Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm

Measurement noise is one of the main sources of errors in currently available quantum devices based on superconducting qubits. At the same time, the complexity of its characterization and mitigation often exhibits exponential scaling with the system size. In this work, we introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to some error for which we derive upper bounds. Characterization of the model is done efficiently using Diagonal Detector Overlapping Tomography – a generalization of the recently introduced Quantum Overlapping Tomography to the problem of reconstruction of readout noise with restricted locality. The procedure allows to characterize k-local measurement cross-talk on N-qubit device using O(k2klog(N)) circuits containing random combinations of X and identity gates. We perform experiments on 15 (23) qubits using IBM's (Rigetti's) devices to test both the noise model and the error-mitigation scheme, and obtain an average reduction of errors by a factor >22 (>5.5) compared to no mitigation. Interestingly, we find that correlations in the measurement noise do not correspond to the physical layout of the device. Furthermore, we study numerically the effects of readout noise on the performance of the Quantum Approximate Optimization Algorithm (QAOA). We observe in simulations that for numerous objective Hamiltonians, including random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of the optimization. Finally, we provide arguments why in the course of QAOA optimization the estimates of the local energy (or cost) terms often behave like uncorrelated variables, which greatly reduces sampling complexity of the energy estimation compared to the pessimistic error analysis. We also show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.

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Lower bounds on circuit depth of the quantum approximate optimization algorithm

Quantum Information Processing ◽

10.1007/s11128-021-03001-7 ◽

2021 ◽

Vol 20 (2) ◽

Author(s):

Rebekah Herrman ◽

James Ostrowski ◽

Travis S. Humble ◽

George Siopsis

Keyword(s):

Lower Bounds ◽

Optimization Algorithm ◽

Approximate Optimization ◽

Circuit Depth

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Classical symmetries and the Quantum Approximate Optimization Algorithm

Quantum Information Processing ◽

10.1007/s11128-021-03298-4 ◽

2021 ◽

Vol 20 (11) ◽

Author(s):

Ruslan Shaydulin ◽

Stuart Hadfield ◽

Tad Hogg ◽

Ilya Safro

Keyword(s):

Optimization Algorithm ◽

Approximate Optimization ◽

Classical Symmetries

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Online Parameter Identification of the Lithium-Ion Battery with Refined Instrumental Variable Estimation

Complexity ◽

10.1155/2020/8854618 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

An Wen ◽

Jinhao Meng ◽

Jichang Peng ◽

Lei Cai ◽

Qian Xiao

Keyword(s):

Instrumental Variable ◽

Equivalent Circuit Model ◽

Lithium Ion ◽

Parameters Estimation ◽

Measurement Noise ◽

Recursive Least Squares ◽

Ar Model ◽

Noise Model ◽

Li Ion Battery ◽

Li Ion

Refined Instrumental Variable (RIV) estimation is applied to online identify the parameters of the Equivalent Circuit Model (ECM) for Lithium-ion (Li-ion) battery in this paper, which enables accurate parameters estimation with the measurement noise. Since the traditional Recursive Least Squares (RLS) estimation is extremely sensitive to the noise, the parameters in the ECM may fail to converge to their true values under the measurement noise. The RIV estimation is implemented in a bootstrap form, which alternates between the estimation in the system model and the noise model. The Box-Jenkins model of the Li-ion battery transformed from the two RC ECM is selected as the transfer function model for the RIV estimation in this paper. The errors of the two RC ECM are independently generated by the residual of high-order Auto Regressive (AR) model estimation. With the benefit of a series of auxiliary models, the data filtering technology can prefilter the measurement and increase the robustness of the parameters against the noise. Reasonable parameters are possible to be obtained regardless of the noise in the measurement by RIV. Simulation and experimental tests on a LiFePO4 battery validate the efficiency of RIV for parameter online identification compared with traditional RLS.

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Design-Space Exploration of Quantum Approximate Optimization Algorithm under Noise

2020 IEEE Custom Integrated Circuits Conference (CICC) ◽

10.1109/cicc48029.2020.9075903 ◽

2020 ◽

Cited By ~ 2

Author(s):

Mahabubul Alam ◽

Abdullah Ash-Saki ◽

Swaroop Ghosh

Keyword(s):

Optimization Algorithm ◽

Design Space Exploration ◽

Design Space ◽

Space Exploration ◽

Approximate Optimization

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Measurement Noise Model for Depth Camera-Based People Tracking

Sensors ◽

10.3390/s21134488 ◽

2021 ◽

Vol 21 (13) ◽

pp. 4488

Author(s):

Otto Korkalo ◽

Tapio Takala

Keyword(s):

Real Life ◽

Measurement Noise ◽

Noise Model ◽

Depth Camera ◽

Depth Sensor ◽

People Tracking ◽

Plan View ◽

Depth Cameras ◽

Depth Sensors ◽

Noise Models

Depth cameras are widely used in people tracking applications. They typically suffer from significant range measurement noise, which causes uncertainty in the detections made of the people. The data fusion, state estimation and data association tasks require that the measurement uncertainty is modelled, especially in multi-sensor systems. Measurement noise models for different kinds of depth sensors have been proposed, however, the existing approaches require manual calibration procedures which can be impractical to conduct in real-life scenarios. In this paper, we present a new measurement noise model for depth camera-based people tracking. In our tracking solution, we utilise the so-called plan-view approach, where the 3D measurements are transformed to the floor plane, and the tracking problem is solved in 2D. We directly model the measurement noise in the plan-view domain, and the errors that originate from the imaging process and the geometric transformations of the 3D data are combined. We also present a method for directly defining the noise models from the observations. Together with our depth sensor network self-calibration routine, the approach allows fast and practical deployment of depth-based people tracking systems.

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Instance Independence of Single Layer Quantum Approximate Optimization Algorithm on Mixed-Spin Models at Infinite Size

Quantum ◽

10.22331/q-2021-09-15-542 ◽

2021 ◽

Vol 5 ◽

pp. 542

Author(s):

Jahan Claes ◽

Wim van Dam

Keyword(s):

Spin Glass ◽

Explicit Formula ◽

Optimization Algorithm ◽

Single Layer ◽

Higher Moments ◽

Spin Models ◽

Approximate Optimization ◽

Mixed Spin ◽

Expected Performance ◽

Multi Body

This paper studies the application of the Quantum Approximate Optimization Algorithm (QAOA) to spin-glass models with random multi-body couplings in the limit of a large number of spins. We show that for such mixed-spin models the performance of depth 1 QAOA is independent of the specific instance in the limit of infinite sized systems and we give an explicit formula for the expected performance. We also give explicit expressions for the higher moments of the expected energy, thereby proving that the expected performance of QAOA concentrates.

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On the universality of the quantum approximate optimization algorithm

Quantum Information Processing ◽

10.1007/s11128-020-02748-9 ◽

2020 ◽

Vol 19 (9) ◽

Cited By ~ 2

Author(s):

M. E. S. Morales ◽

J. D. Biamonte ◽

Z. Zimborás

Keyword(s):

Optimization Algorithm ◽

Quantum Circuit ◽

Original Form ◽

Complete Proof ◽

One Dimensional ◽

Approximate Optimization ◽

Near Term ◽

Set Up ◽

The Cost ◽

Universal Gate

Abstract The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different Hamiltonians, called the mixer and the cost Hamiltonian, in alternation with the goal being to approach the ground state of the cost Hamiltonian. Recently, it has been suggested that one might use such a set-up as a parametric quantum circuit with possibly some other goal than reaching ground states. From this perspective, a recent work (Lloyd, arXiv:1812.11075) argued that for one-dimensional local cost Hamiltonians, composed of nearest neighbour ZZ terms, this set-up is quantum computationally universal and provides a universal gate set, i.e. all unitaries can be reached up to arbitrary precision. In the present paper, we complement this work by giving a complete proof and the precise conditions under which such a one-dimensional QAOA might produce a universal gate set. We further generalize this type of gate-set universality for certain cost Hamiltonians with ZZ and ZZZ terms arranged according to the adjacency structure of certain graphs and hypergraphs.

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