Related papers: Halving the Cost of Quantum Algorithms with Random…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
We present a quantum circuit optimization technique that takes into account the variability in error rates that is inherent across present day noisy quantum computing platforms. This method can be run post qubit routing or post-compilation,…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Although linear quantum amplification has proven essential to the processing of weak quantum signals, extracting higher-order quantum features such as correlations in principle demands nonlinear operations. However, nonlinear processing of…
Quantum signal processing (QSP) studies quantum circuits interleaving known unitaries (the phases) and unknown unitaries encoding a hidden scalar (the signal). For a wide class of functions one can quickly compute the phases applying a…
Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on…
Quantum computing is a promising paradigm that may overcome the current computational power bottlenecks. The increasing maturity of quantum processors provides more possibilities for the development and implementation of quantum algorithms.…
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…
The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…
Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables. In…
The Quantum Skip Gate (QSG) is a unitary circuit primitive that coherently superposes the execution and omission of an expensive quantum subroutine based on the outcome of a cheaper preceding subroutine, without mid-circuit measurement or…
One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding…
Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to…
Probabilistic error cancellation is a quantum error mitigation technique capable of producing unbiased computation results but requires an accurate error model. Constructing this model involves estimating a set of parameters, which, in the…
We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with…
We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state…