Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session F73: Error Mitigation Theory and ExtensionsFocus
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Sponsoring Units: DQI Chair: Andrew Eddins, IBM Quantum Room: Room 405 |
Tuesday, March 7, 2023 8:00AM - 8:12AM |
F73.00001: Exponentially tighter bounds on quantum error mitigation Sumeet Khatri, Yihui Quek, Johannes J Meyer, Daniel S França, Jens Eisert Quantum error mitigation has been proposed as a means to combat both unwanted and unavoidable errors in near term quantum computing by classically post-processing outcomes of multiple quantum circuits. It does so in a fashion that requires no or few additional quantum resources, in contrast to fault-tolerant schemes that come along with heavy overheads. Error mitigation leads to noise reduction in small schemes of quantum computation. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively 'undone' for larger system sizes. We start out by presenting a formal framework that rigorously encapsulates large classes of meaningful and practically applied schemes for quantum error mitigation, including virtual distillation, Clifford data regression, zero-noise extrapolation and probabilistic error cancellation. Technically, we construct families of random circuits that are highly sensitive to noise, in the sense that even at log(log(n)) depth, a whisker beyond constant, quantum noise is seen to super-exponentially rapidly scramble their output into the maximally-mixed state. Our results exponentially tighten arguments that have been used in the literature for error mitigation, but they go beyond that: Our results also tighten distinguishability arguments used in kernel estimation for quantum machine learning, and the depth at which barren plateaus emerge or quantum advantage is lost for sampling from noisy random quantum circuits, implying that the scrambling due to noise kicks in at exponentially smaller depths than originally thought. Finally, our results also say that a noisy device must be applied exponentially-many times (in the number of gates in the light-cone of the observable) to estimate an expectation value of an observable. There are classical algorithms that exhibit the same scaling in complexity. While improvements in quantum hardware will push noise levels down, if error mitigation is used, ultimately this can only lead to an exponential time algorithm with a better exponent when compared with classical algorithms, putting paid to the hope of exponential quantum speedups in this setting. |
Tuesday, March 7, 2023 8:12AM - 8:24AM |
F73.00002: Dynamical uncertainty propagation with noisy quantum parameters Felix Motzoi, Carrie Weidner, Mogens Dalgaard Many quantum technologies rely on high-precision dynamics, which |
Tuesday, March 7, 2023 8:24AM - 8:36AM |
F73.00003: Error Mitigation Thresholds in Random Circuits Michael J Gullans, Sarang Gopalakrishnan, Pradeep Niroula Noise in quantum devices can be corrected with quantum error correction or it can be mitigated via classical post-processing. The latter can be done without overhead in the spacetime volume of the circuit, but eventually incurs exponential overhead in sampling complexity. Such error mitigation techniques require accurate noise tomography and one might wonder if they are robust to imperfections in the learned noise model. We show that noisy random quantum circuit models with imperfectly characterized noise can exhibit a disorder-driven error mitigation threshold at a finite rate of disorder. Based on Imry-Ma arguments, we conjecture that this transition is in the same universality class as the classical random field Ising model in D+1 dimension for D>1 spatial dimensions of the qubits. Our results are based on a replica analysis of statistical mechanics models for random circuits, as well as numerical simulations of error mitigated random quantum circuits. We discuss the implications for quantum algorithms in near-term devices. |
Tuesday, March 7, 2023 8:36AM - 8:48AM |
F73.00004: Quancorde: Boosting Quantum Fidelity with an Ordered Diverse Ensemble of Clifford Canary Circuits Gokul Subramanian Ravi, Jonathan M Baker, Kaitlin N Smith, Nathan Earnest, Ali Javadi-Abhari, Frederic T Chong On today's noisy quantum devices, execution fidelity tends to collapse dramatically for most applications beyond a handful of qubits. This paper aims to boost quantum fidelity with Clifford canary circuits, by proposing Quancorde: Quantum Canary Ordered Diverse Ensembles, a fundamentally new approach to identifying the correct outcomes of extremely low-fidelity quantum applications. It is based on the key idea of diversity in quantum devices - variations in noise sources, make each (portion of a) device unique, and therefore, their impact on an application's fidelity, also unique. |
Tuesday, March 7, 2023 8:48AM - 9:00AM |
F73.00005: Logical Error Rates for the Variational Quantum Eigensolver using a [[4,2,2]] Encoded Ansatz Meenambika Gowrishankar, Daniel Claudino, Alex McCaskey, Jerimiah Wright, Travis S Humble Application benchmarks that run on noisy intermediate scale quantum computing (NISQ) devices require techniques for detecting and mitigating errors to assess accuracy and performance. Quantum error detection codes offer a framework in which to encode these computations and track the presence of errors, but the subsequent logical error rate depends on the application circuit as well as the underlying hardware noise. Here we extend recent results using the [[4,2,2]] error detection code to improve the accuracy of computational chemistry calculations by calculating the logical error rate of an encoded variational ansatz. Within the context of the variational quantum eigensolver (VQE), we numerically simulate the mixed state generated by noisy execution of a UCC ansatz circuit for the case of the hydrogen molecule, accounting for variations in circuit parameters due to noise and the underlying noise models. Simulations of the unencoded, encoded, and post-selected states lead to estimates of logical error rate and probabilities for error-free calculations. For the case of one- and two-qubit depolarizing gate noise, we find that the error detection code reduces the logical infidelity by 4% relative to the unencoded physical rate when the noise parameter is <5%. This yields a corresponding decrease in the estimated energy by 6% (0.07 Ha). We also evaluate the change in the logical state fidelity with circuits modified to account for hardware connectivity constraints for comparison with simulations on hardware. |
Tuesday, March 7, 2023 9:00AM - 9:12AM |
F73.00006: Hypothesis Testing for Error Mitigation: How to Judge Error Mitigation Abdullah Ash Saki, Salonik Resch, George Umbrarescu, Archismita Dalal, Amara Katabarwa There is a plethora of error mitigation (EM) techniques available in the literature to combat errors in Noisy Intermediate-Scale Quantum (NISQ) machines. In an experiment one then uses a set of EM techniques to mitigate errors, which we refer to as an EM pipeline. Although EM pipelines successfully mitigate errors in theory, we observe in practice that for a modest number of qubits EM does not always improve results while moreover also incurring circuit and/or shots overhead. |
Tuesday, March 7, 2023 9:12AM - 9:48AM |
F73.00007: Exponential Error Suppression Techniques for Near-Term Quantum Devices Invited Speaker: Balint Koczor Suppressing noise in physical systems is of fundamental importance. As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level. However in the noisy, intermediate-scale quantum (NISQ) era, the complexity and scale required to adopt even the smallest QEC is prohibitive: a single logical qubit needs to be encoded into many thousands of physical qubits. Recent breakthroughs [Phys. Rev. X 11, 031057; Phys. Rev. X 11, 041036] have shown that for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms) one can indeed achieve an effective exponential suppression. The core idea of these techniques is to take multiple independently prepared circuit outputs to create a state whose symmetries prevent errors from contributing bias to the expected value. A number of recent works have built on these ideas and developed various theoretical generalisations as well as specific hardware architectures. For example, in a multicore approach multiple quantum processors perform the same noisy quantum computation whose outputs are used to `verify' each other using imperfect quantum links. In this talk I will review the basic principles of exponential error suppression techniques and also discuss the more recent developments. |
Tuesday, March 7, 2023 9:48AM - 10:00AM |
F73.00008: Universal framework for simultaneous tomography of quantum states and measurement noise. Sidhant Misra, Abhijith Jayakumar, Stefano Chessa, Marc Vuffray, Andrey Y Lokhov, Carleton Coffrin We present a general denoising algorithm for performing quantum tomography in the presence of detector noise. Our method is based on analyzing the properties of the linear operator space induced by unitary gate operations and given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge degree of freedom is unavoidable in the general case and show how to eliminate this degeneracy and fix the gauge for several interesting special cases including pure quantum states and block independent detector noise. Our framework can readily use prior information available about the system to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes many previous approaches to the problem and many of the methods in the literature that require an invertible noise matrix or specific probe states can be obtained as special cases. |
Tuesday, March 7, 2023 10:00AM - 10:12AM |
F73.00009: Post-selection-free preparation of high-quality physical qubits Ben Barber Preparation and measurement of qubits could become a dominant source of error as gate fidelities improve. Preparation can be improved using auxiliary qubits and post-selection, but post-selection greatly complicates the scheduling of processes like syndrome extraction. I will present a family of quantum circuits that prepare high-quality |0⟩ states without post-selection, instead using CNOT and Toffoli gates to non-linearly permute the computational basis. |
Tuesday, March 7, 2023 10:12AM - 10:24AM |
F73.00010: Quantum Error Mitigation by Pauli Check Sandwiching Alvin Gonzales, Ruslan Shaydulin, zain H Saleem, Martin Suchara We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one layer of the technique. We build on the results on extended flag gadgets and put it on a firm theoretical foundation. We prove that this technique can recover the noiseless state under the assumption of noise not affecting the checks. The method does not incur any encoding overhead and instead chooses the checks based on the input circuit. We provide an algorithm for obtaining such checks for an arbitrary target circuit. Since the method applies to any circuit and input state, it can be easily combined with other error mitigation techniques. We evaluate the performance of the proposed methods using extensive numerical simulations on 1,850 random input circuits composed of Clifford gates and non-Clifford single-qubit rotations, a class of circuits encompassing most commonly considered variational algorithm circuits. We observe average improvements in fidelity of 34 percentage points with six layers of checks. |
Tuesday, March 7, 2023 10:24AM - 10:36AM |
F73.00011: Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups Yusuke Hama, Hirofumi Nishi In this work, we develop our quantum-error-mitigation (QEM) scheme for quantum computational errors induced by quantum noise effects (decoherence effects) with using ensembles of quantum circuits called “quantum-noise-effect circuit groups”, which enable us to estimate the quantum computational errors. We discuss both theoretically and numerically the effectiveness of our QEM scheme and show that it has three advantages, (i) it can be performed with any type of quantum device, (ii) it can be applied to any type of quantum algorithm and any quantum noise effects with arbitrary strengths, (iii) the computational cost (practically) scales polynomial with respect to the product of the number of qubits and the depth of a quantum algorithm. |
Tuesday, March 7, 2023 10:36AM - 10:48AM |
F73.00012: Q-Trainer: A Software Package for Training Variational Quantum Algorithms with Quantum Error Mitigation Min Li, Haoxiang Wang The training of variational quantum algorithms (VQA) on modern quantum computers inevitably involves large noises, and quantum error mitigation (QEM) can be used to mitigate such noises. However, currently, it requires much domain knowledge (of both VQA and QEM) to apply QEM to VQA in practice, making QEM less accessible to beginners in quantum computing. Motivated by this, we developed Q-Trainer, a Python package with high-level API for VQA training with QEM. Our package is built on i) PennyLane, a quantum software platform with many VQA implementations, and ii) Mitiq, a software library of QEM methods. |
Tuesday, March 7, 2023 10:48AM - 11:00AM |
F73.00013: Keyldysh assisted evaluation of decoherence errors in driven qubits Ziwen Huang, Yunwei Lu, Alexander Romanenko, Anna Grassellino, Jens Koch, Shaojiang Zhu Decoherence errors have been a bottleneck in realizing high-fidelity qubit operations. Such errors are usually modeled using the Lindblad master equation. However, when correlated noise (both classical and quantum) is present and when the qubit is driven by a short pulse, the Lindblad master equation is not sufficiently accurate. To overcome this obstacle, we develop a more accurate estimation tool based on the Keldysh expansion. After suitable approximation, this yields a completely positive and trace preserving (CPTP) map of the qubit density matrix. We further show how this tool catches the influence of qubit driving in the presence of classical and quantum noise. This advanced technique can be integrated with gradient ascent pulse engineering, which can be used to mitigate decoherence errors during gate operations. |
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