Session F51: Quantum Error Mitigation in the Near-term

Evidence for the utility of quantum computing before fault tolerance

Quantum computers can offer dramatic speed-ups over their classical counterparts for certain problems. However, noise remains the biggest impediment to realizing the full potential of quantum computing. While the theory of quantum error correction offers a solution to this challenge, a large scale realization of fault tolerance seems currently inaccessible. What can one hope to do then, with existing noisy processors? In this talk, I will present experiments that produce reliable expectation values from noisy 100+ qubit processors, at a scale that is well beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. I will also discuss recent classical benchmarking of our experiments beyond exact verification.    

Improved error mitigation protocol by restricted evolution

To perform any meaningful computation using NISQ processors, error mitigation protocols need to be deployed in the quantum circuits. Here, we propose a constant runtime error mitigation protocol. Further, we propose a hybrid error mitigation protocol by combining our methods with the probabilistic error cancellation to improve the bias and the sampling overhead in estimating the expectation value of an observable. We showed that the sampling overhead and the bias of our protocol depend on a measure called generalized robustness and we also found bounds on this measure under general noise scenario.   

Unification and Improvement of Quantum Error Mitigation Methods by Generalized Quantum Subspace Expansion

Numerous quantum error mitigation methods are proposed to make the most of noisy quantum devices that lack the capability of quantum error correction. Probabilistic error cancellation (PEC) and symmetry verification are representative quantum error mitigation methods. PEC can effectively mitigate well-characterized noise by inverting the noise virtually. However, if the characterization or modeling of noise is inaccurate, PEC may mitigate the bias to a limited extent or even increase it. Furthermore, although the symmetry verification mitigates detectable errors, the method is by construction vulnerable to undetectable errors. In this study, we show that generalized quantum subspace expansion (GSE) enables us to apply the PEC without the need for an accurate characterization or modeling of noise and mitigates the bias of the undetectable errors for the symmetry verification. As a demonstration of these techniques, we numerically estimate the ground energy of the transverse-field Ising model. We believe that our proposed methods and results offer practical insights for implementing the existing quantum error mitigation methods.   

Inverted-circuit zero-noise extrapolation for quantum gate error mitigation

Current quantum computing hardware suffers from errors due to environmental effects, nearest neighbour interactions and imperfect gate operations. Techniques such as zero-noise extrapolation (ZNE) mitigate errors rather than eliminate them, and can be used with current hardware. For the ZNE, it is essential to know the exact noise gain factor so that an effective extrapolation can be performed. We propose a method for estimating the error strength occurring in a given quantum circuit in order to improve the results of zero-noise extrapolation. The circuit error rate is increased by inserting a sequence of gates that are equivalent to the identity in the noise-free case. Furthermore, the impact of gate errors on expectation values of observables can be reduced by twirling, which converts arbitrary errors into stochastic Pauli errors. The use of adaptive spacing and a maximum for the noise scaling factors appears to be advantageous for zero-noise extrapolation. We present results of the inverted-circuit error mitigation technique and compare them to results of the conventional zero-noise extrapolation.   

Uniformly Decaying Subspaces for Quantum Computation

We show that uniformly decaying subspaces can be created in a system of qubits undergoing strong relaxation with different decay rates and can be used to perform analog quantum computation. All expectation values of the dynamics encoded in such a subspace can be re-scaled by a common factor to obtain the dissipationless counterpart upto a small error which depends on the inhomogeneity of the decay rates. We provide a method that ensures that the dynamics can be simulated for times up to the inverse square root of the largest deviation of any decay rate from the mean. The cost of the error-mitigation is paid by taking exponentially more shots in time, and the error can be made arbitrarily small and time arbitrarily long by choosing the operating frequencies of qubits to align their decay rate with that of the fastest decaying qubit.    

Error Mitigation for Analog Simulators

Analog quantum simulators have shown impressive results in regimes that are challenging to simulate with classical computational methods. However, the influence of noise hampers their use as precision simulators. Recently, digital computation in noisy systems has made extensive use of error mitigation strategies to recover quasi-exact results. Such techniques have not largely been adapted to analog quantum simulators. In this work, we target the dominant noise sources in analog simulation platforms by extending methods from digital computation to work within the restrictions of analog quantum simulators. We explore the feasibility of these methods in mitigating characteristic sources of noise for trapped ion and neutral atom devices.   

Error Mitigation for IBM Quantum Devices via Online Testing and Post-selection

Online testing is essential to verify the functionality of a classical chip during operation. 

Online testing detects disruptive errors in real-time while leaving non-disruptive errors undetected.

Therefore, real-time quantum error detection via online testing is promising.

By assuming the occurrence of error is related to initialization, we execute a single shot online test before the original quantum circuit.

We aim to distinguish faulty and fault-free circuits with a high confidence level in a single shot.

To verify our assumption, we execute the online test twice in a single shot and analyze the consequent failure rate. 

We demonstrate the effectiveness of this idea by executing quantum characterization, calibration, and verification experiments with our error mitigation technique. 

The standard randomized benchmarking results show that our method significantly improved the two-qubit Error Per Clifford (EPC).   

A graph-based embedding of dynamical decoupling for quantum computing

Dynamical decoupling (DD) is a key error suppression technique for quantum computing. Ideally, DD suppresses both single-qubit phase errors and unwanted crosstalk between coupled qubits during idle delays. The precise timing of the DD gates or pulses affects the efficiency of error-suppression and ultimately the circuit fidelity. Here, we present an automated and efficient method for determining an embedding of DD to suppress phase and cross talk errors for an arbitrary input circuit. Our method relies on representing the DD embedding task as a graph, and using the structure and properties of the graph to determine an order in which each idle delay should be addressed. This ordering allows optimal DD embeddings to be found analytically (without using numerical optimization). Our procedure finds a tailored DD scheme that refocuses all quasi-static ZI and ZZ error terms, up to minor unavoidable rounding errors due to device timing constraints. Moreover, the protocol uses a small number of gates compared to alternative techniques. Our method provides a clear boost to overall empirical algorithmic success probability compared to other DD embedding schemes. We present the DD embedding algorithm as well as side-by-side empirical tests with other known DD embedding schemes.   

Scheduling Protocols for Context Aware Dynamical Decoupling

Effectively suppressing decoherence remains an ongoing problem in the control of quantum systems. An approach called Dynamical Decoupling (DD) has been shown to be effective in reducing error caused by a quantum system becoming increasingly entangled with its environment as it evolves. A specific type of error caused by crosstalk between qubits, parasitic ZZ-coupling, is a major problem affecting the usability of superconducting quantum systems [1, 2]. We introduce an adaptive DD approach based on various methods developed to address parasitic ZZ-coupling as well as more general environment induced decoherence. Our methods work by scheduling neighbor-aware DD sequences according to pulse and timing criteria across idling periods such that crosstalk cannot accumulate beyond a certain measure. One such method uses graph coloring to ensure that DD sequences are staggered in a way that mitigates crosstalk. Another method dynamically determines how to space sequences given pulse information and the device's timing constraints. Our approach was motivated by and validated using experiments on IBM hardware.

[1] Suppression of Crosstalk in Superconducting Qubits Using Dynamical Decoupling. Tripathi et al. Phys. Rev. Applied 18, 024068. 25 August 2022. 

[2] Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit. Mundada et al. Phys. Rev. Applied 12, 054023. 11 November 2019.   

Empirical optimization of dynamical decoupling on quantum processors

Dynamical decoupling (DD) is an effective way to suppress quantum computation errors with a low resource overhead. Here, we employ a combinatorial optimization scheme to empirically discover device-tailored DD sequences. We test our method on various quantum algorithms and show that our empirically optimized DD sequences significantly outperform theoretically-derived DD sequences.   

Detection of thermal noise dynamics in quantum computer interconnects

We report a systematic study of thermal noise in five typical qubit drive lines in a dilution refrigerator. The measurements were recorded using an in situ hot electron microwave nanobolometer with a designed-50- Ω absorber [1] that is coupled to a coaxial input. We demonstrate new methodology of calibrating power with a temperature variable noise source spanning the range 0.1 K –0.5 K [2]. In steady state, we measure radiation temperatures of 50 mK – 70 mK without heating and up to 200 mK with tens of nanowatts of applied rf power. Subsequent lock-in measurements exhibit thermal latencies of 3 ms -- 30 ms crucially revealing thermal heat capacities in the nJ/K range. Our measurement results are essential for understanding and suppressing qubit dephasing due to photon shot noise [3] and the methodology is directly applicable in studies of future interconnects for quantum computers.

 

[1] Phys. Rev. Lett. 117, 030802 (2016)

[2] Review of Scientific Instruments 92, 034708 (2021)

[3] Phys. Rev. A 106, 042605 (2022)   

Fast Universal Robust Quantum Gates against Various Noises

Reducing coherent noises in large-scale quantum processors is a critical step to further advance quantum information processing. The spatiotemporal correlations of the noise, which are relatively insignificant in isolated qubits or shallow circuits, pose a great challenge for quantum error correction (QEC) and potential applications in the noisy intermediate-scale quantum (NISQ) era. In this work, we report on experimental studies of robust quantum gates using superconducting qubits, based on a recent geometric framework for analyzing and mitigating generic errors. We demonstrate robust single-qubit quantum gates that withstand a broad spectrum of (quasi-)static noise, a common source of temporal-correlated errors in various platforms, and observe a significant reduction of coherent noise in randomized benchmarking. The applications of robust gates against non-static noise and the implementation of specific robust two-qubit gates are also discussed. Our work offers a versatile robust control toolbox to enable noise-resilient quantum circuits and benefit both QEC and NISQ applications.   

Statistical properties of environmental and intrinsic decoherence

In addition to providing a versatile platform for quantum information and quantum optics applications, the utilization of superconducting qubits as quantum sensors has emerged as an active area of research (see Refs. 1--3 among others). Superconducting qubits are sensitive to both intrinsic and environmental [4] perturbations that induce dephasing and relaxation. In this talk we present experimental data on time-dependent fluctuations of the properties of multiple transmon qubits spanning up to several days. We analyze histograms and Allan plots of energy relaxation time, coherence time, and frequency jumps. The method enables direct tests of specific noise hypotheses [5,6]. The aims of our study are to: 1) define the minimum required sampling time to accurately capture system performance and, 2) separate decoherence mechanisms intrinsic to the circuit versus environmental factors. For the latter we implement added thermal noise within the dilution refrigerator measurement system as a diagnostic resource [7].

[1] K. Serniak, et al. Phys. Rev. Applied 12, 014052 (2019)

[2] S. Schlör et al. Phys. Rev. Lett. 123, 190502 (2019)

[3]  R.T. Gordon, et al. Appl. Phys. Lett. 120, 074002 (2022)

[4] Vepsäläinen, et al. Nature 584, 551–556 (2020)

[5] Burnett, J.J. et al. npj Quantum Inf. 5, 54 (2019).

[6] K. Li, et al. IEEE Trans. Appl. Supercond., 33, 1, (2023)

[7] S. Simbierowicz, et al. Rev. Sci. Instrum.  92 (3): 034708 (2021)