297 research outputs found
Leakage in restless quantum gate calibration
Quantum computers require high fidelity quantum gates. These gates are
obtained by routine calibration tasks that eat into the availability of
cloud-based devices. Restless circuit execution speeds-up characterization and
calibration by foregoing qubit reset in between circuits. Post-processing the
measured data recovers the desired signal. However, since the qubits are not
reset, leakage -- typically present at the beginning of the calibration -- may
cause issues. Here, we develop a simulator of restless circuit execution based
on a Markov Chain to study the effect of leakage. In the context of error
amplifying single-qubit gates sequences, we show that restless calibration
tolerates up to 0.5% of leakage which is large compared to the gate
fidelity of modern single-qubit gates. Furthermore, we show that restless
circuit execution with leaky gates reduces by 33% the sensitivity of the ORBIT
cost function developed by J. Kelly et al. which is typically used in
closed-loop optimal control~[Phys. Rev. Lett. 112, 240504 (2014)]. Our results
are obtained with standard qubit state discrimination showing that restless
circuit execution is resilient against misclassified non-computational states.
In summary, the restless method is sufficiently robust against leakage in both
standard and closed-loop optimal control gate calibration to provided accurate
results
A SAT approach to the initial mapping problem in SWAP gate insertion for commuting gates
Most quantum circuits require SWAP gate insertion to run on quantum hardware
with limited qubit connectivity. A promising SWAP gate insertion method for
blocks of commuting two-qubit gates is a predetermined swap strategy which
applies layers of SWAP gates simultaneously executable on the coupling map. A
good initial mapping for the swap strategy reduces the number of required swap
gates. However, even when a circuit consists of commuting gates, e.g., as in
the Quantum Approximate Optimization Algorithm (QAOA) or trotterized
simulations of Ising Hamiltonians, finding a good initial mapping is a hard
problem. We present a SAT-based approach to find good initial mappings for
circuits with commuting gates transpiled to the hardware with swap strategies.
Our method achieves a 65% reduction in gate count for random three-regular
graphs with 500 nodes. In addition, we present a heuristic approach that
combines the SAT formulation with a clustering algorithm to reduce large
problems to a manageable size. This approach reduces the number of swap layers
by 25% compared to both a trivial and random initial mapping for a random
three-regular graph with 1000 nodes. Good initial mappings will therefore
enable the study of quantum algorithms, such as QAOA and Ising Hamiltonian
simulation applied to sparse problems, on noisy quantum hardware with several
hundreds of qubits.Comment: 7 page
Option Pricing using Quantum Computers
We present a methodology to price options and portfolios of options on a
gate-based quantum computer using amplitude estimation, an algorithm which
provides a quadratic speedup compared to classical Monte Carlo methods. The
options that we cover include vanilla options, multi-asset options and
path-dependent options such as barrier options. We put an emphasis on the
implementation of the quantum circuits required to build the input states and
operators needed by amplitude estimation to price the different option types.
Additionally, we show simulation results to highlight how the circuits that we
implement price the different option contracts. Finally, we examine the
performance of option pricing circuits on quantum hardware using the IBM Q
Tokyo quantum device. We employ a simple, yet effective, error mitigation
scheme that allows us to significantly reduce the errors arising from noisy
two-qubit gates.Comment: Fixed a typo. This article has been accepted in Quantu
Adiabatic quantum simulations with driven superconducting qubits
We propose a quantum simulator based on driven superconducting qubits where
the interactions are generated parametrically by a polychromatic magnetic flux
modulation of a tunable bus element. Using a time-dependent Schrieffer-Wolff
transformation, we analytically derive a multi-qubit Hamiltonian which features
independently tunable and -type interactions as well as local bias
fields over a large parameter range. We demonstrate the adiabatic simulation of
the ground state of a hydrogen molecule using two superconducting qubits and
one tunable bus element. The time required to reach chemical accuracy lies in
the few microsecond range and therefore could be implemented on currently
available superconducting circuits. Further applications of this technique may
also be found in the simulation of interacting spin systems.Comment: 11 pages, 6 figure
Squeezing and quantum approximate optimization
Variational quantum algorithms offer fascinating prospects for the solution
of combinatorial optimization problems using digital quantum computers.
However, the achievable performance in such algorithms and the role of quantum
correlations therein remain unclear. Here, we shed light on this open issue by
establishing a tight connection to the seemingly unrelated field of quantum
metrology: Metrological applications employ quantum states of spin-ensembles
with a reduced variance to achieve an increased sensitivity, and we cast the
generation of such squeezed states in the form of finding optimal solutions to
a combinatorial MaxCut problem with an increased precision. By solving this
optimization problem with a quantum approximate optimization algorithm (QAOA),
we show numerically as well as on an IBM quantum chip how highly squeezed
states are generated in a systematic procedure that can be adapted to a wide
variety of quantum machines. Moreover, squeezing tailored for the QAOA of the
MaxCut permits us to propose a figure of merit for future hardware benchmarks.Comment: 8+7 pages, 4+8 figure
Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation
Simulating the time-evolution of a Hamiltonian is one of the most promising
applications of quantum computers. Multi-Product Formulas (MPFs) are well
suited to replace standard product formulas since they scale better with
respect to time and approximation errors. Hamiltonian simulation with MPFs was
first proposed in a fully quantum setting using a linear combination of
unitaries. Here, we analyze and demonstrate a hybrid quantum-classical approach
to MPFs that classically combines expectation values evaluated with a quantum
computer. This has the same approximation bounds as the fully quantum MPFs,
but, in contrast, requires no additional qubits, no controlled operations, and
is not probabilistic. We show how to design MPFs that do not amplify the
hardware and sampling errors, and demonstrate their performance. In particular,
we illustrate the potential of our work by theoretically analyzing the benefits
when applied to a classically intractable spin-boson model, and by computing
the dynamics of the transverse field Ising model using a classical simulator as
well as quantum hardware. We observe an error reduction of up to an order of
magnitude when compared to a product formula approach by suppressing hardware
noise with Pauli Twirling, pulse efficient transpilation, and a novel
zero-noise extrapolation based on scaled cross-resonance pulses. The MPF
methodology reduces the circuit depth and may therefore represent an important
step towards quantum advantage for Hamiltonian simulation on noisy hardware
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