Related papers: Quantum circuit lower bounds in the magic hierarch…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
Modeling and simulation is essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. We…
Magic-state resource theory is a fundamental framework with far-reaching applications in quantum error correction and the classical simulation of quantum systems. Recent advances have significantly deepened our understanding of magic as a…
We investigate the dynamics of nonstabilizerness - also known as `magic' - in monitored quantum circuits composed of random Clifford unitaries and local projective measurements. For measurements in the computational basis, we derive an…
In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation. However, implementing these gates using methods like magic state distillation and code switching requires significant…
We present a discussion of the generalized Clifford group over non-cyclic finite abelian groups. These Clifford groups appear naturally in the theory of topological error correction and abelian anyon models. We demonstrate a generalized…
The Clifford hierarchy is a fundamental structure in quantum computation whose mathematical properties are not fully understood. In this work, we characterize permutation gates -- unitaries which permute the $2^n$ basis states -- in the…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…
We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…
Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…
Clifford circuits play an important role in quantum computation. Gottesman and Chuang proposed a gate teleportation protocol so that a quantum circuit can be implemented by the teleportation circuit with specific ancillary qubits. In…
Achieving chemical accuracy with shallow quantum circuits is a significant challenge in quantum computational chemistry, particularly for near-term quantum devices. In this work, we present a Clifford-based Hamiltonian engineering…
We show that the low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged, and cannot be eliminated by a constant-depth local unitary circuit. This refines conventional notions of complexity beyond…
We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…
The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A persistent obstacle to using such algorithms for solving a wide range of real-world…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
We introduce the notion of dismagicker: non-Clifford unitary gate designed to reduce the non-stabilizerness (also called magic) of quantum many-body states. Although both entanglement and non-stabilizerness are fundamental quantum…
Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually…
Nonstabilizerness, also known as magic, is a crucial resource for quantum computation. The growth in complexity of quantum processing units (QPUs) demands robust and scalable techniques for characterizing this resource. We introduce the…