A number of exciting recent results have been seen in the field quantum error correction. These include initial demonstrations correction on current hardware and resource estimates which improve understanding requirements to run large-scale algorithms for real-world applications. In this work, we bridge gap between these two developments by performing careful estimation resources required fault-tolerantly perform phase (QPE) a minimal chemical example. Specifically, describe detailed...

Quantum computing offers significant speedups, but the large number of physical qubits required for quantum error correction introduces engineering challenges a monolithic architecture. One solution is to distribute logical computation across multiple small computers, with non-local operations enabled via distributed Bell states. Previous investigations have largely focused on surface code, which good suppression poor encoding rates, each code instance only able encode single qubit. In this...

We simulate the logical Hadamard gate in surface code under a circuit-level noise model, compiling it to physical circuit on square-grid connectivity hardware. Our paper is first do this for unitary quantum error-correction code. consider two proposals, both via patch-deformation: one that applies transversal (i.e. domain wall through time) interchange <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> and...

The Travelling Salesman Problem is one of the most famous problems in graph theory. However, little currently known about extent to which quantum computers could speed up algorithms for problem. In this paper, we prove a quadratic speedup when degree each vertex at 3 by applying backtracking algorithm classical Xiao and Nagamochi. We then use similar techniques accelerate 4, before speeding higher-degree graphs via reductions these instances.

Boson Sampling is the problem of sampling from same distribution as indistinguishable single photons at output a linear optical interferometer. It an example non-universal quantum computation which believed to be feasible in near term and cannot simulated on classical machine. Like all purported demonstrations "quantum supremacy", this motivates optimizing simulation schemes for realistic model problem, case when implementations experience lost or distinguishable photons. Although current...

Boson Sampling is the problem of sampling from same output probability distribution as a collection indistinguishable single photons input into linear interferometer. It has been shown that, subject to certain computational complexity conjectures, in general difficult solve classically, motivating optical experiments aimed at demonstrating quantum ``supremacy.'' There are number challenges faced by such experiments, including generation photons. We provide circuit that simulates with...

Floquet codes are an intriguing generalisation of stabiliser and subsystem codes, which can provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware. A recent question interest has been how to run on devices have defective -- therefore unusable qubits. This is under-studied issue crucial importance for running such realistic To address this challenge, we introduce a new method accommodating qubits wide range two-dimensional requires no...

Floquet codes are an intriguing generalisation of stabiliser and subsystem codes, which can provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware. A recent question interest has been how to run on devices have defective – therefore unusable qubits. This is under-studied issue crucial importance for running such realistic To address this challenge, we introduce a new method accommodating qubits wide range two-dimensional requires no...

A number of exciting recent results have been seen in the field quantum error correction. These include initial demonstrations correction on current hardware, and resource estimates which improve understanding requirements to run large-scale algorithms for real-world applications. In this work, we bridge gap between these two developments by performing careful estimation resources required fault-tolerantly perform phase (QPE) a minimal chemical example. Specifically, describe detailed...

We simulate the logical Hadamard gate in surface code under a circuit-level noise model, compiling it to physical circuit on square-grid connectivity hardware. Our paper is first do this for unitary quantum error-correction code. consider two proposals, both via patch-deformation: one that applies transversal (i.e. domain wall through time) interchange $X$ and $Z$ strings, another space achieve interchange. explain detail why they perform by tracking how stabilisers operators are transformed...