64 research outputs found
Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers
Quantum simulation of strongly correlated systems is potentially the most
feasible useful application of near-term quantum computers. Minimizing quantum
computational resources is crucial to achieving this goal. A promising class of
algorithms for this purpose consists of variational quantum eigensolvers
(VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build
variational ans\"atze step by step from a predefined operator pool perform
particularly well in terms of circuit depths and variational parameter counts.
However, this improved performance comes at the expense of an additional
measurement overhead compared to standard VQEs. Here, we show that this
overhead can be reduced to an amount that grows only linearly with the number
of qubits, instead of quartically as in the original ADAPT-VQE. We do this
by proving that operator pools of size can represent any state in
Hilbert space if chosen appropriately. We prove that this is the minimal size
of such "complete" pools, discuss their algebraic properties, and present
necessary and sufficient conditions for their completeness that allow us to
find such pools efficiently. We further show that, if the simulated problem
possesses symmetries, then complete pools can fail to yield convergent results,
unless the pool is chosen to obey certain symmetry rules. We demonstrate the
performance of such symmetry-adapted complete pools by using them in classical
simulations of ADAPT-VQE for several strongly correlated molecules. Our
findings are relevant for any VQE that uses an ansatz based on Pauli strings.Comment: 15+10 pages, 7 figure
TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ans\"atze
Adaptive quantum variational algorithms are particularly promising for
simulating strongly correlated systems on near-term quantum hardware, but they
are not yet viable due, in large part, to the severe coherence time limitations
on current devices. In this work, we introduce an algorithm called
TETRIS-ADAPT-VQE, which iteratively builds up variational ans\"atze a few
operators at a time in a way dictated by the problem being simulated. This
algorithm is a modified version of the ADAPT-VQE algorithm in which the
one-operator-at-a-time rule is lifted to allow for the addition of multiple
operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in
denser but significantly shallower circuits, without increasing the number of
CNOT gates or variational parameters. Its advantage over the original algorithm
in terms of circuit depths increases with the system size. Moreover, the
expensive step of measuring the energy gradient with respect to each candidate
unitary at each iteration is performed only a fraction of the time compared to
ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a
practical quantum advantage on quantum hardware.Comment: 10 pages, 7 figure
An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer
The quantum approximate optimization algorithm (QAOA) is a hybrid variational
quantum-classical algorithm that solves combinatorial optimization problems.
While there is evidence suggesting that the fixed form of the original QAOA
ansatz is not optimal, there is no systematic approach for finding better
ans\"atze. We address this problem by developing an iterative version of QAOA
that is problem-tailored, and which can also be adapted to specific hardware
constraints. We simulate the algorithm on a class of Max-Cut graph problems and
show that it converges much faster than the original QAOA, while simultaneously
reducing the required number of CNOT gates and optimization parameters. We
provide evidence that this speedup is connected to the concept of shortcuts to
adiabaticity.Comment: 5 pages, 3 figure
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