Research interests
My broad research motivation is deciphering and discovering quantum phenomena
in interesting chemical and physical systems underlying critical scientific
challenges impacting our world.
Some of my specific technical expertise and interests are mentioned below.
- Quantum methods implementable in classical and quantum computers.
- Algebra emerging from many-body quantum mechanics.
- Tensor networks, decompositions, and symmetries.
I mention some of my past research experiences below.
Yale University
Electronic structure calculations with bosons.
A rapidly progressing field in quantum hardware is the circuit quantum electrodynamics (cQED)
approach,
where microwave resonators act as quantum harmonic oscillators and the bosonic quantum
gates are implemented by
coupling
the resonators with a superconducting transmon qubit.
This hybrid qubit-oscillator hardware approach has many advantages over the traditional
qubit-based quantum devices such as more control over noise and has been applied to
study various bosonic problems in
chemistry.
We have
shown
for the first time how the universality of qubit-oscillator devices
allows us to represent the electronic structure Hamiltonian on bosonic
quantum computers and explore native qubit-qumode gates to represent electronic states.
Bosonic gates for quantum optimization algorithms.
We explored the potential of bosonic qumode gates further for optimization problems.
The Hamiltonians in this case are diagonal in nature, which allows us to compute
expectation vlaues by measuring the number of photons
inside
a microwave resonator.
It is known that native qumode gates such as phase space displacement operators
are
hard
to mimic using qubit-centric gates.
We have shown for the first time that the expressiveness of such qumode gates coupled to a qubit
can
outperform
qubit-centric ansatz circuits for benchmark constrained optimization problems.
Rice University
Classical computing methods for electron pairing.
It is known that electron pairing in the Hilbert space of a suitable one-electron basis
is
critical
for understanding strongly correlated electronic systems.
However, exactly solving the electronic structure problem on a
paired basis is still an impractical problem beyond a certain system size.
My thesis work asked the question: Is it possible to develop classical computing algorithms
that can efficiently tackle strong correlation when the problem is only restricted to the
subspace where the electrons are paired? We have shown that the answer is yes for certain
flavors of strongly correlated pairing interactions by developing pair wavefunctions
inspired by
chemical bonding
and
superconductivity.
These newly developed electronic structure methods started from the so-called
antisymmetrized geminal power (AGP) wavefunction where all the pairs were
identical,
and then brought more
diversity
to different electron pairs, which can also be
selectively tuned.
Quantum state preparation algorithms.
Electron pairs are isomorphic to qubits due to their shared
su(2) Lie algebraic structure.
This allows AGP to be understood as a multi-qubit state with unique entanglement properties.
The elementary symmetric polynomial (ESP) structure of the AGP allowed us to develop an
efficient quantum state preparation
algorithm
for the qubit-AGP state with potential applications in quantum optimization.
Exploration of the polynomial structure of AGP also allowed us to develop a polynomial
that generalizes the notion of ESP and allowed us to design a quantum state with more
flexibility than AGP. We have shown the resulting binary tree state (BTS) can be
efficiently
simulated on a classical computer, thus introducing a quantum-inspired classical algorithm.
Contact
Rishab Dutta
Pacific Northwest National Laboratory
rishab(dot)dutta(at)pnnl(dot)gov