Related papers: Efficient equivalence checking of Clifford-U circu…
We show that any $n$-qubit Clifford unitary can be implemented using at most $2n$ multi-qubit joint measurements. All the multi-qubit joint measurements used for implementing the Clifford unitary can be chosen to form at most two sets of…
With the advent of quantum processors exceeding $100$ qubits and the high engineering complexities involved, there is a need for holistically benchmarking the processor to have quality assurance. Linear cross-entropy benchmarking (XEB) has…
In 2021, Broadbent and Kazmi developed a gate-teleportation-based protocol for computational indistinguishability obfuscation of quantum circuits. This protocol is efficient for Clifford+T circuits with logarithmically many T-gates, where…
Parallel computation enables multiple processors to execute different parts of a task simultaneously, improving processing speed and efficiency. In quantum computing, parallel gate implementation involves executing gates independently in…
A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
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…
Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase…
We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one…
This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…
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…
The Linear Combination of Unitaries (LCU) method is a powerful scheme for the block encoding of operators but suffers from high overheads. In this work, we discuss the parallelisation of LCU and in particular the SELECT subroutine of LCU…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
In recent years, quantum computers and algorithms have made significant progress indicating the prospective importance of quantum computing (QC). Especially combinatorial optimization has gained a lot of attention as an application field…
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
We provide and experimentally demonstrate an accreditation protocol that upper-bounds the variation distance between noisy and noiseless probability distributions of the outputs of arbitrary quantum computations. We accredit the outputs of…
In this paper, we introduce the model of quantum Mealy machines and study the equivalence checking and minimisation problems of them. Two efficient algorithms are developed for checking equivalence of two states in the same machine and for…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
As quantum devices progress towards a quantum advantage regime, they become harder to benchmark. A particularly relevant challenge is to assess the quality of the whole computation, beyond testing the performance of each single operation.…
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…