Learning State Preparation Circuits for Quantum Phases of Matter

• URL: http://arxiv.org/abs/2410.23544v2
• Date: Mon, 04 Nov 2024 03:21:39 GMT
• Title: Learning State Preparation Circuits for Quantum Phases of Matter
• Authors: Hyun-Soo Kim, Isaac H. Kim, Daniel Ranard,
• Abstract summary: We introduce a flexible and efficient framework for obtaining a state preparation circuit for a large class of many-body ground states. We use a variant of the quantum Markov chain condition that remains robust against constant-depth circuits.
• Score: 0.294944680995069
• License:
• Abstract: Many-body ground state preparation is an important subroutine used in the simulation of physical systems. In this paper, we introduce a flexible and efficient framework for obtaining a state preparation circuit for a large class of many-body ground states. We introduce polynomial-time classical algorithms that take reduced density matrices over $\mathcal{O}(1)$-sized balls as inputs, and output a circuit that prepares the global state. We introduce algorithms applicable to (i) short-range entangled states (e.g., states prepared by shallow quantum circuits in any number of dimensions, and more generally, invertible states) and (ii) long-range entangled ground states (e.g., the toric code on a disk). Both algorithms can provably find a circuit whose depth is asymptotically optimal. Our approach uses a variant of the quantum Markov chain condition that remains robust against constant-depth circuits. The robustness of this condition makes our method applicable to a large class of states, whilst ensuring a classically tractable optimization landscape.

Related papers

• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• Learning quantum states prepared by shallow circuits in polynomial time [1.127500169412367]
  We learn a constant depth quantum circuit that prepares $vertpsirangle$ on a finite-dimensional lattice. The algorithm extends to the case when the depth of $U$ is $mathrmpolylog(n)$, with a quasi-polynomial run-time. As an application, we give an efficient algorithm to test whether an unknown quantum state on a lattice has low or high quantum circuit complexity.
  arXiv  Detail & Related papers  (2024-10-31T04:12:49Z)
• Efficient learning of quantum states prepared with few fermionic non-Gaussian gates [0.0]
  We present an efficient algorithm for learning states on $n$ fermion modes prepared by any number of Gaussian gates. Our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity.
  arXiv  Detail & Related papers  (2024-02-28T19:18:27Z)
• Calculating the many-body density of states on a digital quantum computer [58.720142291102135]
  We implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer. We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18bits.
  arXiv  Detail & Related papers  (2023-03-23T17:46:28Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Compilation of algorithm-specific graph states for quantum circuits [55.90903601048249]
  We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages. The computation can then be implemented using a series of non-Pauli measurements on this graph state.
  arXiv  Detail & Related papers  (2022-09-15T14:52:31Z)
• Approximate encoding of quantum states using shallow circuits [0.0]
  A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. Here, we aim at creating an approximate encoding of the target state using a limited number of gates. Our work offers a universal method to prepare target states using local gates and represents a significant improvement over known strategies.
  arXiv  Detail & Related papers  (2022-06-30T18:00:04Z)
• Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions [0.8315657895474382]
  We show that there exist families of quantum states that can be prepared to high precision with circuits of linear size and depth. We further develop an algorithm that requires only linear classical time to generate accurate linear-depth circuits.
  arXiv  Detail & Related papers  (2020-05-09T02:31:44Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.