Related papers: Realistic Cost to Execute Practical Quantum Circui…
The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of…
Quantum circuit simulation is paramount to the verification and optimization of quantum algorithms, and considerable research efforts have been made towards efficient simulators. While circuits often contain high-level gates such as oracles…
Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
Magic state distillation, a process for preparing magic states needed to implement non-Clifford gates fault-tolerantly, plays a crucial role in fault-tolerant quantum computation. Historically, it has been a major bottleneck, leading to the…
We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\log(1/\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary…
In a model of fault-tolerant quantum computation with quick and noiseless polyloglog-time auxiliary classical computation, we construct a fault tolerance protocol with constant-space and $\widetilde{O}(\log N)$-time overhead, where…
Lattice surgery is a measurement-based technique for performing fault-tolerant quantum computation in two dimensions. When using the surface code, the most general lattice surgery operations require lattice irregularities called twist…
Equational reasoning is central to quantum circuit optimisation and verification: one replaces subcircuits by provably equivalent ones using a fixed set of rewrite rules viewed as equations. A finite rule set is most informative when it…
The speed of a fault-tolerant quantum computer is dictated by the reaction time of its classical electronics, that is, the total time required by decoders and controllers to determine the outcome of a logical measurement and execute…
Quantum error correction is critical to the design and manufacture of scalable quantum computing systems. Recently, there has been growing interest in quantum low-density parity-check codes as a resource-efficient alternative to surface…
Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings, but their fault-tolerant advantage over qubit encodings remains unclear. We compare the non-Clifford cost…
Preparing a quantum circuit that implements a given sparse state is an important building block that is necessary for many different quantum algorithms. In the context of fault-tolerant quantum computing, the so-called non-Clifford gates…
Fault-tolerant quantum computing requires a universal gate set, but the necessary non-Clifford gates represent a significant resource cost for most quantum error correction architectures. Magic state cultivation offers an efficient…
We refine ideas from Knill 1996, Jones 2016, Chamberland 2020, Gidney 2023+2024, Bombin 2024, and Hirano 2024 to efficiently prepare good $|T\rangle$ states. We call our construction "magic state cultivation" because it gradually grows the…
Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them…
We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational…
We systematically construct and classify fault-tolerant logical gates implemented by constant-depth circuits for quantum codes using cohomology operations and symmetry. These logical gates are obtained from unitary operators given by…
We show that the cost of strong simulation of quantum circuits using $t$ $T$ gate magic states exhibits non-trivial reductions on its upper bound for $t=1$, $t=2$, $t=3$, and $t=6$ with odd-prime-qudits. This agrees with previous numerical…
We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a 2D grid of logical qubits with nearest-neighbor logical operations. Embedding an input circuit's qubits in…