Classically Simulating Quantum Circuits with Local Depolarizing Noise

We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small constant rate is applied to each qubit at the end of computation. We show that, under this noise model, if an approximate value of the noise rate is known, any CT-ECS circuit with an anti-concentrated output probability distribution is classically simulatable. This indicates that the presence of small noise drastically affects the classical simulatability of CT-ECS circuits. Then, we consider an extension of the noise model where the noise rate can vary with each qubit, and provide a similar sufficient condition for classically simulating CT-ECS circuits with anti-concentrated output probability distributions

A Bayesian Approach for Characterizing and Mitigating Gate and Measurement Errors

Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise which is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates are critical to these models. We use a Bayesian inference approach to identity posterior distributions of these parameters, such that they can be characterized more elaborately. By characterizing the device errors in this way, we can further improve the accuracy of quantum error mitigation. Experiments conducted on IBM's quantum computing devices suggest that our approach provides better error mitigation performance than existing techniques used by the vendor. Also, our approach outperforms the standard Bayesian inference method in such experiments.Comment: Updated the introduction and the description of methodology in the new versio

Fault-tolerant quantum speedup from constant depth quantum circuits

A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can be done efficiently quantumly, but are not possible efficiently classically, assuming strongly held conjectures in complexity theory. A feature dubbed quantum speedup. However, the effect of noise on these proposals is not well understood in general, and in certain cases it is known that simple noise can destroy the quantum speedup. Here we develop a fault-tolerant version of one family of these sampling problems, which we show can be implemented using quantum circuits of constant depth. We present two constructions, each taking $poly(n)$ physical qubits, some of which are prepared in noisy magic states. The first of our constructions is a constant depth quantum circuit composed of single and two-qubit nearest neighbour Clifford gates in four dimensions. This circuit has one layer of interaction with a classical computer before final measurements. Our second construction is a constant depth quantum circuit with single and two-qubit nearest neighbour Clifford gates in three dimensions, but with two layers of interaction with a classical computer before the final measurements. For each of these constructions, we show that there is no classical algorithm which can sample according to its output distribution in $poly(n)$ time, assuming two standard complexity theoretic conjectures hold. The noise model we assume is the so-called local stochastic quantum noise. Along the way, we introduce various new concepts such as constant depth magic state distillation (MSD), and constant depth output routing, which arise naturally in measurement based quantum computation (MBQC), but have no constant-depth analogue in the circuit model.Comment: 26 pages, 6 figures, comments are welcome, new references adde