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Quantum error mitigation schemes (QEM) have greatly enhanced the performance of quantum computers, mostly by reducing errors caused by interactions with the environment. Nevertheless, the presence of coherence errors, typically arising from…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
Holistic resource estimates are essential for guiding the development of fault-tolerant quantum algorithms and the computers they will run on. This is particularly true when we focus on highly-constrained early fault-tolerant devices. Many…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e.,…
In existing general-purpose architectures for surface-code-based fault-tolerant quantum computers, the cost of a quantum computation is determined by the circuit volume, i.e., the number of qubits multiplied by the number of non-Clifford…
Quantum circuits for mathematical functions such as division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
Recent advances in quantum hardware are bringing fault-tolerant quantum computing (FTQC) closer to reality. In the early stage of FTQC, however, the numbers of available logical qubits and high-fidelity $T$ gates remain limited, making it…
Neutral atoms are a promising choice for scalable quantum computing architectures. Features such as long distance interactions and native multiqubit gates offer reductions in communication costs and operation count. However, the trapped…
Fault-tolerant quantum computers rely on Quantum Error-Correcting Codes (QECCs) to protect information from noise. However, no single error-correcting code supports a fully transversal and therefore fault-tolerant implementation of all…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
We introduce a measure for evaluating the efficiency of finite universal quantum gate sets $\mathcal{S}$, called the Quantum Circuit Overhead (QCO), and the related notion of $T$-Quantum Circuit Overhead ($T$-QCO). QCO compares the circuit…
Numerous quantum algorithms require the use of quantum error correction to overcome the intrinsic unreliability of physical qubits. However, error correction imposes a unique performance bottleneck, known as T-complexity, that can make an…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
Since an n-qubit circuit consisting of CNOT gates can have up to $\Omega(n^2/\log{n})$ CNOT gates, it is natural to expect that $\Omega(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the…
Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and…