Related papers: Quantum Circuits for Matrix-Product Unitaries
Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
Yao (1993) proved that quantum Turing machines and uniformly generated quantum circuits are polynomially equivalent computational models: $t \geq n$ steps of a quantum Turing machine running on an input of length $n$ can be simulated by a…
Matrix product states provide efficient classical descriptions of quantum systems that may be useful as reference states for quantum algorithms such as quantum phase estimation and quantum-selected configuration interaction. Shallow circuit…
As quantum computing advances, the complexity of quantum circuits is rapidly increasing, driving the need for robust methods to aid in their design. Equivalence checking plays a vital role in identifying errors that may arise during…
Boolean circuits of McCulloch-Pitts threshold gates are a classic model of neural computation studied heavily in the late 20th century as a model of general computation. Recent advances in large-scale neural computing hardware has made…
Pseudo-unitary circuits are recurring in both S-matrix theory and analysis of No-Go theorems. We propose a matrix and diagrammatic representation for the operation that maps S-matrices to T-matrices and, consequently, a unitary group to a…
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…
Quantum computing promises advantages over classical computing. The manufacturing of quantum hardware is in the infancy stage, called the Noisy Intermediate-Scale Quantum (NISQ) era. A major challenge is automated quantum circuit design…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…
As the number of qubits in a sensor increases, the complexity of designing and controlling the quantum circuits grows exponentially. Manually optimizing these circuits becomes infeasible. Optimizing entanglement distribution in large-scale…
We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth…
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor…
Topological quantum states cannot be created from product states with local quantum circuits of constant depth and are in this sense more entangled than topologically trivial states, but how entangled are they? Here we quantify the…
We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over $n$ qubits in $\log n$ depth. In a similar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in…
Implementing many important sub-circuits on near-term quantum devices remains a challenge due to the high levels of noise and the prohibitive depth on standard nearest-neighbour topologies. Overcoming these barriers will likely require…
We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…
We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via…
Large-scale programmable photonic circuits are opening up new possibilities for information processing providing fast and energy-efficient means for matrix-vector multiplication. Here, we introduce a novel architecture of photonic circuits…