Related papers: A graph-state based synthesis framework for Cliffo…
Exact synthesis is a tool used in algorithms for approximating an arbitrary qubit unitary with a sequence of quantum gates from some finite set. These approximation algorithms find asymptotically optimal approximations in probabilistic…
The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of…
We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
The Clifford hierarchy is a nested sequence of sets of quantum gates that can be fault-tolerantly performed using gate teleportation within standard quantum error correction schemes. The groups of Pauli and Clifford gates constitute the…
Obtaining the symmetries of a model is a critical step towards developing an understanding and ultimately analytically or numerically solving the model. However, finding symmetries is generally extremely complicated, often being the result…
As quantum processors grow in scale and reliability, the need for efficient quantum gate decomposition of circuits to a set of specific available gates, becomes ever more critical. The decomposition of a particular algorithm into a sequence…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…
Quantum circuit synthesis and compilation are critical components in the quantum computing stack, both for contemporary quantum systems, where efficient use of limited resources is essential, as well as for large-scale fault-tolerant…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
Quantum error correction and fault-tolerance have provided the possibility for large scale quantum computations without a detrimental loss of quantum information. A very natural class of gates for fault-tolerant quantum computation is the…
For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…
We describe a new method for the decomposition of an arbitrary $n$ qubit operator with entries in $\mathbb{Z}[i,\frac{1}{\sqrt{2}}]$, i.e., of the form $(a+b\sqrt{2}+i(c+d\sqrt{2}))/{\sqrt{2}^{k}}$, into Clifford+$T$ operators where $n\le…
Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which…
The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill-then-synthesize. In…
We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely…
Though Cliffords and matchgates are both examples of classically simulable circuits, they are considered simulable for different reasons. The celebrated Gottesman-Knill explains the simulability Cliffords, and the efficient simulability of…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
One learned from Gottesman-Knill theorem that the Clifford model of quantum computing \cite{Clark07} may be generated from a few quantum gates, the Hadamard, Phase and Controlled-Z gates, and efficiently simulated on a classical computer.…
This paper presents a deep reinforcement learning approach for synthesizing unitaries into quantum circuits. Unitary synthesis aims to identify a quantum circuit that represents a given unitary while minimizing circuit depth, total gate…