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Variational quantum algorithms (VQAs) face an inherent trade-off between expressivity and trainability: deeper circuits can represent richer states but suffer from noise accumulation and barren plateaus, while shallow circuits remain…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the…
Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to execute on current hardware. Here we…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model,…
We propose a scheme for an exact efficient transformation of a tensor product state of many identically prepared qubits into a state of a logarithmically small number of qubits. Using a quadratic number of elementary quantum gates we…
In a previous paper [quant-ph/0408045] we described a quantum algorithm to prepare an arbitrary state of a quantum register with arbitrary fidelity. Here we present an alternative algorithm which uses a small number of quantum oracles…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
Cat states are an important resource for fault-tolerant quantum computing, where they serve as building blocks for a variety of fault-tolerant primitives. Consequently, the ability to prepare high-quality cat states at large fault distances…
We present a Dicke state preparation scheme which uses global control of $N$ spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke…
Initializing classical data in a quantum device is an essential step in many quantum algorithms. As a consequence of measurement and noisy operations, some algorithms need to reinitialize the prepared state several times during its…
Assemblies of strongly interacting fermions, whether in a condensed-matter or a quantum chemistry context, range amongst the most promising candidate systems for which quantum computing platforms could provide an advantage. Near-term…
Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…
We propose a general-purpose quantum algorithm for preparing ground states of quantum Hamiltonians from a given trial state. The algorithm is based on techniques recently developed in the context of solving the quantum linear systems…
The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes…
Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like…
For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into…
Quantum Computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry…
Recently, the technique of counterdiabatic driving, which provides an effective strategy for accelerating adiabatic quantum evolution, has been widely applied in the preparation of many-body quantum states. In this work, we propose a…