Related papers: Short remarks on shallow unitary circuits
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…
Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed matter theory and quantum thermodynamics. However, despite their…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric. Deviations…
We consider a model of quantum computation we call "Varying-$Z$" (V$Z$), defined by applying controllable $Z$-diagonal Hamiltonians in the presence of a uniform and constant external $X$-field, and prove that it is universal, even in 1D.…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on…
The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses,…
It is known that a computationally universal gate set $\{H,CCZ\}$ can be transformed to a strictly universal one $\{H, \Lambda(S)\}$ using one maximally imaginary state $|+i \rangle$ and non-imaginary ancillary qubits. We succeed this…
While quantum state tomography is notoriously hard, most states hold little interest to practically-minded tomographers. Given that states and unitaries appearing in Nature are of bounded gate complexity, it is natural to ask if efficient…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
The variational quantum eigensolver has been proposed as a low-depth quantum circuit that can be employed to examine strongly correlated systems on today's noisy intermediate-scale quantum computers. We examine details associated with the…
Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications…
The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…
We show that every correctable subsystem for an arbitrary noise operation can be recovered by a unitary operation, where the notion of recovery is more relaxed than the notion of correction insofar as it does not protect the subsystem from…