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One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface…
We propose a general framework for computing Retarded Green's Functions (RGFs) on quantum computers by recasting their evaluation as a problem of circuit differentiation. Our proposal is based on real-time evolution and specifically…
The native gate set is fundamental to the performance of quantum devices, as it governs the accuracy of basic quantum operations and dictates the complexity of implementing quantum algorithms. Traditional approaches to extending gate sets…
This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a…
The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with $n$ wires, each corresponding to one…
In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we…
We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic…
Quantum low-density parity-check (qLDPC) codes are a promising construction for drastically reducing the overhead of fault-tolerant quantum computing (FTQC) architectures. However, all of the known hardware implementations of these codes…
As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the…
Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…
We present a fault-tolerant universal gate set consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal non-Clifford gates on these codes are intriguing in that higher levels of the Clifford…
In universal fault-tolerant quantum computing, implementing logical non-Clifford gates often demands substantial spacetime resources for many error-correcting codes, including the high-threshold surface code. A critical mission for…
We study a Grover-type method for Quadratic Unconstrained Binary Optimization (QUBO) problems. For an $n$-dimensional QUBO problem with $m$ nonzero terms, we construct a marker oracle for such problems with a tuneable parameter, $\Lambda…
The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses…
The practical use of many types of near-term quantum computers requires accounting for their limited connectivity. One way of overcoming limited connectivity is to insert swaps in the circuit so that logical operations can be performed on…
Decoherence is inevitable when manipulating quantum systems. It decreases the quality of quantum manipulations and thus is one of the main obstacles for large-scale quantum computation, where high-fidelity quantum gates are needed.…
I present a new approach for designing quantum error-correcting codes that guarantees a physically natural implementation of Clifford operations. Inspired by the scheme put forward by Gottesman, Kitaev, and Preskill for encoding a qubit in…
We found that the actual computational time-cost of the QFT is O(n 2^n) for large n in a quantum computer using nuclear spins. The computational cost of a quantum algorithm has usually been estimated as the sum of the universal gates…