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A Pulse-Gated, Predictive Neural Circuit
[article]
2017
arXiv
pre-print
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, (x + t , x − t ), where x + t − x − t = x t . ...
After gating into a neural population, we have from the gating operation, x(t) = z(t) * G(t), where G(t) is the pulse envelope G(t) = t τ e −t/τ , 0 < t < T T τ e −t/τ , T < t < ∞ . ...
arXiv:1703.05406v1
fatcat:mv5i6l22kfgt5azzigar65cvuq
Quantum computing with superconductors I: Architectures
[article]
2006
arXiv
pre-print
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We then calculate the interaction-representation probability amplitude c mn (t) ≡ e iE mn t/ mn|e −iHt/ |10 (82) for the system at a later time t to be in the state |mn . Here E mn ≡ ǫ m + n ω 0 . ...
Inserting complete sets of the dressed states leads to c 00 (t) = σ j ψ σ j |10 00|e −iHt/ |ψ σ j , (83) and, for mn 00, c mn (t) = e iE mn t/ ∞ j=0 ψ + j |mn ψ − j |mn † G ++ j0 G +− j0 G −+ j0 G −− j0 ...
arXiv:quant-ph/0603224v1
fatcat:zufbvcih3bezflidtnnzu7tvie
Exact, Dynamically Routable Current Propagation in Pulse-Gated Synfire Chains
[article]
2014
arXiv
pre-print
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To recap, we have the solution I d (t) = SA t τ e −t/τ , 0 < t < T SA T τ e −t/τ , T < t < ∞ and m d (t) = 0, 0 < t < T SA T τ e −t/τ , T < t < 2T 0, 2T < t < ∞ . ...
So that we have I d (t) = SA T τ e −T /τ e −(t−T )/τ and m d = I d (t) + I Exc 0 − I Inh 0 − g 0 + = I d (t). For exact transfer, we need I d (t − T ) = I u (t), requiring S exact = τ T e T /τ . ...
arXiv:1410.1115v1
fatcat:5u5t2v2lo5ecxkqvq2g5bfgcfy
On nonlinear transformations in quantum computation
[article]
2021
arXiv
pre-print
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The total operator whose expectation value we need to estimate is given by T = O ⊗ M ⊗ I (C1) We estimate T with T using T = 1 s s i=1 ν t(i) . ...
(C2) Here, s is the number of circuit evaluations and ν t(i) is the outcome of i'th measurement i.e. the t(i)'th eigenvalue of T . Since T is a normal operator T is a complex number. ...
We would like to find a density operator σ and normal matrix M such that α = σ M T . ...
arXiv:2112.12307v1
fatcat:hfuzkoyp25cijpze3ikqwmdx3y
A Unified Framework for Information Coding: Oscillations, Memory, and Zombie Modes
[article]
2014
arXiv
pre-print
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The solution was I j+1 (t) = SA t τ e −t/τ , 0 < t < T SA T τ e −t/τ , T < t < ∞ and m j+1 (t) = 0, 0 < t < T SA T τ e −t/τ , T < t < 2T 0, 2T < t < ∞ with p j+1 (t) = −I Inh 0 , 0 < t < T ...
In summary, we have the solution m j+1 (t) = SA t τ e −t/τ , 0 < t < T SA T τ e −t/τ , T < t < ∞ and p j+1 (t) = m T hres , 0 < t < T 0, T < t < ∞ In our previous mechanism, the circuit transferred synaptic ...
arXiv:1410.1116v1
fatcat:wndtgwykbvfmfhtnnfn5q47ncq
Quantum Simulation of Molecular Collisions in the Time-Dependent Formulation
[article]
2016
arXiv
pre-print
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2 ] = T exp tn+∆t tn S(t )dt + O(∆t 5 ) . ...
Using the notation j exp(a n j γ j m∆t) ≡ (m∆t) n , we can write the full evolution approximated by this and higherorder schemes [31] as T exp t 0 S(t )dt + O(N ∆t 2 ) = n (∆t) n (2a) T exp t 0 S(t ...
arXiv:1601.06419v1
fatcat:jsoksuvy3nccvexui6pm3nvw6q
Superconducting Phase Qubit Coupled to a Nanomechanical Resonator: Beyond the Rotating-Wave Approximation
[article]
2004
arXiv
pre-print
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G σσ ′ jj ′ (t) = e −iW σ j t/ ψ σ j |T e −(i/ ) t 0 dτ V (τ ) |ψ σ ′ j ′ , where V (t) ≡ e iH JC t/ V e −iH JC t/ , and where T is the timeordering operator. ...
As before, we start at time t = 0 in the state |10 . ...
arXiv:quant-ph/0407106v1
fatcat:y4ixyq2zgrgkjbjfzl55hrkz4e
Improving the efficiency of learning-based error mitigation
[article]
2022
arXiv
pre-print
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For N t < 12 we choose randomly N t /2 observables O i for which we generate the training circuits with O exact i ≈ −0.5, 0.5. ...
, O noisy ji )}, i = 1, . . . , N t , j = 1, . . . , M. ...
arXiv:2204.07109v1
fatcat:y2izzchu5fbgbjou55nusb2xxu
Barren plateaus preclude learning scramblers
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2009.14808v1 fatcat:l3tkuqoz7rdtdm57dohxqgn5cqOther Versions
The degree to which V S (t) is scrambling increases over time t, with the rate of increase determined by the entangling rate g. ...
Here our time parameter t is effectively the circuit depth. ...
arXiv:2009.14808v2
fatcat:ezdkzcvvcfhi7kpvkj3tibvmni
Variational consistent histories as a hybrid algorithm for quantum foundations
2019
Nature Communications
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The parameter optimization loop results in an approximately consistent family, F , of histories, where the consistency parameter e -iHΔt e -iHΔt t a b t e -iHΔt e -iHΔt e -iHΔt {p ( )} X 1 X 2 F y While ...
projector, chosen so that γBΔt = 2rad. ...
doi:10.1038/s41467-019-11417-0
pmid:31366888
pmcid:PMC6668436
fatcat:znyjqmvmrzhh3bd5hmbsn3e4di
The evolution of fidelity in sensory systems
2008
Journal of Theoretical Biology
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Sornborger, M.R.Adams / Journal of Theoretical Biology 253 (2008) 142-150 ...
Thus W is a T valued random variable. For t 2 T we let P W ðtÞ denote the probability of application of the operator t on the environment (the expectation that W has value t). ...
doi:10.1016/j.jtbi.2008.03.002
pmid:18407294
fatcat:vhhn3lbwkzf55idup73e7t7i5y
Quantum Simulation of Tunneling in Small Systems
2012
Scientific Reports
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VzK ð Þ t y init j ĩ e {iVDt e {iKDt e O Dt 2 ð Þ t Dt y init j i: Higher order methods that give more accurate time integration have been developed [52] [53] [54] , but methods of order higher than ...
This leads to the digital quantum particle simulation algorithm: y t ð Þ j i:~e {iVDt Fe {iTDt F { À Á t Dt y 0 ð Þ j i: The QFT takes of order n 2 gates to calculate 55 and general algorithms implementing ...
doi:10.1038/srep00597
pmid:22916333
pmcid:PMC3424524
fatcat:wkifwznfszftzpugnolf5jxubi
Analysis of a certain class of replicator equations
2006
Journal of Mathematical Biology
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Sornborger and M. Adams, in preparation). ...
i ((A x(t)) i − x(t) T A x(t)) (20) = − n i=1 η i (A x(t)) i (21) = − η T A x(t) (22) < −ε. ( 2 3 ) This implies that lim t→∞ v(t) = −∞ which in turn implies that n j=1 x η j j (t) limits to zero. ...
Using the special form of our game matrix (3), we have A T = B a T − u c T . ( 5 4 ) Thus we see that A T ( v) = ( a · v) B − ( c · v) u. ( 5 5 ) From this it follows that v T A( η) = η T A T ( v) (56) ...
doi:10.1007/s00285-006-0055-5
pmid:17119967
fatcat:r2vfmusqwrcpdmpbcd6qs7ufjy
Quantum Simulation of Molecular Collisions with Superconducting Qubits
[article]
2010
arXiv
pre-print
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A mapping is given between the control parameters of the quantum computer and the matrix elements of H_ s(t), an arbitrary, real, time-dependent n× n dimensional Hamiltonian that is simulated in the n-dimensional ...
i (t qc (t)) = max + ∆E i (t)/λ(t) g ij (t qc (t)) = H ij s (t)/λ(t).(13) ...
We integrate over λ(t) to calculate t qc as a function of t: t qc (t) = t ti λ(t )dt + t qc (t i ). (12) With both λ(t) and t qc (t) known, we can explicitly map the matrix elements of H s to the control ...
arXiv:1008.0701v1
fatcat:grqv6aw3rbgyxepidcix4uamjq
A Multitaper, Causal Decomposition for Stochastic, Multivariate Time Series: Application to High-Frequency Calcium Imaging Data
[article]
2017
arXiv
pre-print
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multitaper-based decomposition for stochastic, multivariate time series that acts on the covariance of the time series at all lags, C(τ), as opposed to standard methods that decompose the time series, X(t) ...
Define the tapered eigenestimate J m (f ) ≡ T t=1 h m (t)X(t)e −2πif t , (12) where h m (t) is a Slepian function. ...
t). ...
arXiv:1703.05414v1
fatcat:a5m4kaqsjfd5plyfciw7kylgwe
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