Session F50: Advanced Randomized Benchmarking and Gate Calibration

Scalable randomized benchmarking with mid-circuit measurements

To date, there exists no efficient method for holistically assessing the performance of mid-circuit measurements (MCMs) performed in parallel with quantum gates, despite their importance to fault-tolerant schemes. We correct this by introducing the first randomized benchmarking (RB) protocol for benchmarking circuit layers with MCMs. Our scalable protocol modifies binary randomized benchmarking, a motion reversal-free RB protocol, to naturally benchmark mixed layers of Clifford gates and MCMs. In our talk, we will provide a detailed overview of the protocol before arguing that our protocol measures an average error rate of mixed circuit layers of Clifford gates and MCMs.   

Scalable Randomized Benchmarking with Mid-Circuit Measurements, Part 2

Mid-circuit measurements (MCMs) are a key primitive for quantum error correction, but there are currently no scalable benchmarking protocols that holistically assess the performance of gates and mid-circuit measurements. Here, we introduce a fully scalable randomized benchmarking (RB) protocol for Clifford gates and mid-circuit measurements. Our protocol is an adaptation of binary RB, a streamlined RB protocol that does not use motion reversal circuits, enabling inclusion of MCMs.

In this talk, we demonstrate how to use our protocol to reliably measure gate and MCM performance. We present the results of running our protocol on current quantum processors and show how to use these results to extract details of MCM performance. Furthermore, we discuss how our protocol can be adapted to assess mid-circuit measurement structures that are commonly used in quantum error correction, such as parity measurements.    

A Simple Statistical Model for Randomized Benchmarking Data

Randomized Benchmarking (RB) techniques are often used to probe the capabilities of quantum processors. RB consists of running random circuits with varied circuit depths; the mathematical theory underpinning RB shows that the mean success probability of RB circuits decay exponentially in the depth of the circuit. However, RB theory makes no claims about the distribution of success probabilities for RB circuits at a given depth. This makes statistically rigorous analysis of RB data difficult; as a result, RB data is typically analyzed with ad hoc curve-fitting. In our work, we solve this problem with a simple statistical model for RB data. We model RB success probabilities with a Beta distribution with mean that decays exponentially in circuit depth and variance that is modelled by a few-parameter ansatz function. This few-parameter statistical model enables maximum likelihood estimation (MLE) of RB error rates with rigorous confidence intervals. Our analysis is easily adaptable to a plethora of RB techniques—including standard/Clifford-group RB, direct RB, binary RB, and (a slight adaptation of) mirror RB Consequently, we demonstrate how it can enable ‘super-efficient’ RB of many-qubit processors.

 

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.   

IN-Situ Pulse Envelope Characterization Technique (INSPECT)

Precise characterization of control pulses is essential to building reliable quantum computers. We use qubits as probes to measure distortions in microwave pulses in the Fourier domain. This allows us to identify and characterize several mechanisms for pulse reflection without using a prescribed model. We also show that the distorted pulses can be deconvolved with one percent precision. Our method can also be used to characterize timing differences between different pulses with 10ps precision. Finally, we show that the pulse shapes for crosstalk are significantly distorted and delayed.   

Automated Calibration of Two-Qubit Gates with Robust Phase Estimation

Robust phase estimation (RPE) is a technique for rapidly learning the rotation angle (or phase) of a quantum gate, in a way that is Heisenberg-limited in accuracy, robust against moderate decoherence effects, and requires only a few tens of circuits. While RPE has heretofore been used for high-accuracy single-qubit gate characterization, we show how RPE may be used to learn all phases present in a two-qubit entangling gate. We use two-qubit RPE as the core of a closed-loop calibration routine for minimizing the coherent errors on a controlled-Z gate on a superconducting transmon qubit platform. With this automated calibration routine we are able to achieve a controlled-Z over-rotation error at about 10^-3 radians on the Advanced Quantum Testbed superconducting transmon platform.   

Experimental characterization of error budgeting of parametric resonance gate with tunable coupler

We study the experimental error budget of parametric resonance gates with a floating tunable coupler. We characterized different error sources including, incoherent, leakage, amplitude, and phase errors by varying the two-qubit gate time.  We measured the coherence times of qubits under gate operating conditions, and benchmarked leakage using leakage randomized benchmarking. We show that incoherent errors are the limiting factors to the two-qubit gate fidelity for gates longer than 100 ns, predominantly due to 1/f flux noise. As we decrease the two-qubit gate time, leakage to non computational states start to contribute to the limitation of the fidelity.    

Mid-circuit Measurements for Superconducting Qubits

There is a growing need for mid-circuit measurements (MCMs) in quantum computing. MCMs are crucial for performing syndrome extraction in quantum error correction, and --- along with feed-forward operations conditioned on the result of the measurement --- can be used to efficiently prepare entangled states in adaptive circuits. However, performing MCMs and feed-forward operations are difficult for superconducting systems due to the classical hardware requirements imposed by the fast gate times of superconducting qubits. In this talk, we will outline the state of MCMs for superconducting processors, discuss the difficulties in implementing feed-forward operations, and demonstrate ways in which MCMs can be improved. We will also provide examples of the various quantum applications that can benefit from MCMs and feed-forward operations.   

Quantum non-Markovian noise effects in randomized benchmarking

In non-Markovian systems, the current state of the system depends on the full or partial history of its past evolution. Non-Markovian noise violates common assumptions in gate characterization protocols such as randomized benchmarking and gate-set tomography.  Here, we perform a case study of the effects of a quantum non-Markovian bath on single-qubit randomized benchmarking experiments. We consider a model consisting of a qubit coupled to a multimode Bosonic bath.  We apply unitary operations on the qubit, interspersed with interactions with the environment.  Allowing for non-Markovianity in the interactions leads to clear differences in the randomized benchmarking decay curves in this model, which we analyze in detail.   

Quantum Noise Spectroscopy via Randomized Benchmarking

Characterizing noise in quantum systems is a crucial aspect of diagnosing errors, designing targeted error protection protocols, and achieving reliable quantum computation. Two powerful methods for characterizing different aspects of quantum systems and operations are: Randomized Benchmarking (RB) and Quantum Noise Spectroscopy (QNS).

RB is a well-established technique used to spot errors in quantum operations that result from the noise. On the other hand, QNS focuses on characterizing time-correlated noise, providing unique insights into the noise encountered by quantum systems.

Here, we investigate the complementary strengths of RB and QNS and explore approaches for combining these methods to exploit their collective power. Specifically, we leverage the filter function formalism and the fluctuations in RB due to time-correlated noise to perform parametric estimation of the power spectral density.

Our analysis covers a wide range of noise spectra and compares the effectiveness of this combined approach to canonical QNS protocols.   

Characterizing two-qubit gates with dynamical decoupling

Precision quantum estimation in the presence of noise remains a serious practical challenge for calibrating state-of-the-art quantum processors. Noise processes, such as flux noise in superconducting qubits, introduce fluctuations that obscure the true values of system parameters and hinder coherent amplification. We demonstrate a novel characterization technique that enables precise estimation of select unitary parameters for two-qubit gates by applying dynamical decoupling to suppress low-frequency noise. Our method exhibits order-of-magnitude improvements in parameter precision, is efficient in the number of experiments required, adapts to a variety of target two-qubit gates, and is robust to implementation imperfections.   

Partial characterization of quantum gates using character eigenvalue estimation

In experimental quantum systems, an accurate understanding of underlying noise processes is pivotal for implementing targeted calibration strategies. One common approach for characterizing errors is quantum phase estimation; however, existing schemes for phase estimation are not entirely robust to state prep errors and are limited to characterizing specific types of noise, i.e coherent errors. To overcome these limitations, we introduce a technique that harnesses tools from representation theory to robustly and precisely estimate parameters of general Markovian noise processes, which call character eigenvalue estimation (CEE). CEE uses linear combinations of circuit outcomes to isolate individual eigenvalues of a noisy gate, which can then be learned to high precision with a simple fitting routine. We validate our method's efficacy through simulations with error models encompassing both coherent and stochastic noise. We also discuss how to use CEE to perform gate set tomography without computationally intensive maximum-likelihood estimation, which offers a pathway towards robust and scalable partial tomography of quantum gate sets.   

The quantum algorithmic reach of a high-Q radio frequency cavity

While NISQ-era quantum computers based on superconducting technology are generally comprised of 2D qubits, high quality 3D resonator cavities coupled to a smaller number of qubits offer potential advantages such as: efficient error correction protocols, better connectivity, and potential quantum memory. To understand such systems' algorithmic capabilities and benchmark their performance both over time and against other platforms, it is important to consider a number of metrics and adapt existing ones as needed. Here, we study a realistic superconducting cavity coupled to a single noisy transmon. Generating Haar random circuits, compiling them into selective number-dependent arbitrary phase (SNAP) and displacement pulses followed by simulating the pulse-level dynamics allow us to extract a "qudit" analog of quantum volume, the cross-entropy benchmark of the cavity, as well as the KL-divergence from the ideal Haar distribution to the real one. We discuss how these metrics depend on dominant noise sources and comment on both the limitations they place on 3D systems as well as potential advantages.