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A Pulse-Gated, Predictive Neural Circuit [article]

Yuxiu Shao, Andrew T. Sornborger, Louis Tao
2017 arXiv   pre-print
, (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]

Michael R. Geller, Emily J. Pritchett, Andrew T. Sornborger, F. K. Wilhelm
2006 arXiv   pre-print
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]

Andrew T. Sornborger, Louis Tao
2014 arXiv   pre-print
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 −(tT )/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 (tT ) = I u (t), requiring S exact = τ T e T /τ .  ... 
arXiv:1410.1115v1 fatcat:5u5t2v2lo5ecxkqvq2g5bfgcfy

On nonlinear transformations in quantum computation [article]

Zoë Holmes, Nolan Coble, Andrew T. Sornborger, Yiğit Subaşı
2021 arXiv   pre-print
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]

Andrew T. Sornborger, Louis Tao
2014 arXiv   pre-print
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]

Andrew T. Sornborger, Phillip Stancil, Michael Geller
2016 arXiv   pre-print
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]

Andrew T. Sornborger, Andrew N. Cleland, Michael R. Geller
2004 arXiv   pre-print
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]

Piotr Czarnik, Michael McKerns, Andrew T. Sornborger, Lukasz Cincio
2022 arXiv   pre-print
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]

Zoë Holmes, Andrew Arrasmith, Bin Yan, Patrick J. Coles, Andreas Albrecht, Andrew T. Sornborger
2021 arXiv   pre-print
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

Andrew Arrasmith, Lukasz Cincio, Andrew T. Sornborger, Wojciech H. Zurek, Patrick J. Coles
2019 Nature Communications  
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

Andrew T. Sornborger, Malcolm R. Adams
2008 Journal of Theoretical Biology  
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

Andrew T. Sornborger
2012 Scientific Reports  
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

Malcolm R. Adams, Andrew T. Sornborger
2006 Journal of Mathematical Biology  
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]

Emily J. Pritchett, Colin Benjamin, Andrei Galiautdinov, Michael R. Geller, Andrew T. Sornborger, Phillip C. Stancil, John M. Martinis
2010 arXiv   pre-print
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]

Andrew T. Sornborger, James D. Lauderdale
2017 arXiv   pre-print
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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