Filters

117 Hits in 0.86 sec

### 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 < ∞ .  ...

### 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  ...

### 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 .  ...

### 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 .  ...

### 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  ...

### 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  ...

### 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 .  ...

### 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.  ...

### 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.  ...

### 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.  ...

### 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).  ...

### 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  ...

### 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)  ...

### 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  ...

### 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).  ...
« Previous Showing results 1 — 15 out of 117 results