1,977 research outputs found
Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
We provide an alternative proof of Wallman's [Quantum 2, 47 (2018)] and
Proctor's [Phys. Rev. Lett. 119, 130502 (2017)] bounds on the effect of
gate-dependent noise on randomized benchmarking (RB). Our primary insight is
that a RB sequence is a convolution amenable to Fourier space analysis, and we
adopt the mathematical framework of Fourier transforms of matrix-valued
functions on groups established in recent work from Gowers and Hatami [Sbornik:
Mathematics 208, 1784 (2017)]. We show explicitly that as long as our faulty
gate-set is close to some representation of the Clifford group, an RB sequence
is described by the exponential decay of a process that has exactly two
eigenvalues close to one and the rest close to zero. This framework also allows
us to construct a gauge in which the average gate-set error is a depolarizing
channel parameterized by the RB decay rates, as well as a gauge which maximizes
the fidelity with respect to the ideal gate-set
Generation and detection of NOON states in superconducting circuits
NOON states, states between two modes of light of the form
allow for super-resolution interformetry. We
show how NOON states can be efficiently produced in circuit quntum
electrodynamics using superconducting phase qubits and resonators. We propose a
protocol where only one interaction between the two modes is required, creating
all the necessary entanglement at the start of the procedure. This protocol
makes active use of the first three states of the phase qubits. Additionally,
we show how to efficiently verify the success of such an experiment, even for
large NOON states, using randomly sampled measurements and semidefinite
programming techniques.Comment: 15 pages and 3 figure
Control of inhomogeneous atomic ensembles of hyperfine qudits
We study the ability to control d-dimensional quantum systems (qudits)
encoded in the hyperfine spin of alkali-metal atoms through the application of
radio- and microwave-frequency magnetic fields in the presence of
inhomogeneities in amplitude and detuning. Such a capability is essential to
the design of robust pulses that mitigate the effects of experimental
uncertainty and also for application to tomographic addressing of particular
members of an extended ensemble. We study the problem of preparing an arbitrary
state in the Hilbert space from an initial fiducial state. We prove that
inhomogeneous control of qudit ensembles is possible based on a semi-analytic
protocol that synthesizes the target through a sequence of alternating rf and
microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several
examples of robust control are studied, and the semi-analytic protocol is
compared to a brute force, full numerical search. For small inhomogeneities, <
1%, both approaches achieve average fidelities greater than 0.99, but the brute
force approach performs superiorly, reaching high fidelities in shorter times
and capable of handling inhomogeneities well beyond experimental uncertainty.
The full numerical search is also applied to tomographic addressing whereby two
different nonclassical states of the spin are produced in two halves of the
ensemble
Experimental accreditation of outputs of noisy quantum computers
We provide and experimentally demonstrate an accreditation protocol that
upper-bounds the variation distance between noisy and noiseless probability
distributions of the outputs of arbitrary quantum computations. We accredit the
outputs of twenty-four quantum circuits executed on programmable
superconducting hardware, ranging from depth nine circuits on ten qubits to
depth twenty-one circuits on four qubits. Our protocol requires implementing
the "target" quantum circuit along with a number of random Clifford circuits
and subsequently post-processing the outputs of these Clifford circuits.
Importantly, the number of Clifford circuits is chosen to obtain the bound with
the desired confidence and accuracy, and is independent of the size and nature
of the target circuit. We thus demonstrate a practical and scalable method of
ascertaining the correctness of the outputs of arbitrary-sized noisy quantum
computers--the ultimate arbiter of the utility of the computer itself.Comment: Accepted versio
Benchmarking Quantum Processor Performance at Scale
As quantum processors grow, new performance benchmarks are required to
capture the full quality of the devices at scale. While quantum volume is an
excellent benchmark, it focuses on the highest quality subset of the device and
so is unable to indicate the average performance over a large number of
connected qubits. Furthermore, it is a discrete pass/fail and so is not
reflective of continuous improvements in hardware nor does it provide
quantitative direction to large-scale algorithms. For example, there may be
value in error mitigated Hamiltonian simulation at scale with devices unable to
pass strict quantum volume tests. Here we discuss a scalable benchmark which
measures the fidelity of a connecting set of two-qubit gates over qubits by
measuring gate errors using simultaneous direct randomized benchmarking in
disjoint layers. Our layer fidelity can be easily related to algorithmic run
time, via defined in Ref.\cite{berg2022probabilistic} that can be used
to estimate the number of circuits required for error mitigation. The protocol
is efficient and obtains all the pair rates in the layered structure. Compared
to regular (isolated) RB this approach is sensitive to crosstalk. As an example
we measure a qubit layer fidelity on a 127 qubit fixed-coupling
"Eagle" processor (ibm\_sherbrooke) of 0.26(0.19) and on the 133 qubit
tunable-coupling "Heron" processor (ibm\_montecarlo) of 0.61(0.26). This can
easily be expressed as a layer size independent quantity, error per layered
gate (EPLG), which is here for
ibm\_sherbrooke and for ibm\_montecarlo.Comment: 15 pages, 8 figures (including appendices
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