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Register a new userTailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries
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A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized truncated Taylor method, and for a range of molecular simulations we report these bounds as well as direct numerical emulation results. We find that our adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth.
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Black-box quantum state preparation is a fundamental primitive in quantum algorithms. Starting from Grover, a series of techniques have been devised to reduce the complexity. In this work, we propose to perform black-box state preparation using the technique of linear combination of unitaries (LCU). We provide two algorithms based on a different structure of LCU. Our algorithms improve upon the existed best results by reducing the required additional qubits and Toffoli gates to 2log(n) and n, respectively, in the bit precision n. We demonstrate the algorithms using the IBM Quantum Experience cloud services. The further reduced complexity of the present algorithms brings the black-box quantum state preparation closer to reality.
Quantum integrated photonics requires large-scale linear optical circuitry, and for many applications it is desirable to have a universally programmable circuit, able to implement an arbitrary unitary transformation on a number of modes. This has been achieved using the Reck scheme, consisting of a network of Mach Zehnder interferometers containing a variable phase shifter in one path, as well as an external phase shifter after each Mach Zehnder. It subsequently became apparent that with symmetric Mach Zehnders containing a phase shift in both paths, the external phase shifts are redundant, resulting in a more compact circuit. The rectangular Clements scheme improves on the Reck scheme in terms of circuit depth, but it has been thought that an external phase-shifter was necessary after each Mach Zehnder. Here, we show that the Clements scheme can be realised using symmetric Mach Zehnders, requiring only a small number of external phase-shifters that do not contribute to the depth of the circuit. This will result in a significant saving in the length of these devices, allowing more complex circuits to fit onto a photonic chip, and reducing the propagation losses associated with these circuits. We also discuss how similar savings can be made to alternative schemes which have robustness to imbalanced beam-splitters.
We consider a direct optimization approach for ensemble density functional theory electronic structure calculations. The update operator for the electronic orbitals takes the structure of the Stiefel manifold into account and we present an optimization scheme for the occupation numbers that ensures that the constraints remain satisfied. We also compare sequential and simultaneous quasi-Newton and nonlinear conjugate gradient optimization procedures, and demonstrate that simultaneous optimization of the electronic orbitals and occupation numbers improve performance compared to the sequential approach.
Speckle structure of parametric down conversion light has recently received a large attention due to relevance in view of applications to quantum imaging The possibility of tailoring the speckle size by acting on the pump properties is an interesting tool for the applications to quantum imaging and in particular to the detection of weak object under shot-noise limit. Here we present a systematic detailed experimental study of the speckle structure produced in type II PDC with particular attention to its variation with pump beam properties.
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $varepsilon$-approximations using circuits of length $O(log(1/varepsilon))$, which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T [arXiv:1212.6253], V-basis [arXiv:1303.1411] and Clifford+$pi/12$ [arXiv:1409.3552], running on average in time polynomial in $O(log(1/varepsilon))$ (conditional on a number-theoretic conjecture). Ours is the first such algorithm that works for a wide range of gate sets and provides insight into what should constitute a good gate set for a fault-tolerant quantum computer.
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