16 research outputs found
Characterizing the geometry of the Kirkwood-Dirac positive states
The Kirkwood-Dirac (KD) quasiprobability distribution can describe any
quantum state with respect to the eigenbases of two observables and . KD
distributions behave similarly to classical joint probability distributions but
can assume negative and nonreal values. In recent years, KD distributions have
proven instrumental in mapping out nonclassical phenomena and quantum
advantages. These quantum features have been connected to nonpositive entries
of KD distributions. Consequently, it is important to understand the geometry
of the KD-positive and -nonpositive states. Until now, there has been no
thorough analysis of the KD positivity of mixed states. Here, we characterize
how the full convex set of states with positive KD distributions depends on the
eigenbases of and . In particular, we identify three regimes where
convex combinations of the eigenprojectors of and constitute the only
KD-positive states: any system in dimension ; an open and dense
set of bases in dimension ; and the discrete-Fourier-transform bases
in prime dimension. Finally, we investigate if there can exist mixed
KD-positive states that cannot be written as convex combinations of pure
KD-positive states. We show that for some choices of observables and
this phenomenon does indeed occur. We explicitly construct such states for a
spin- system.Comment: 35 pages, 2 figure
Quantum simulations of time travel can power nonclassical metrology
Gambling agencies forbid late bets, placed after the winning horse crosses
the finish line. A time-traveling gambler could cheat the system. We construct
a gamble that one can win by simulating time travel with experimentally
feasible entanglement manipulation. Our gamble echoes a common metrology
protocol: A gambler must prepare probes to input into a metrology experiment.
The goal is to infer as much information per probe as possible about a
parameter's value. If the input is optimal, the information gained per probe
can exceed any value achievable classically. The gambler chooses the input
state analogously to choosing a horse. However, only after the probes are
measured does the gambler learn which input would have been optimal. The
gambler can "place a late bet" by effectively teleporting the optimal input
back in time, via entanglement manipulation. Our Gedankenexperiment
demonstrates that not only true time travel, but even a simulation offers a
quantum advantage in metrology.Comment: 5+1 pages. 2 figures. Comments are welcomed
Dynamic-ADAPT-QAOA: An algorithm with shallow and noise-resilient circuits
The quantum approximate optimization algorithm (QAOA) is an appealing
proposal to solve NP problems on noisy intermediate-scale quantum (NISQ)
hardware. Making NISQ implementations of the QAOA resilient to noise requires
short ansatz circuits with as few CNOT gates as possible. Here, we present
Dynamic-ADAPT-QAOA. Our algorithm significantly reduces the circuit depth and
the CNOT count of standard ADAPT-QAOA, a leading proposal for near-term
implementations of the QAOA. Throughout our algorithm, the decision to apply
CNOT-intensive operations is made dynamically, based on algorithmic benefits.
Using density-matrix simulations, we benchmark the noise resilience of
ADAPT-QAOA and Dynamic-ADAPT-QAOA. We compute the gate-error probability
below which these algorithms provide, on average, more
accurate solutions than the classical, polynomial-time approximation algorithm
by Goemans and Williamson. For small systems with qubits, we show that
for Dynamic-ADAPT-QAOA. Compared to standard
ADAPT-QAOA, this constitutes an order-of-magnitude improvement in noise
resilience. This improvement should make Dynamic-ADAPT-QAOA viable for
implementations on superconducting NISQ hardware, even in the absence of error
mitigation.Comment: 15 pages, 9 figure
Qubit-excitation-based adaptive variational quantum eigensolver
Abstract: Molecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Constructing accurate molecular ansätze that are easy to optimize and implemented by shallow quantum circuits is crucial for the successful implementation of such simulations. Ansätze are, generally, constructed as series of fermionic-excitation evolutions. Instead, we demonstrate the usefulness of constructing ansätze with "qubit-excitation evolutions”, which, contrary to fermionic excitation evolutions, obey "qubit commutation relations”. We show that qubit excitation evolutions, despite the lack of some of the physical features of fermionic excitation evolutions, accurately construct ansätze, while requiring asymptotically fewer gates. Utilizing qubit excitation evolutions, we introduce the qubit-excitation-based adaptive (QEB-ADAPT)-VQE protocol. The QEB-ADAPT-VQE is a modification of the ADAPT-VQE that performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending evolutions of qubit excitation operators. By performing classical numerical simulations for small molecules, we benchmark the QEB-ADAPT-VQE, and compare it against the original fermionic-ADAPT-VQE and the qubit-ADAPT-VQE. In terms of circuit efficiency and convergence speed, we demonstrate that the QEB-ADAPT-VQE outperforms the qubit-ADAPT-VQE, which to our knowledge was the previous most circuit-efficient scalable VQE protocol for molecular simulations
Variational quantum chemistry requires gate-error probabilities below the fault-tolerance threshold
The variational quantum eigensolver (VQE) is a leading contender for useful
quantum advantage in the NISQ era. The interplay between quantum processors and
classical optimisers is believed to make the VQE noise resilient. Here, we
probe this hypothesis. We use full density-matrix simulations to rank the noise
resilience of leading gate-based VQE algorithms in ground-state computations on
a range of molecules. We find that, in the presence of noise: (i) ADAPT-VQEs
that construct ansatz circuits iteratively outperform VQEs that use "fixed"
ansatz circuits; and (ii) ADAPT-VQEs perform better when circuits are
constructed from gate-efficient elements rather than physically-motivated ones.
Our results show that, for a wide range of molecules, even the best-performing
VQE algorithms require gate-error probabilities on the order of to
to reach chemical accuracy. This is significantly below the
fault-tolerance thresholds of most error-correction protocols. Further, we
estimate that the maximum allowed gate-error probability scales inversely with
the number of noisy (two-qubit) gates. Our results indicate that useful
chemistry calculations with current gate-based VQEs are unlikely to be
successful on near-term hardware without error correction.Comment: 17 pages, 8 figure