivity to measurement errors, but on the other hand only functions in a limited number of circumstances. In their theoretical study, the researchers demonstrate how randomized benchmarking approaches can be expanded to a much broader range of logical operations. The procedure can be readily implemented experimentally, and provides access to important experimental noise parameters in quantum computing.
Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But, scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on one, two, and three qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the n-qubit Clifford gates at its core have to be compiled into large circuits over the one- and two-qubit gates native to a device. As n grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low n. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on two to five qubits using the publicly available ibmqx5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But, it can be extended to processors with more qubits-we present simulations on 10+ qubits-and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. We show how to use this flexibility to measure separate error rates for distinct sets of gates, and we use this method to estimate the average error rate of a set of cnot gates.
Dynamic circuit operations (measurements with feedforward) are important components for future quantum computing efforts, but lag behind gates in the availability of characterization methods. Here we introduce a series of dynamic circuit benchmarking routines based on interleaving dynamic circuit operation blocks F in one-qubit randomized benchmarking sequences of data qubits. F spans between the set of data qubits and a measurement qubit and may include feedforward operations based on the measurement. We identify six candidate operation blocks, such as preparing the measured qubit in $|0\ensuremath{\rangle}$ and performing a Z-Pauli on the data qubit conditioned on a measurement of ``1''. Importantly, these blocks provide a methodology to accumulate readout assignment errors in a long circuit sequence. We also show the importance of dynamical decoupling in reducing ZZ crosstalk and measurement-induced phase errors during dynamic circuit blocks. When measured on an IBM Eagle device with appropriate dynamical decoupling, the results are consistent with measurement assignment error and the decoherence of the data qubit as the leading error sources.