Statistical constraints on state preparation for a quantum computer

We consider the problem of minimizing the resources required for approximate universality in measurement-only quantum computation. This problem is important not only for realizing a quantum computer, but also for understanding the computational power of quantum computation. The resources we focus on are observables, which describe projective measurements, and ancillary qubits. We show that, if we are allowed to use two ancillary qubits, the set of observables { cos (π/8)X - sin (π/8)Y ,Z ⊗ X} is approximately universal for quantum computation. This is the first construction of an approximately universal set consisting only of one one-qubit observable and one two-qubit observable. Using the proof of the approximate universality, we also show that, if we are allowed to use two initialized ancillary qubits, one two-qubit observable is sufficient for graph state preparation. The use of only one two-qubit observable is optimal in terms of the number of observables available and the number of qubits to be measured jointly.

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Toward simulating superstring/M-theory on a quantum computer

Journal of High Energy Physics ◽

10.1007/jhep07(2021)140 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Hrant Gharibyan ◽

Masanori Hanada ◽

Masazumi Honda ◽

Junyu Liu

Keyword(s):

Matrix Models ◽

Real Time ◽

Matrix Model ◽

Fock Space ◽

Quantum Computer ◽

Explicit Construction ◽

Time Dynamics ◽

State Preparation ◽

M Theory ◽

Adiabatic State

Abstract We present a novel framework for simulating matrix models on a quantum computer. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in an appropriate limit of parameters. Furthermore, for certain states in the Berenstein-Maldacena-Nastase (BMN) matrix model, several supersymmetric quantum field theories dual to superstring/M-theory can be realized on a quantum device. Our prescription consists of four steps: regularization of the Hilbert space, adiabatic state preparation, simulation of real-time dynamics, and measurements. Regularization is performed for the BMN matrix model with the introduction of energy cut-off via the truncation in the Fock space. We use the Wan-Kim algorithm for fast digital adiabatic state preparation to prepare the low-energy eigenstates of this model as well as thermofield double state. Then, we provide an explicit construction for simulating real-time dynamics utilizing techniques of block-encoding, qubitization, and quantum signal processing. Lastly, we present a set of measurements and experiments that can be carried out on a quantum computer to further our understanding of superstring/M-theory beyond analytic results.

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Testing the context-independence of quantum gates

Quantum Information and Computation ◽

10.26421/qic20.15-16-3 ◽

2020 ◽

Vol 20 (15&16) ◽

pp. 1304-1352

Author(s):

Andrzej Veitia ◽

Steven J. van Enk

Keyword(s):

Probability Distribution ◽

Relative Frequency ◽

Quantum Computer ◽

Laser Pulses ◽

Quantum Gates ◽

State Preparation ◽

Statistical Fluctuations ◽

Initial States ◽

Context Dependent ◽

Heating Up

The actual gate performed on, say, a qubit in a quantum computer may depend, not just on the actual laser pulses and voltages we programmed to implement the gate, but on its context as well. For example, it may depend on what gate has just been applied to the same qubit, or on how much a long series of previous laser pulses has been heating up the qubit's environment. This paper analyzes several tests to detect such context-dependent errors (which include various types of non-Markovian errors). A key feature of these tests is that they are robust against both state preparation and measurement (SPAM) errors and gate-dependent errors. Since context-dependent errors are expected to be small in practice, it becomes important to carefully analyze the effects of statistical fluctuations and so we investigate the power and precision of our tests as functions of the number of repetitions and the length of the sequences of gates. From our tests an important quantity emerges: the logarithm of the determinant (log-det) of a probability (relative frequency) matrix $\mP.$ For this reason, we derive the probability distribution of the log-det estimates which we then use to examine the performance of our tests for various single- and two-qubit sets of measurements and initial states. Finally, we emphasize the connection between the log-det and the degree of reversibility (the unitarity) of a context-independent operation.

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Quantum computer race intensifies as alternative technology gains steam

Nature ◽

10.1038/d41586-020-03237-w ◽

2020 ◽

Vol 587 (7834) ◽

pp. 342-343

Author(s):

Elizabeth Gibney

Keyword(s):

Quantum Computer ◽

Alternative Technology

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Replication of Quantum Computing towards an Unconventional Environment using QuIDE

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.d9739.118419 ◽

2019 ◽

Vol 8 (4) ◽

pp. 9461-9464

Keyword(s):

Quantum Computer ◽

Source Code ◽

Circuit Diagram ◽

Quantum Computers ◽

Coordinated Development ◽

Development Environment ◽

Integrated Development ◽

Complexity Of Algorithms ◽

Performance Results ◽

Exponential Complexity

Current quantum computer simulation strategies are inefficient in simulation and their realizations are also failed to minimize those impacts of the exponential complexity for simulated quantum computations. We proposed a Quantum computer simulator model in this paper which is a coordinated Development Environment – QuIDE (Quantum Integrated Development Environment) to support the improvement of algorithm for future quantum computers. The development environment provides the circuit diagram of graphical building and flexibility of source code. Analyze the complexity of algorithms shows the performance results of the simulator and used for simulation as well as result of its deployment during simulation

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