Microsoft Technology Licensing, LLC

Guang Hao Low

Nathan O Wiebe

Vadym Kliuchnikov

Matthew Benjamin Hastings

Jeongwan Haah

Robin Ashok Kothari

Natalie M Klco

Yuan Su

Anirban Ch Narayan Chowdhury

A quantum-computation method comprises (a) sampling a random bit string from a predetermined distribution of bit strings, where each bit of the random bit string enables or disables a corresponding fixed-angle rotation of a state vector and where the product of the enabled fixed-angle rotations approximates an arbitrary rotation of the state vector through an angle of a multiplexed-rotation gate; and (b) enacting on the state vector each of the fixed-angle rotations enabled by a corresponding bit of the bit string.

Stochastic compilation of multiplexed quantum rotations

In this disclosure, quantum algorithms are presented for simulating Hamiltonian time-evolution ein the interaction picture of quantum mechanics on a quantum computer. The interaction picture is a known analytical tool for separating dynamical effects due to trivial free-evolution A from those due to interactions B. This is especially useful when the energy-scale of the trivial component is dominant, but of little interest. Whereas state-of-art simulation algorithms scale with the energy &#x2225;A+B&#x2225;&#x2264;&#x2225;A&#x2225;+&#x2225;B&#x2225; of the full Hamiltonian, embodiments of the disclosed approach generally scale linearly with the sum of the Hamiltonian coefficients from the low-energy component B and poly-logarithmically with those from A.

Hamiltonian simulation in the interaction picture

Methods for preparing a Gibbs state in a qubit register of a quantum computer include applying one or more quantum gates to one or more qubits of the qubit register to prepare a trial quantum state spanning the one or more qubits, the trial quantum state being defined as a function of parameters {right arrow over (&#x3b8;)} and being selected to provide an initial estimate of the Gibbs state. The methods further include evaluating the Gibbs free energy of the trial quantum state, adjusting the parameters {right arrow over (&#x3b8;)}, re-applying the one or more quantum gates to the one or more qubits to refine the trial quantum state according to the parameters {right arrow over (&#x3b8;)} as adjusted, and re-evaluating the Gibbs free energy of the trial quantum state.

Variational quantum Gibbs state preparation

In methods for simulating the evolution of a real-world quantum system over time, a state-preparation sequence of quantum gates is applied to a qubit register of a quantum computer. The state-preparation sequence is configured to prepare in the qubit register an initial model state representing an initial state of the real-world quantum system. A Hamiltonian operator for the real-world quantum system is received and used in the example method. The Hamiltonian operator represents two-body potential-energy interactions in a factorized form comprising at least one Majorana operator. A time-evolution-operator sequence of quantum gates comprising a block-encoded form of the Hamiltonian operator is now applied to the qubit register of the quantum computer, yielding a changed model state that represents a time-evolved state of the real-world quantum system. A measurement operation is applied subsequently to the qubit register. The measurement operation is configured to reveal an observable property of the changed model state.

Optimized block encoding of low-rank fermion Hamiltonians

A quantum computer and methods of operating the quantum computer, such that the quantum computer is enabled to fully simulate molecular chemistry, are described. The circuit depth of the quantum computer is reduced by at least an order of magnitude, as compared to conventional quantum computing methods. Parallelized qubit or fermionic swap networks are employed to render the non-local terms of the second quantized Hamiltonian, as local on consecutive qubits of the computer. Thus, non-local quantum dynamics are rendered local. By localizing the non-local interactions, the quantum computations may be significantly parallelized and a single template circuit, simulating the time-evolution operator for 4-qubit interactions, may be applied to the localized groupings of four qubits. In addition to chemistry, the quantum computer and the methods of operating the quantum computer may be employed to localize any many-body interaction, while reducing the required circuit depth, via parallelizations of the localized computations.

Swap networks for quantum computation

Examples are disclosed relating to obtaining a solution to a multiproduct formula of order m to solve a quantum computing problem comprising a product formula. One example provides a method comprising selecting a set of exponents k, wherein each kis a real number and is an exponent in a linear combination of product formulas. Based on the set of exponents k, a set of pre-factors ais determined based on an underdetermined solution to an m&#xd7;M system of linear equations, where M is a number of lower-order product formulas in the linear combination of product formulas. The set of exponents kand the set of pre-factors aare used to solve the quantum computing problem comprising the product formula. By minimizing the set of exponents kand the set of pre-factors a, sparse solutions to the multiproduct formula are generated, reducing computational time and scaling.

Methods for obtaining solutions to multiproduct formulas

Embodiments of the disclosed technology concern a quantum circuit configured to implement a real time evolution unitary of a Hamiltonian in a quantum computing device, wherein a unit time evolution unitary operator is decomposed into overlapping smaller blocks of unitary operators. In some implementations, (a) the size of the overlap is proportional to the logarithm of a number of qubits in the simulated system, (b) the size of the overlap is proportional to the logarithm of a total simulated evolution time, and/or (c) the size of the overlap is proportional to a Lieb-Robinson velocity.

Quantum simulation of real time evolution of lattice Hamiltonians

Efficient synthesis of arbitrary quantum states and unitaries from a universal fault tolerant gate-set (e.g., Clifford+T) is a goal in quantum computation. As physical quantum computers are fixed in size, all available qubits should be used if it minimizes overall gate counts, especially that of the expensive T-gates. In this application, a quantum algorithm is described for preparing any dimension-N quantum state specified by a list of N classical numbers, that realizes a trade-off between space and T-gates. Example embodiments exploit(&#x3bb;) ancilla qubits, to reduce the T-gate cost to Notably, this it proven to be optimal up to logarithmic factors for any &#x3bb;=o(&#x221a;{square root over (N)}) through an unconditional gate counting argument. Though(N) Clifford gates are always required, only(&#x221a;{square root over (N)}) T-gates are needed in the best case, which is a quadratic improvement over prior art. Similar statements are provien for unitary synthesis by reduction to state preparation.

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Redmond, WA, United States of America

Guang Hao Low