Related papers: Hardness of efficiently generating ground states i…
The generation of a large amount of entanglement is a necessary condition for a quantum computer to achieve quantum advantage. In this paper, we propose a method to efficiently generate pseudo-random quantum states, for which the degree of…
Quantum PCP conjecture is one of the most influential open problems in quantum complexity theory, which states that approximating the ground state energy for a sparse local Hamiltonian upto a constant is QMA-complete. However, even though…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…
Tensor network states are for good reasons believed to capture ground states of gapped local Hamiltonians arising in the condensed matter context, states which are in turn expected to satisfy an entanglement area law. However, the…
We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…
Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have…
We construct examples of highly entangled two-dimensional states by exploiting a correspondence between stochastic processes in $d$ dimensions and quantum states in $d+1$ dimensions. The entanglement structure of these states, which we…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
We present a method to construct number-conserving Hamiltonians whose ground states exactly reproduce an arbitrarily chosen BCS-type mean-field state. Such parent Hamiltonians can be constructed not only for the usual $s$-wave BCS state,…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
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…
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local…
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum…
In this paper we develop general techniques for classes of computable real numbers generated by subsets of total computable (recursive functions) with special restrictions on basic operations in order to investigate the following problems:…
The ground state energy and the free energy of Quantum Local Hamiltonians are fundamental quantities in quantum many-body physics, however, it is QMA-Hard to estimate them in general. In this paper, we develop new techniques to find…
There is a large body of work studying what forms of computational hardness are needed to realize classical cryptography. In particular, one-way functions and pseudorandom generators can be built from each other, and thus require equivalent…