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Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more…
Quantum state preparation is an important class of quantum algorithms that is employed as a black-box subroutine in many algorithms, or used by itself to generate arbitrary probability distributions. We present a novel state preparation…
One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a…
We explore the effect of Shor state construction methods on logical state encoding and quantum error correction for the [[7,1,3]] Calderbank-Shor-Steane quantum error correction code in a nonequiprobable error environment. We determine the…
Recent experimental breakthroughs have signalled the imminent arrival of the early fault-tolerant era. However, for a considerable period in the foreseeable future, relying solely on quantum error correction for full error suppression will…
Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes,…
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls,…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
Methods to control errors will be essential for quantum information processing. It is widely believed that fault-tolerant quantum error correction is the leading contender to achieve this goal. Although the theory of fault-tolerant quantum…
Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by…
Quantum computers have advanced rapidly in qubit count and gate fidelity. However, large-scale fault-tolerant quantum computing still relies on quantum error correction code (QECC) to suppress noise. Manually or experimentally verifying the…
Quantum error mitigation is essential for computing on the noisy quantum computer with a limited number of qubits. In this paper, we propose a practical protocol of error mitigation by virtually purifying the quantum state without qubit…
High quality, fully-programmable quantum processors are available with small numbers (<1000) of qubits, and the scientific potential of these near term machines is not well understood. If the small number of physical qubits precludes…
The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]] quantum code, together with a fault-tolerant syndrome extraction by means of several ancilla states, have been numerically studied. A simple probability expression to…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited…
If a quantum computer is stabilized by fault-tolerant quantum error correction (QEC), then most of its resources (qubits and operations) are dedicated to the extraction of error information. Analysis of this process leads to a set of…