Improved Simulation of Quantum Circuits by Fewer Gaussian Eliminations

• URL: http://arxiv.org/abs/2003.01130v1
• Date: Mon, 2 Mar 2020 19:00:04 GMT
• Title: Improved Simulation of Quantum Circuits by Fewer Gaussian Eliminations
• Authors: Lucas Kocia and Mohan Sarovar
• Abstract summary: We show that the cost of strong simulation of quantum circuits using $t$ $T$ gate magic states exhibits non-trivial reductions on its upper bound. This agrees with previous numerical bounds found for qubits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the cost of strong simulation of quantum circuits using $t$ $T$ gate magic states exhibits non-trivial reductions on its upper bound for $t=1$, $t=2$, $t=3$, and $t=6$ with odd-prime-qudits. This agrees with previous numerical bounds found for qubits. We define simulation cost by the number of terms that require Gaussian elimination of a $t \times t$ matrix and so capture the cost of simulation methods that proceed by computing stabilizer inner products or evaluating quadratic Gauss sums. Prior numerical searchs for qubits were unable to converge beyond $t=7$. We effectively increase the space searched for these non-trivial reductions by $>10^{10^4}$ and extend the bounds to $t=14$ for qutrits. This is accomplished by using the Wigner-Weyl-Moyal formalism to algebraically find bounds instead of relying on numerics. We find a new reduction in the upper bound from the $12$-qutrit magic state of ${3^{\sim 0.469t}}$, which improves on the bound obtained from the $6$-qutrit magic state of ${3^{\sim 0.482t}}$.

Related papers

• Optimal Sketching for Residual Error Estimation for Matrix and Vector Norms [50.15964512954274]
  We study the problem of residual error estimation for matrix and vector norms using a linear sketch. We demonstrate that this gives a substantial advantage empirically, for roughly the same sketch size and accuracy as in previous work. We also show an $Omega(k2/pn1-2/p)$ lower bound for the sparse recovery problem, which is tight up to a $mathrmpoly(log n)$ factor.
  arXiv  Detail & Related papers  (2024-08-16T02:33:07Z)
• Optimized Quantum Simulation Algorithms for Scalar Quantum Field Theories [0.3394351835510634]
  We provide practical simulation methods for scalar field theories on a quantum computer that yield improveds. We implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of $4times 106$ physical qubits and $1012$ $T$-gates.
  arXiv  Detail & Related papers  (2024-07-18T18:00:01Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Near-optimal fitting of ellipsoids to random points [68.12685213894112]
  A basic problem of fitting an ellipsoid to random points has connections to low-rank matrix decompositions, independent component analysis, and principal component analysis. We resolve this conjecture up to logarithmic factors by constructing a fitting ellipsoid for some $n = Omega(, d2/mathrmpolylog(d),)$. Our proof demonstrates feasibility of the least squares construction of Saunderson et al. using a convenient decomposition of a certain non-standard random matrix.
  arXiv  Detail & Related papers  (2022-08-19T18:00:34Z)
• More Optimal Simulation of Universal Quantum Computers [0.0]
  Worst-case sampling cost has plateaued at $le(2+sqrt2)xi_t delta-1$ in the limit that $t rightarrow infty$. We reduce this prefactor 68-fold by a leading-order reduction in $t$ through correlated sampling.
  arXiv  Detail & Related papers  (2022-02-02T19:00:03Z)
• On Submodular Contextual Bandits [92.45432756301231]
  We consider the problem of contextual bandits where actions are subsets of a ground set and mean rewards are modeled by an unknown monotone submodular function. We show that our algorithm efficiently randomizes around local optima of estimated functions according to the Inverse Gap Weighting strategy.
  arXiv  Detail & Related papers  (2021-12-03T21:42:33Z)
• Improved Weak Simulation of Universal Quantum Circuits by Correlated $L_1$ Sampling [0.0]
  Weak simulation is often called weak simulation and is a way to determine when they confer a quantum advantage. We constructively tighten the upper bound on the worst-case $L_$ norm sampling cost to next order in $t$ from $mathcal O(xit delta-2)$. This is the first weak simulation algorithm that has lowered this bound's dependence on finite $t$ in the worst-case to our knowledge.
  arXiv  Detail & Related papers  (2021-04-15T05:50:11Z)
• Improved Strong Simulation of Universal Quantum Circuits [0.0]
  We find a scaling reduction in the stabilizer rank of the twelve-qubit tensored $T$ gate magic state. This lowers its bound to $2sim 0.463 t$ for multi-Pauli measurements on $t$ magic states. This constructively produces the most efficient strong simulation of the Clifford+$T$ gateset.
  arXiv  Detail & Related papers  (2020-12-21T23:13:20Z)
• An improved quantum-inspired algorithm for linear regression [15.090593955414137]
  We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm. We show that quantum computers can achieve at most a factor-of-12 speedup for linear regression in this QRAM data structure setting.
  arXiv  Detail & Related papers  (2020-09-15T17:58:25Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)
• Naive Exploration is Optimal for Online LQR [49.681825576239355]
  We show that the optimal regret scales as $widetildeTheta(sqrtd_mathbfu2 d_mathbfx T)$, where $T$ is the number of time steps, $d_mathbfu$ is the dimension of the input space, and $d_mathbfx$ is the dimension of the system state. Our lower bounds rule out the possibility of a $mathrmpoly(logT)$-regret algorithm, which had been
  arXiv  Detail & Related papers  (2020-01-27T03:44:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.