Related papers: Efficient Equivalent of Shallow Quantum Hashing
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
Quantum hardware is advancing rapidly across various platforms, yet implementing large-scale quantum error correction (QEC) remains challenging. As hardware continues to improve, there is a growing need to identify potential applications on…
Quantum fully homomorphic encryption (QFHE) allows to evaluate quantum circuits on encrypted data. We present a novel QFHE scheme, which extends Pauli one-time pad encryption by relying on the quaternion representation of SU(2). With the…
We study an efficient algorithm to hash any single qubit gate (or unitary matrix) into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different…
We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In our hybrid scheme, a classical information feed-forward is required from the quantum phase estimation…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be…
Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit…
In the paper, we consider quantum circuits for Quantum fingerprinting (quantum hashing) and quantum Fourier transform (QFT) algorithms. Quantum fingerprinting (quantum hashing) is a well-known technique for comparing large objects using…
Quantum compiling means fast, device-aware implementation of quantum algorithms (i.e., quantum circuits, in the quantum circuit model of computation). In this paper, we present a strategy for compiling IBM Q -aware, low-depth quantum…
Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few…
The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher…
A ($t$, $n$) threshold quantum secret sharing (QSS) is proposed based on a single $d$-level quantum system. It enables the ($t$, $n$) threshold structure based on Shamir's secret sharing and simply requires sequential communication in…
Quantum computing applications in the noisy intermediate-scale quantum (NISQ) era require algorithms that can generate shallower circuits feasible for today's quantum systems. This is particularly challenging for quantum chemistry…
Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any…
We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on…
Cloud-accessible quantum processors enable direct execution of quantum algorithms on heterogeneous hardware platforms. Unlike classical systems, however, identical quantum circuits may exhibit substantially different behavior across devices…
We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…