572 research outputs found
Constructing Smaller Pauli Twirling Sets for Arbitrary Error Channels
Twirling is a technique widely used for converting arbitrary noise channels
into Pauli channels in error threshold estimations of quantum error correction
codes. It is vitally useful both in real experiments and in classical quantum
simulations. Minimising the size of the twirling gate set increases the
efficiency of simulations and in experiments it might reduce both the number of
runs required and the circuit depth (and hence the error burden). Conventional
twirling uses the full set of Pauli gates as the set of twirling gates. This
article provides a theoretical background for Pauli twirling and a way to
construct a twirling gate set with a number of members comparable to the size
of the Pauli basis of the given error channel, which is usually much smaller
than the full set of Pauli gates. We also show that twirling is equivalent to
stabiliser measurements with discarded measurement results, which enables us to
further reduce the size of the twirling gate set.Comment: Fixed typos, added another example and improve presentation
Quantum Error Mitigation using Symmetry Expansion
Even with the recent rapid developments in quantum hardware, noise remains
the biggest challenge for the practical applications of any near-term quantum
devices. Full quantum error correction cannot be implemented in these devices
due to their limited scale. Therefore instead of relying on engineered code
symmetry, symmetry verification was developed which uses the inherent symmetry
within the physical problem we try to solve. In this article, we develop a
general framework named symmetry expansion which provides a wide spectrum of
symmetry-based error mitigation schemes beyond symmetry verification, enabling
us to achieve different balances between the estimation bias and the sampling
cost of the scheme. We show that certain symmetry expansion schemes can achieve
a smaller estimation bias than symmetry verification through cancellation
between the biases due to the detectable and undetectable noise components. A
practical way to search for such a small-bias scheme is introduced. By
numerically simulating the Fermi-Hubbard model for energy estimation, the
small-bias symmetry expansion we found can achieve an estimation bias 6 to 9
times below what is achievable by symmetry verification when the average number
of circuit errors is between 1 to 2. The corresponding sampling cost for random
shot noise reduction is just 2 to 6 times higher than symmetry verification.
Beyond symmetries inherent to the physical problem, our formalism is also
applicable to engineered symmetries. For example, the recent scheme for
exponential error suppression using multiple noisy copies of the quantum device
is just a special case of symmetry expansion using the permutation symmetry
among the copies
Multi-exponential Error Extrapolation and Combining Error Mitigation Techniques for NISQ Applications
Noise in quantum hardware remains the biggest roadblock for the
implementation of quantum computers. To fight the noise in the practical
application of near-term quantum computers, instead of relying on quantum error
correction which requires large qubit overhead, we turn to quantum error
mitigation, in which we make use of extra measurements. Error extrapolation is
an error mitigation technique that has been successfully implemented
experimentally. Numerical simulation and heuristic arguments have indicated
that exponential curves are effective for extrapolation in the large circuit
limit with an expected circuit error count around unity. In this article, we
extend this to multi-exponential error extrapolation and provide more rigorous
proof for its effectiveness under Pauli noise. This is further validated via
our numerical simulations, showing orders of magnitude improvements in the
estimation accuracy over single-exponential extrapolation. Moreover, we develop
methods to combine error extrapolation with two other error mitigation
techniques: quasi-probability and symmetry verification, through exploiting
features of these individual techniques. As shown in our simulation, our
combined method can achieve low estimation bias with a sampling cost multiple
times smaller than quasi-probability while without needing to be able to adjust
the hardware error rate as required in canonical error extrapolation
A Practical Framework for Quantum Error Mitigation
Quantum error mitigation is expected to play a crucial role in the practical
applications of quantum machines for the foreseeable future. Thus it is
important to put the numerous quantum error mitigation schemes proposed under a
coherent framework that can highlight their underlying connections while
providing guidance for their practical performance. In this article, we
construct a general framework named linear quantum error mitigation that
includes most of the state-of-the-art quantum error mitigation schemes. Within
the framework, quantum error mitigation can be effectively viewed as extracting
the error-mitigated state out of the noisy state. The fraction of
error-mitigated state that is successfully extracted, called extraction rate,
will indicate the cost-effectiveness of the given mitigation scheme. Using the
framework, we can derive and compare the fidelity boost, sampling overhead and
extraction rate across various mitigation schemes under practical assumptions.
The structure, insights and intuitions provided by the framework can serve as a
basis for further developments of new schemes
Psychophysical Responses Comparison in Spatial Visual, Audiovisual, and Auditory BCI-Spelling Paradigms
The paper presents a pilot study conducted with spatial visual, audiovisual
and auditory brain-computer-interface (BCI) based speller paradigms. The
psychophysical experiments are conducted with healthy subjects in order to
evaluate a difficulty and a possible response accuracy variability. We also
present preliminary EEG results in offline BCI mode. The obtained results
validate a thesis, that spatial auditory only paradigm performs as good as the
traditional visual and audiovisual speller BCI tasks.Comment: The 6th International Conference on Soft Computing and Intelligent
Systems and The 13th International Symposium on Advanced Intelligent Systems,
201
Mitigating Coherent Noise Using Pauli Conjugation
Coherent noise can be much more damaging than incoherent (probabilistic)
noise in the context of quantum error correction. One solution is to use
twirling to turn coherent noise into incoherent Pauli channels. In this
Article, we show that some of the coherence of the noise channel can actually
be used to improve its logical fidelity by simply sandwiching the noise with a
chosen pair of Pauli gates, which we call Pauli conjugation. Using the optimal
Pauli conjugation, we can achieve a higher logical fidelity than using twirling
and doing nothing. We devise a way to search for the optimal Pauli conjugation
scheme and apply it to Steane code, 9-qubit Shor code and distance-3 surface
code under global coherent noise. The optimal conjugation schemes show
improvement in logical fidelity over twirling while the weights of the
conjugation gates we need to apply are lower than the average weight of the
twirling gates. In our example noise and codes, the concatenated threshold
obtained using conjugation is consistently higher than the twirling threshold
and can be up to 1.5 times higher than the original threshold where no
mitigation is applied. Our simulations show that Pauli conjugation can be
robust against gate errors. With the help of logical twirling, the undesirable
coherence in the noise channel can be removed and the advantages of conjugation
over twirling can persist as we go to multiple rounds of quantum error
correction.Comment: Added explanations about the mechanism of conjugation
Biased Estimator Channels for Classical Shadows
Extracting classical information from quantum systems is of fundamental
importance, and classical shadows allow us to extract a large amount of
information using relatively few measurements. Conventional shadow estimators
are unbiased and thus approach the true mean in the infinite-sample limit. In
this work, we consider a biased scheme, intentionally introducing a bias by
rescaling the conventional classical shadows estimators can reduce the error in
the finite-sample regime. The approach is straightforward to implement and
requires no quantum resources. We analytically prove average case as well as
worst- and best-case scenarios, and rigorously prove that it is, in principle,
always worth biasing the estimators. We illustrate our approach in a quantum
simulation task of a -qubit spin-ring problem and demonstrate how
estimating expected values of non-local perturbations can be significantly more
efficient using our biased scheme.Comment: 13 pages, 5 figure
A Silicon Surface Code Architecture Resilient Against Leakage Errors
Spin qubits in silicon quantum dots are one of the most promising building
blocks for large scale quantum computers thanks to their high qubit density and
compatibility with the existing semiconductor technologies. High fidelity
single-qubit gates exceeding the threshold of error correction codes like the
surface code have been demonstrated, while two-qubit gates have reached 98\%
fidelity and are improving rapidly. However, there are other types of error ---
such as charge leakage and propagation --- that may occur in quantum dot arrays
and which cannot be corrected by quantum error correction codes, making them
potentially damaging even when their probability is small. We propose a surface
code architecture for silicon quantum dot spin qubits that is robust against
leakage errors by incorporating multi-electron mediator dots. Charge leakage in
the qubit dots is transferred to the mediator dots via charge relaxation
processes and then removed using charge reservoirs attached to the mediators. A
stabiliser-check cycle, optimised for our hardware, then removes the
correlations between the residual physical errors. Through simulations we
obtain the surface code threshold for the charge leakage errors and show that
in our architecture the damage due to charge leakage errors is reduced to a
similar level to that of the usual depolarising gate noise. Spin leakage errors
in our architecture are constrained to only ancilla qubits and can be removed
during quantum error correction via reinitialisations of ancillae, which ensure
the robustness of our architecture against spin leakage as well. Our use of an
elongated mediator dots creates spaces throughout the quantum dot array for
charge reservoirs, measuring devices and control gates, providing the
scalability in the design
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